http://astro1.panet.utoledo.edu/~ljc/serfau23.

html
1 Telescopes
1.2 Optical elements
In order to understand how telescopes work, it is useful to outline the basic
principles of curved lenses and mirrors. A surface which is the same shape as a
small portion of a sphere is called a spherical (or more correctly spheroidal) surface.
Surfaces with this shape have a special optical property which makes them highly
valuable: their ability to bring light to a focus. Actually, the focusing properties of a
spheroidal surface are not perfect, as we shall see later, but the imperfection is
often more than compensated for by the purely practical consideration that a
precise spheroidal optical surface can be produced much more easily and hence
at much lower cost than a precise aspheroidal (non-spheroidal) optical surface.
Three important focusing properties of spheroidal surfaces are described in the
three following statements. Unfortunately, neither of the first two statements is
exactly true for any real optics, but they are extremely valuable approximations to
the truth and will greatly aid your ability to understand the layouts of optical
instruments such as telescopes and spectrographs.

1. When parallel rays of light pass through a lens with convex spheroidal
surfaces, or reflect from the surface of a spheroidal concave mirror, they
are brought to a focus. The distance of the focal pointfrom the lens (or
mirror) is called the focal length, f. This is a single quantity that
characterises the optical performance of the lens or mirror in question.
2. Light rays passing through the centre of a lens do not deviate from their
original path.
3. Light paths do not depend on the direction in which light is travelling. So,
for example, since parallel rays of light are brought to a focus by a convex
lens at a distance f from the lens, then rays of light emanating from a point
a distance f away from the lens will be converted into a parallel beam. A
lens which is used in such a way is called a collimator, and the beam of
parallel light that is produced is said to be collimated.
Broadly speaking there are two sorts of lenses and mirrors used in optical systems.
Converging (convex) lenses and converging (concave) mirrors each cause parallel
rays of light to come together at the focal point, or focus, of the lens or mirror
(Figure 1a and b). In contrast, diverging (concave) lenses and diverging (convex)
mirrors each cause parallel rays of light to spread out as if emanating from the focal
point situated at a distance of one focal length from the centre of the lens or mirror
concerned (Figure 1c and d).

Figure 1: (a) A convex lens will cause parallel rays of light to converge to the
focal point. (b) A concave mirror will cause parallel rays of light to converge to
the focal point. (c) A concave lens will cause parallel rays to diverge as if from
the focal point. (d) A convex mirror will cause parallel rays to diverge as if from
the focal point. The reflecting surface of the mirror is shown by a thicker black
line
Converging lenses and mirrors used individually can each produce real images of
distant objects, by which is meant an image that may be captured on a screen or
directly on a detector such as photographic film. Real images are those images
made by the convergence of actual rays of light. However, when eyepiece lenses
are used with telescopes, the final image formed by the telescope is said to be
a virtual image, since it is situated at a location from which rays of light appear to
emanate (see Figure 2 and Figure 3 below). Such an image cannot be captured
directly on a detector. However, eyepieces are always used in conjunction with
another lens namely the lens of the eye itself which converts the virtual
image produced by the telescope into a real image on the retina of the eye.
Two additional comments should be made relating to the term focal length.
Firstly, a series of two or more lenses and/or mirrors can also bring parallel incident
light rays to a focus, though obviously at a different point from that of any of the
elements independently. The focal length of such a series of optical elements is
defined as the focal length of a single lens that would bring the same rays of light to
a focus at the same angle of convergence. The effective focal length may therefore
be quite different from the actual distance between the optics and the focus. As we
shall see later, this allows long focal lengths to be compressed into short path
lengths.
Secondly, it is sometimes common to quote the number that is obtained by dividing
the focal length of an optical assembly by the diameter of the bundle of parallel light
rays that is brought to a focus. In some optical systems, such as telescopes, the
diameter of this bundle of light rays is the same as the diameter of the main optical
element, though this is not always the case, particularly for most camera lenses.
The number obtained by calculating this ratio is referred to as the f-number,
written f/# or F/# where # is the numerical value.

What is the f-number of a 200 mm diameter telescope with a focal

length of 2400 mm?

Optics
Objectives:

EXPLAIN the law of reflection

DISTINGUISH between specular and diffuse reflection
LOCATE the images formed by plane mirrors
EXPLAIN how concave and convex mirrors form images
DESCRIBE properties and uses of spherical mirrors
DETERMINE the locations and sizes of spherical mirror images
SOLVE problems involving refraction
EXPLAIN total internal reflection
EXPLAINE some optical effects caused by refraction
DESCRIBE how real and virtual images are formed by single convex and concave
lenses
LOCATE images formed by lenses using ray tracing and equations
EXPLAIN how chromatic aberration can be reduced
DESCRIBE how the eye focuses light to form an image
EXPLAIN nearsightedness and farsightedness and how eyeglass lenses correct these
defects
DESCRIBE the optical systems in some common optical instruments

VOCAB:
Specular reflection- parallel light rays are reflected in parallel
Diffuse reflection- scattering of light off a rough surface
Plane mirror- a flat, smooth surface from which light is reflected by specular reflection
Object- source of light rays that are to be reflected off a mirrored surface
Image- combination of image points fromed by reflected light rays
Virtual image- type of image formed by diverging light rays
Concave mirror- miror with edges bent towards the observer
Principal axis- straight line perpendicular to the mirror that divides the mirror in half
Focal point- the point at which incident light rays parallel to the prinicpal axis converge
Focal length- position of the focal point with respect to the mirror along the principal axis
Real image- type of image fromed by converging light rays
Magnification- the ratio of image height to object height; how much larger or smaller the
image is than the object
Convex mirror- reflective surface with edges that bend away from the observer
Lens- piece of transparent material that is used to focus light into an image
Convex Lens- lens thicker at the center than the edges
Concave Lens- lens thinner at the center than at the edges
Mirrors
Mirror Equation: 1/f=1/di+1/do
do= object distance, di= image distance, f= focal length, c= center of curvature
hi= image height, ho= object height
Magnification Equation: m= hi/ho= -di/do

Le
Le
do=
hi =
Ma

Law of reflection: The angle that a reflected ray makes with the surface of the mirror is equal to the
angle that the incident ray makes with the surface of the mirror.

Co
tha
ref

Ray tracing is a method for finding the location, size and magnification of a reflected image by drawing
rays coming off of the object and tracing where and how they would reflect. Using scale drawings is the
only way to get accurate results.

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Be
im

Images can be either real or virtual. Real images are formed by converging light rays, or light rays
coming together, and will be located on the same side of the mirror as the object. Virtual images are
formed when reflected light rays diverge, or move away from each other. As shown in the picture above,
the diverging rays can be traced back behind the mirror to show where the virtual image is located.
3 TYPES OF MIRRORS
Plane mirrors are simply flat, smooth surfaces that light reflects off of. All light rays falling on the
mirror simply follow the law of reflection, and are easy to trace. Plane mirror images are always virtual.

Concave mirrors are bent inward, meaning the edges are bent towards the observer. They have a center
Th
of curvature, which means that if the mirror were cut from a whole sphere, this point would be at the
very center. This point lies on the principal axis, which is the line going through the center of the mirror. tra
The focal point is one half of the distance of the center of curvature, Concave mirrors can produce both
real and virtual images.

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Convex mirrors are the exact opposite of concave mirrors. They are bent so that the edges of the mirror
face away from the observer. Like concave mirrors, they can produce real and virtual images depending
on abject location.
RULES FOR RAY TRACING TO FIND AN IMAGE
1. Light rays coming in parallel to the principal axis will reflect out through the focal point.
2. A ray coming in through the focal point will reflect oout parallel to the principal axis.
3.Rays coming through the center of curvature will reflecet back on themselves.
4. A ray coming in to the vertex (the point where the principal axis and mirror meet) above the principal
axis will reflect at an equal angle below the principal axis.
In the section on mirrors, I learned how light rays reflect off of simple, concave, and convex
mirrors. I learned how an image of an object is produced, and that a real image, not just a
virtual image can be produced and can be projected on a screen from a mirror. From this, I
have a better idea of how a projectorworks. From my understanding of focal poins, I
understand how flashlights and a car's headlights produce a beam of light. The bulb is
focused at the focal point of the convex mirror behind it and because of this all light rays
coming off the bulb reflect out straight ahead. I also now know that security mirros are
convex because they shrink the image size down to allow for more of the room to be shown.
It is clear to me now ho weyeglasses work as well. For a person who has trouble seeing
things far away, they are prescribed a lens that will diverge the light rays slightly, so that they
focus correctly on the back of the eye. For problems seeing things up close, a converging
lense is prescribed.

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Reflection and Refraction

If a ray of light could be observed approaching and reflecting off of a flat mirror,
then the behavior of the light as it reflects would follow a predictable law known as
the law of reflection. The diagram illustrates the law of reflection.

In the diagram, the ray of light approaching the mirror is known as the incident ray
(see diagram). The ray of light leaving the mirror is known as the reflected ray. At
the point of incidence where the ray strikes the mirror, a line can be drawn
perpendicular to the surface of the mirror; this line is known as a normal line. The
angle between the incident ray and the normal is known as the angle of incidence,
i. The angle between the reflected ray and the normal is known as the angle of
reflection, qr. The law of reflection states that when a ray of light reflects off a
surface, the angle of incidence is equal to the angle of reflection, i = r.
Reflection off of smooth surfaces leads to a type of reflection known as specular
reflection. Reflection off of rough surfaces such as clothing, paper, and the asphalt
roadway leads to a type of reflection known as diffuse reflection. The diagram
below depicts two beams of light incident upon a rough and a smooth surface.

The velocity of light, c, in a vacuum is about 3x108 meters per second. In other
media (glass, for example) the velocity is less. The ratio of c to the actual velocity
is called the refractive index, n:

since

e = electric permittivity
m = magnetic permeability
ke = dielectric constant (e/eo)
km = relative permeability (m/mo)

The color of the light and its frequency are the same in both media. Therefore, the
wavelength must shorten by the same ratio as the velocity. You can think of this
"slowing down" of light in a transparent medium if you picture the medium
composed of individual atoms or molecules that can interact with the passing light
by absorbing and re-emitting the light. This absorbed and re-emitted light is added
to the component passing through at c in such a way that the sum is continually
slowed down with respect to c. This continuous slowing down is equivalent to a
phase velocity less than c.
You can think of it like this: The electrons in the glass are driven to oscillate by the
light's E-field. This causes the electrons to become dipoles themselves and they
begin to re-radiate or scatter. However, only the wavelets in the forward direction
are IN PHASE and interfere constructively. The others interfere destructively and
cancel out.

3 Basic Laws
Three fundamental laws describe how a wavefront of light interacts with a surface
that forms the boundary between materials with different refractive indices e.g. airglass interface where air has a refractive index of 1 and glass is typically 1.5.
1) Incident, reflected, and transmitted waves lie all in the same plane
2) Angle of incidence is equal to the angle of reflection
i = r
3) SNELL'S LAW:
ni sin(i) = nt sin(t)
Where ni is index of refraction of the medium 1 and nt is index of refraction of
medium 2

Snell's Law allows us to calculate the new direction of propagation when light
passes through an interface between two materials with different indices of
refraction. The angles are measured between the normal to the surface and the light
beam. Light passing from a material with a high index of refraction to a material
with a low index of refraction bends away from the normal whereas light passing
from material with a low to material with a high index of refraction bends toward
the normal.

Fresnel's Equations
While Snell's law and the law of reflection tell us something about the direction in
which reflected and refracted light propagate, it does not say anything about how
much light goes where. When light strikes the interface between two materials with
different indices of refraction, a fraction of the light is reflected (R) and a fraction
is transmitted (T). The values of R and T may be calculated using Fresnel's
equations. It is important to realize that 1) the sum of reflected and transmitted
light must equal the total incident light (since these are fractions R + T = 1); and 2)
the angle of polarization of the incident EM wave with respect to the plane of the
incident material has an effect on the respective fractions of light that are
transmitted or reflected.
a) E-Field perpendicular to the plane of incidence

r = amplitude reflection coefficient, ratio of reflected to incident electric field

amplitudes.

t = amplitude transmission coefficient, ratio of transmitted to incident electric field

amplitudes.
b) E-field parallel to the plane of incidence

Given that,
R = Reflectance (W/m2)
T = Transmittance (W/m2)
When there is no absorption, R + T = 1, and

If i = 0, the incident plane becomes undefined and

Examples:
1. What percent of light is reflected at the interface of air (n = 1.0) to glass
(n = 1.5) if the angle of incidence is 0?
Answer:

This means that in a lens, which has 2 air-glass interfaces, transmission through
each interface = 96%. This means that the transmission through the lens even it
absolutely non-absorbing is (0.96)2 = 0.9216. In other words 7.84% of the light is
lost due to reflection. Note that this property is multiplicative.
2. What percent of light is transmitted from air (n = 1.0) to glass (n = 1.4) if the
angle of incidence is 48. Assume that the light is unpolarized.
Answer:
The easiest way to approach this is to calculate the fraction of light that is
reflected. Assuming no absorption, the remainder is transmitted into the second
medium.
First start with calculating the angle of refracted light using Snell's law. Given that
i = 48

We can thus calculate the reflection coefficients for parallel and perperdicularly
polarized light using Fresnel equations.
Substituting this into:

Next we have to realize the light is unpolarized. Practically we can handle this in
terms of Fresnel's equations by assuming that there is equal quantities of parallel
and perpendicularly polarized light and the simply take the average:

Thus R = 4.02%
with T = 1 - R it follows that: T = 1 - 0.0402 = 0.9598

An Application of Fresnel Equations

The Fresnel equations describe the effects of an incoming electromagnetic plane

wave on the interface between two media with different dielectric constants or
indices of refraction.
From the different Fresnel equations we obtain,

Here, note that while R can never be zero, R// is zero when (i + t) = 90. As a
result, for E-field parallel to the plane of incidence, the reflectance vanishes and
the beam is completed transmitted. This is Brewster's Law (see figure).

Another way to look at this is that for parallel polarized light, there is an angle of
incidence where the reflectivity = 0. This angle, known as the Brewster's angle can
be calculated by:

Lenses and Lens Systems

A lens is typically made up of an optically translucent material containing two or
more refracting surfaces, at least one of which is curved. Lenses may be used in an
optical system to modify a beam of light or to form an image of an object. There
are a number of factors that need to be considered when characterizing a lens:
Diameter: The diameter of a lens is typically chosen based on the size of the beam
and object that needs to be modified.
Radius of Curvature: R determines how curved the lens is and the direction of the
curvature. It also relates to the focal length of the lens (see lens equations section).
Focal length: Focal point is defined as the point at which parallel rays coming into
the lens converge. The distance between the center of the lens at this point is the
focal length f of the lens. This point may be on the opposite side of the lens as in a

convex lens or the same side as in a concave lens.

Transmission range: Any given material will allow light of certain wavelengths to
be transmitted while allowing others to be absorbed. The lens material is chosen
based on the wavelength of the light that is being modified. e.g. glass transmits
well from 400 to 2500 nm, however quartz needs to be used to transmit light in the
UV while more exotic materials need to be used for transmission further in the IR
(for example: sapphire, CaF2, etc.).
Aberrations: Aberrations are limitations in lens behavior that can be detrimental
to its performance. These include spherical aberrations, chromatic aberrations,
coma, and astigmatism.
There are six kinds of lenses, divided in two main categories; a) the positive or
convex lenses and b) the negative or concave lenses. The convex lenses have in
common that they are thicker in the center than at the edge while the concave
lenses are thinner in the center than at the edges:

R1 > 0
R2 < 0

R1 < 0
R2 > 0

R1 =
R2 < 0

R1 =
R2 > 0

R1 > 0
R2 > 0

R1 > 0
R2 > 0

where,
R1 = Radius of Curvature of the first lens surface from the left)
R2 = Radius of Curvature of the second lens surface (from the left)

Since all rays issuing from a source point will arrive at the image point, any two
rays will fix that point. There are three rays that are easiest to apply. Two of these
make use of the fact that a ray passing through the focal point will emerge from the
lens parallel to the optical axis and vice versa; the third is the undeviated ray
through the center of the lens. They are illustrated below for both positive and
negative lenses.

Basic Lens Equations

1) The focal length of a lens can be calculated by the Gaussian Lens Formula:

where, f = focal length,

o = object distance,
i = image distance
2) Another useful lens equation is the Lensmaker's Formula;

where nl = index of refraction of the lens

n2 = index of refraction of the surrounding medium typically air)
R1 = Radius of Curvature of the first lens surface from the left)
R2 = Radius of Curvature of the second lens surface (from the left)
3) Transverse Magnification (MT) is defined as the magnification of the image in
the direction perpendicular to the direction of propagation and is given as:

4) Longitudinal Magnification (ML) is defined as the magnification of the image

in the direction of propagation and is given as

5) The transverse magnification of a two-lens system that is separated by a distance

d that is greater than the sum of their focal lengths is given by:

The magnification in such a two-lens system is simply the product of the

magnifications from each element:

Based on the location of the object relative to the focal point the location, size and
type of image will vary for a positive or negative lens.

Curved Mirrors behave similar to lenses except that the formation of the image is
reversed, i.e. the concave mirror behaves like a convex lens and a convex mirror
behaves like a concave lens.

EXAMPLES:

1. Construct the rays to form the image for a positive lens given that the focal
length of the lens is 2 m and an object (1.5 m high) is placed at a distance of 3.5 m
from the lens.

Answer:
Given,
f=2m
o = 3.5 m
h(object) = 1.5 m
(Hint: To construct the image, draw the three rays described earlier)

Given that,
Thus i = 4.67 m
The magnification is given as,

Therefore, an object 1.5 m high will be magnified 1.33 times to yield an image
1.995 m high. This image is real, inverted and magnified.
2. Construct the rays to form the image for a lens with focal length -10 cm and an
object that is placed at a distance of 10 cm from the lens. What kind of image do
you get?
Answer:
Given,

o = 10 cm
f = -10 cm, therefore it is a concave (negative) lens.
Draw rays to construct the image.

Therefore i = - 5 cm
The magnification is given as,

Thus the image is a virtual, erect, minified image located at f/2.

Aberrations
The formulas developed earlier for image formation by spherical reflecting and
refracting surfaces are, of course, only approximately correct. In deriving those
formulas it was necessary to assume paraxial rays, rays both near to the optical axis
and making small angles with it. However, in considering these lens situations will
arise when these assumptions are no longer valid and aberrations are observed.
1. Spherical Aberrations
Spherical aberrations occur due to the severe curvature of short focal length or
smaller lenses because rays incident on the outer regions of a lens bend more than
the rays towards the center, causing the image to appear out of focus.

Spherical aberrations are corrected by:

using a larger lens
orienting the lens correctly
using the right type of lens
2. Coma
Coma is an off-axis aberration that is nonsymmetrical about the optical axis. This
arises from the dependence of transverse magnification on the ray height at the
lens. Because of coma, an off-axis object point is imaged as a blurred shape that
resembles a comet with a head and a tail. This type of image can be minimized by
appropriate selection of the diameter of the lens to be used.

3. Astigmatism
When an object point lies far away from the optical axis, the incident cone of rays
will strike the lens asymmetrically giving rise to astigmatism. If the rays incident
on the lens in the plane of the paper (tangential plane) has a given focal length,
then the rays in the plane that is obliquely angled with respect to the paper (sagittal
plane) has a different focal length. Thus, for the incident conical bundle of rays, the
cross-section of beam as it leaves the lens is initially circular and gradually
becomes elliptical until it meets in a line at the focal point that is tangential to the
plane of the paper.

4. Field of Curvature
In this type of aberration, a given planar object is imaged on a parabolic surface
instead of a plane as can be seen in the figure.

5. Distortion
Distortion shows up as a variation in the transverse magnification for points of the
object away from the optical axis. In other words, distortion occurs because
different areas of the lens have different focal lengths and different transverse
magnifications.

6. Chromatic Aberration
Chromatic aberration occurs for incident rays that contain many wavelengths.
Since the index of refraction varies with wavelength, the focal properties of a
simple lens will vary as well. The refractive index is higher for blue light than red
light. Therefore, the focal length of a convex lens is shorter for blue light than red
light.

Chromatic aberration can be corrected for using an achromatic doublet. An

achromatic doublet consists of a convex and concave lens made of different
materials cemented together. By choosing materials with appropriate refractive
indices, you can create a doublet that will have the same focal length at two
wavelengths. The two lenses correct for each other and a focal point is found
somewhere in the middle.

Tissue Optics
The two fundamental tasks of the field of tissue optics are:
1) Find the light per unit area per unit time that reaches a target chromophore at
some position, r, in the tissue and determine how much of that light is absorbed.
2) Determine the absorption and scattering properties of tissue.
In describing the optical properties and light propagation in tissues, light is treated
as photons. Photons in a turbid medium such as tissue can move randomly in all
directions and may be scattered (described by its scattering coefficient s [m-1]) or
absorbed (described by its absorption coefficient a [m-1]). These coefficients
along with anisotropy (i.e. the direction in which a photon is scattered if it is
scattered) and index of refraction are referred to as the optical properties of a
material.
First let's consider a slab of tissue. If photons are hitting the tissue several things
can happen:

1) Some photons will reflect off the surface of the material (similar to what
happens to glass and other materials - Fresnel's equations hold for tissue as well)
2) The majority of the photons will enter the tissue upon which the following can
happen:

a) the photon is absorbed (and can be converted to heat, trigger a chemical reaction
or cause fluorescence emission)
b) the photon is scattered (bumps into a particle and changes direction but
continues to exist)
c) nothing (some photons can make it through the entire slab without running into
anything, they are neither scattered nor absorbed and will emerge on the other side
- these are called ballistic photons).
For now let's forget about scattering and consider absorption first.

Mirrors & Lenses

23.1 Flat Mirrors (also called plane mirrors)

An object viewed using a flat mirror

appears to be located behind the mirror,
because to the observer the diverging rays
from the source appear to come from
behind the mirror.

The images reflected in flat mirrors have the following properties:

The image distance q behind the mirror equals the object
distance p from the mirror

The image height h equals the object heighth so that the

lateral

magnification

The image has an apparent left-right reversal

The image is virtual, not real!

Real Image where the light ray actually come to a focus

the object projected on a screen placed at that location

you can actually see

Virtual Image no light rays actually come directly from a virtual image, they just
appear to the eye to do so. (When you see yourself in the mirror, are you actually
located behind it as you appear?)

To figure out what happens: draw rays, use law of reflection, use geometry

Example: I can see myself

see all of himself?

how high must the mirror be for the man to

23.2 Images Formed by Spherical Mirrors

Spherical Mirror:

Principle Axis: OCIV

Center of Curvature C

Radius of Curvature R

Light rays converge to a real image at image

point I

Where is the image formed? What is its height?

and the other passing through C:

.
We give this location a special name &

Draw two rays: one hitting V

designation : the focal point

. With this designation we can re-write
the concave spherical mirror equation

as:

Note, however, that truly spherical mirrors

do not bring all rays to focus at the same
location!
Spherical Aberration
this is the problem
the Hubble Space Telescope had when first
launched.

23.3 Convex Mirrors (diverging mirrors) and Sign Conventions

Is the entry for Image location q correct?

Example: Problem #6

A spherical Christmas tree ornament is 6.00 cm in diameter. What is the

magnification of an object placed 10.0 cm away from the ornament?

Example: Problem #11

A 2.00-cm-high object is placed 3.00 cm in front of a concave mirror. If the image

is 5.00 cm high and virtual, what is the focal length of the mirror?
Example: Problem #16

A convex spherical mirror with a radius of curvature of 10.0 cm produces a virtual

image one-third the size of the real object. Where is the object?

23.5 Atmospheric Refraction (read)

23.6 Thin Lenses

Note: a convex-concave lenses is sometimes

referred to as a meniscus. It is the shape used
for most eyeglasses.

Using the same sign convention for thin lenses:

Same as for mirrors!

(This is the thin lens equation)

If you are on a computer with Java installed go here and play with the mirrors &
lenses. If it doesnt fire up after a few seconds, go down to 8 and hit the start
button. These little applets will give you a feel for what happens. Also try
this converging lens and diverging lens applets. Simpler & prettier (but no mirrors).
Example: Problem #32

A convex lens of focal length 15.0 cm is used as a magnifying glass. At what

distance from a postage stamp should you hold this lens to get a magnification of
+2.00?

Example: Problem #36

An objects distance from a converging lens is ten times the focal length. How far
is the image from the focal point? Express the answer as a fraction of the focal
length.
Multiple Lenses

This is more complicated, but straightforward if you follow these rules:

1. Do the first lens as if the others werent there.

2. Use the image formed by this lens as the object of the next lens
3. Repeat this process for all the lenses in the system
4. The total magnification is just the product of the individual magnifications of each lens.

See Example 23.9 of the book

Example: Problem #41

Two converging lenses, each of focal length 15.0 cm, are placed 40.0 cm apart,
and an object is placed 30.0 cm in front of the first. Where is the final image
formed, and what is the magnification of the system?

Microscope: Object very close to F0 makes a real inverted larger image. This image
is then viewed & magnified further using the eyepiece.

Telescope: Object near infinity forms a real inverted smaller image near the focal
point. Eyepiece is used to magnify this image.

The angular magnification (how much bigger it looks) is just

. To get different magnifications, just change eyepieces!

Most large telescopes use a concave mirror

instead of a lens to form the image.

Physics Tools for optics - Find Focal Length of thin lens using R1 and R2 radii
Use this simple tool to solve physics problem related to thin lenses. You can use this tool find focal
length for thin lens by giving lens radii and index of refraction of the material this lens made of. Please
remember to use correct sign convention when you enter radii.
Sign convention of lens radii R1 and R2
The signs of the lens radii indicate whether the corresponding surfaces are convex (R > 0, bulging
outwards from the lens) or concave (R < 0, depressed into the lens). If R is infinite, the surface is flat,
or has zero curvature, and is said to be planar.

Type of lenses

Using lensmaker's equation for thin lens, we can find focal length for lens

Concave and Convex mirrors[edit]

A concave mirror

A convex mirror

A convex mirror - SVG version

Reasons of nomination:

According to the standards page, the images are:

Of High Quality
Have a free license
Add value to an article
Accurate
With good captions

According to the same standards, the images might be:

Wikipedia's best work

pleasing to the eye

However, also according to the standards, the images are not:

of a high resolution

The image is approximately 450x450, but I believe it still does qualify under being a featured
image because it is a diagram, and not a photo. It is also sharp, clear, and looks good.
What I want to be reviewed is: 1- is the resolution okay 2- is it considered wikipedia's bets work
or pleasuring to the eye .. and therefore, should it be nominated as a featured picture or not.
Author: Myself User:Eshcorp
Pages they appear in: Curved mirror, but more could be added.

Nominate and support. - Eshcorp 07:43, 19 August 2006 (UTC)

Comments:

People are going to want svg. BrokenSegue 15:10, 19 August 2006 (UTC)
I don't know if it could be done as svg.. at least not with the tools I use, is there a good
vector drawing tool other than Inkscape that might provide more functionality? -Eshcorp 16:14, 19 August 2006 (UTC)

One small mistake - "curvature" is misspelled. Also, I think showing multiple rays of light and
their reflections would be better. See, for comparison, DrBob's lens diagrams (in svg). -Davepape 16:52, 19 August 2006 (UTC)
I will fix the mistake and add examples. It may take a while though. --Eshcorp 17:29, 19
August 2006 (UTC)

I've made an SVG version in Inkscape. I'm dabbling in things I know nothing about as usual,
so let me know if anything needs to be changed on it and I'll get it sorted. If you like that I'll
make a similar one for the concave mirror. Icey 21:44, 25 August 2006 (UTC)

Seconder:

15. Light
You might have seen a beam of sunlight when it enters a room through a narrow opening or a
hole.You may have also seen beams of light from the headlamps of scooters, cars and engines
of trains [Fig.1(a)]. Similarly, a beam of light can be seen from a torch. Some of

Fig.1(a) Rail Engine

Fig.1(b) Light House

Fig.1:Beam of light

you may have seen a beam of searchlight from a light house or from an airport tower [Fig.1(b)].
What do these experiences suggest?

15.1 LIGHT TRAVELS ALONG A STRAIGHT LINE

Boojho recalls an activity he performed in Class VI. In that activity he looked

(a)

(b)
Fig.2 Looking at a candle through a straight and bent pipe

Fig.3 Reflection of objects in water

at a lighted candle first through a straight pipe and then through a bent pipe (Fig. 2). Why was
Boojho
not
able
to
see
the
candle
flame
through
a
bent
pipe?
This
activity
showed
that
light
travels
along
straight
lines.
How can we change the path of light? Do you know, what happens when light falls on a
polished or a shiny surface?

15.2 REFLECTION OF LIGHT

One way to change the direction of light is to let it fall on a shiny surface. For example, a
shining stainless steel plate or a shining steel spoon can change the direction of light. The
surface of water can also act like a mirror and change the path of light. Have you ever seen the
reflection
of
trees
or
buildings
in
water
(Fig.3)?
Any polished or a shiny surface can act as a mirror. What happens when light falls on a mirror?
You have learnt in Class VI that a mirror changes the direction of light that falls on it. This
change of direction by a mirror is called reflection of light. Can you recall the activity in which
you got the light of a torch reflected from a mirror? Let us perform a similar activity.

Activity 15.1

Take a torch. Cover its glass with a chart paper which has three slits as shown in Fig.5.
Spread a sheet of chart paper
Paheli remembers the story of the lion and the rabbit from the Panchtantra, in which
the rabbit fooled the lion by showing him his reflection in water (Fig.4).

Fig.4 Reflection of the lion in water

Fig.5 Reflection of light from a mirror

on a smooth wooden board. Fix a plane mirror strip vertically on the chart paper
(Fig.5). Now direct the beam of light on the mirror from the torch with slits. Place the
torch in such a way that its light is seen along the chart paper on the board. Now adjust
its position so that the light from the torch strikes the plane mirror at an angle (Fig.5).
Does the mirror change the direction of light that falls on it? Now move the torch
slightly to either side. Do you find any change in the direction of reflected light?
Look into the mirror along the direction of the reflected light. Do you see the slits in
the mirror? This is the image of the slits.
Paheli wants to know, what makes things visible to us? Boojho thinks that objects are visible only
when light reflected from them reaches our eyes. Do you agree with him?This activity shows how
light gets reflected from a plane mirror.
Let us play around with the images formed in mirrors and know a little more about them.
Activity 15.2
CAUTION

Never touch a lighted electric bulb connected to the mains. It may be very hot and your
hand may get burnt badly. Do not experiment with the electric supply from the mains
or a generator or an inverter. You may get an electric shock, which may be dangerous.
Use only electric cells for all the activities suggested here.
Place a lighted candle in front of a plane mirror. Try to see the flame of the candle in
the mirror. It appears as if a similar candle is placed behind the mirror. The candle,
which appears behind the mirror, is the image of the candle formed by the
mirror(Fig.6).
The
candle
itself
is
the object.
Now move the candle to different positions in front of the mirror. Observe the image in
each case.

Fig.6 Image of a candle in a plane mirror

Boojho noted in his notebook: Is it not surprising that my image is of the same size as me whether
the mirror is small or large?

Was the image upright in each case? Did the flame appear on top of the candle as in the
object? Such an image is called erect. An image formed by a plane mirror is erect and
of
the
same
size
as
the
object.
Now place a vertical screen behind the mirror. Try to obtain the image of the candle on
this screen. Can you get the image on the screen? Now place the screen in front of the
mirror. Can you get the image on the screen now? You will find that the image of the
candle
cannot
be
obtained
on
the
screen
in
either
case.
What about the distance of the image from mirror? Let us perform another activity.
Activity 15.3

Take a chess board. If a chess board is not available, draw on a chart paper 64 (88)
squares of equal size. Draw a thick line in the middle of the paper. Fix a plane mirror
vertically on this line. Place any small object, such as a pencil sharpner, at the
boundary of the third square counting from the mirror (Fig.7). Note the position of the
image. Now shift the object to the boundary of the fourth square. Again note the
position of the image. Did you find any relation between the distance of the image from
the mirror and that of the object in front of it?

Fig.7 Locating image in a plane mirror

Paheli made a note in her notebook: In a plane mirror the image is formed behind the mirror. It is
erect, of the same size and is at the same distance from the mirror as the object is in front of it.

You will find that the image is at the same distance behind the mirror as the object is in
front of it. Now verify this by placing the object anywhere on the chart paper.

15.3 RIGHT OR LEFT!

When you see your image in a plane mirror, is it exactly like you? Have you ever noticed that
there is one interesting difference between you and your image in a mirror? Let us find out.

Activity 15.4

Stand in front of a plane mirror and look at your image. Raise your left hand. Which
hand does your image raise (Fig. 8)? Now touch your right ear. Which ear does your
hand touch in your image? Observe carefully. You will find that in the mirror the
right appears left and the left appears right. Note that only sides are
interchanged;
the
image
does
not
appear
upside
down.
Now write down your name on a piece of paper and hold it in front of a plane mirror.
How does it appear in the mirror?

Fig.8 Left hand appears on the right side in the image

Fig.9 An Ambulance
Image will be here
Boojho saw an ambulance on the road. He was surprised to see that the word AMBULANCE in front
was written in a strange manner.

Can you now understand why the word AMBULANCE is written as in Fig. 9 ? When
the driver of a vehicle ahead of an ambulance looks in her/his rear view mirror, he/she
can read AMBULANCE written on it and give way to it. It is the duty of every one of
us to allow an ambulance to pass without blocking its way.
You might have observed that in the side mirror of a scooter or a car the images of all
the objects appear smaller than the objects themselves. Have you ever wondered why it
is so?

15.4 PLAYING WITH SPHERICAL MIRRORS

Paheli and Boojho were waiting for their dinner. Boojho lifted a stainless steel plate and saw
his image in it. Oh! This plate acts as a plane mirror. My image is erect and is of the same size.
Paheli saw her image using the back of a steel spoon. Boojho look here! I can also see my
erect image though it is smaller in size. This spoon also acts as a mirror of some kind, said
Paheli.
You can also use a spoon or any curved shining surface to see your image.

Activity 15.5

Take a stainless steel spoon. Bring the outer side of the spoon near your face and look
into it. Do you see your image in it (Fig. 10)? Is this image different from what you see
in a plane mirror? Is this image erect? Is the size of the image the same, smaller or
larger?

Fig.10 Image from the outer side of a spoon

Now look at your image using the inner side of the spoon. This time you may find that
your image is erect and larger in size. If you increase the distance of the spoon from
your face, you may see your image inverted (Fig.11). You can also compare the image
of your pen or pencil instead of your face.

Fig.11 Image from the inner side of a spoon

The curved shining surface of a spoon acts as a mirror. The most common example of a
curved
mirror
is
a
spherical
mirror.
If the reflecting surface of a spherical mirror is concave, it is called a concave mirror. If
the reflecting surface is convex, then it is a convex mirror (Fig.12).

Fig.12 A Comcave and Convex mirror

Why are concave

and convex
mirrors
called
spherical
mirrors?
Take a rubber ball and cut a portion of it with a knife or a hacksaw blade
[Fig.13(a)]. (Be careful. Ask an elder person to help you in cutting the ball). The
inner surface of the cut ball is called concave and the outer surface is called convex
(Fig.13(b)).

Fig.13 A spherical mirror is a part of a sphere

The inner surface of a spoon acts like a concave mirror, while its outer surface acts like
a
convex
mirror.
We know that the image of an object formed by a plane mirror cannot be obtained on a
screen. Let us investigate if it is also true for the image formed by a concave mirror.
Activity 15.6
CAUTION

You will conduct Activity 6 in the sunlight. Be careful, never look directly towards the
sun or its image as it may damage your eyes. You may look at the image of the sun
when it is thrown on a screen or a wall.

Fig.14 A concave mirror forms a real image of the sun

Take a concave mirror. Hold it facing the sun. Try to get the light reflected by the
mirror on a sheet of paper. Adjust the distance of the paper until you get a sharp bright
spot on it (Fig. 14). Hold the mirror and the sheet of paper steady for a few minutes.
Does
the
paper
start
burning?
This bright spot is, in fact, the image of the sun. Notice that this image is formed on a
screen. An image formed on a screen is called a real image. Recollect that in Activity
2 the image formed by a plane mirror could not be obtained on a screen. Such an image
is
called
a virtual
image.
Now let us try to obtain on the screen the image of a candle flame formed by a concave
mirror.
Activity 15.7

Fix a concave mirror on a stand (any arrangement to keep the mirror steady would do)
and place it on a table(Fig.15). Paste a piece of white paper on a cardboard sheet (say
about

Fig.15 Real images formed by a concave mirror

15cm x 10cm). This will act as a screen. Keep a lighted candle on the table at a
distance of about 50 cm from the mirror. Try to obtain the image of the flame on the
screen. For this, move the screen till a sharp image of the flame is obtained. Make sure
that, the screen does not

Fig.16 Virtual image formed by a concave mirror

obstruct the light from the candle falling on the mirror. Is this image real or virtual? Is
it
of
the
same
size
as
the
flame?
Now move the candle towards the mirror and place it at different distances from it. In
each case try to obtain the image on the screen. Record your observation in Table 1. Is
it possible to obtain the image on the screen when the candle is too close to the mirror
(Fig.16)?
We see that the image formed by a concave mirror can be smaller or larger in size than
the
object.
The
image
may
also
be
real
or
virtual.
Concave mirrors are used for many purposes. You might have seen doctors using
concave mirrors for examining eyes, ears, nose and throat. Concave mirrors are also
used by dentists to see an enlarged image of the teeth (Fig.17). The reflectors of
torches,headlights of cars and scooters are concave in shape (Fig.18).

Fig.17 A Dentist examining a patient

Boojho observed his image in the shiny surface of the bell on his new bicycle. He
found that his image was erect and smaller in size. He wondered

Fig.18 Reflector of a torch

if the bell is also a kind of spherical mirror. Can you recognise the type of the mirror?
Note that the reflecting surface of the bell is convex.
Activity 15.8

Repeat Activity 7 now with a convex mirror in place of a concave mirror (Fig.19).
Record
your
observations
in
a
Table
similar
to
Table
1.
Could you get a real image at any distance of the object from the convex

Fig.19 Image formed by a convex mirror

Table 1 Image formed by a concave mirror for object placed at different distances from it

Character of the image

Distance of the object from
the mirror

Smaller/larger than the

object

Inverted/
erect

Real/virtual

50 cm

...

..

40 cm

...

...

30 cm
20 cm
10 cm
5 cm

...

Fig.20 Convex mirror as a side view mirror

mirror? Did you get an image larger in size than the object?
Can you now recognise the mirrors used as side mirrors in scooters? These are convex
mirrors. Convex mirrors can form images of objects spread over a large area. So, these
help the drivers to see the traffic behind them (Fig.20).

15.5 IMAGES FORMED BY LENSES

You might have seen a magnifying glass. It is used to read very small print (Fig.21).
You might have also used it to observe the body parts of a cockroach or an earthworm.
The
magnifying
glass
is
actually
a
type
of
a
lens.
Lenses are widely used in spectacles, telescopes and microscopes. Try to add a few
more
uses
of
lenses
to
this
list.
Get some lenses. Touch and feel them. Can you find some difference just by touching?
Those lenses which feel thicker in the middle than at the edges are convex lenses
[Fig.22(a)]. Those

Fig.21 A magnifying glass

which feel thinner in the middle than at the edges are concave lenses [Fig.22(b)].
Notice that the lenses are transparent and light can pass through them.

Fig.22 A convex lens and concave lens

Let us play with lenses.

CAUTION

It is dangerous to look through a lens at the sun or a bright light. You should also be
careful not to focus sunlight with a convex lens on any part of your body.
Activity 15.9

Take a convex lens or magnifying glass. Put it in the path of sunrays. Place a sheet of
paper as shown (Fig.23). Adjust the distance between the lens and the paper till you get
a bright spot on the paper. Hold the lens and the paper in this position for a few

minutes.
Does
the
paper
begin
to
Now replace the convex lens with a concave lens. Do you see a bright spot

burn?

Fig.23 Real image of the sun by a convex lens

on the paper this time, too? Why are you not getting a bright spot this time?
We have seen in the case of mirrors that for different positions of the object the nature
and
size
of
the
image
change.Is
it
true
for
lenses
also?
Let us find out. .
Activity 15.10

Take a convex lens and fix it on a stand as you did with the concave mirror. Place it on
a table. Place a lighted candle at a distance of about 50 cm from the lens [Fig.25 (a)].
Try to obtain the image
A convex lens converges (bends inward) the light generally falling on it [Fig.24 (a)].
Therefore, it is called a converging lens. On the other hand, a concave lens diverges
(bends outward) the light and is called a diverging lens [Fig.24 (b)].

Fig.24 Diverging lens

of the candle on a paper screen placed on the other side of the lens. You may have to
move the screen towards or away from the lens to get a sharp image of the flame. What
kind
of
image
did
you
get?
Is
it
real
or
virtual?
Now vary the distance of the candle from the lens [Fig.25 (b)]. Try to obtain the image
of the candle flame every time on the paper screen by moving it. Record your
observations as you did in Activity 7 for the concave mirror.
It means that we can see the image formed by a lense from the side opposite to that of the object.

(a)

(b)
Fig.25 Image by a convex lens for object placed at different distance from it

Fig.26 Virtual image formed by the convex lens

Fig.27 Image formed by a concave lens

Did you get in any position of the object an image which was erect and magnified
(Fig.26). Could this image be obtained on a screen? Is the image real or virtual? This is
how
a
convex
lens
is
used
as
a
magnifying
glass.
In a similar fashion study the images formed by a concave lens. You will find that the
image formed by a concave lens is always virtual, erect and smaller in size than the
object (Fig.27).

15.6 SUNLIGHT WHITE OR COLOURED?

Have you ever seen a rainbow in the sky? You might have noticed that it appears usually after
the rain when the sun is low in the sky. The rainbow is seen as a large arc in the sky with many
colours (Fig.28).

Fig.28 A rainbow

Fig.29A CD placed in sun

How many colours are present in a rainbow? When observed carefully, there are seven colours
in a rainbow, though it may not be easy to distinguish all of them. These are red, orange,
yellow, green, blue, indigo and violet.

Does this mean that the white light consists of seven colours?(a) A disc with seven colours (b) It
appears white on rotating
You might have seen that when you blow soap bubbles, they appear colourful. Similarly, when
light is reflected from the surface of a Compact Disk (CD), you see many colours (Fig.29).
On the basis of these experiences, could we say that the sunlight is a mixture of different
colours? Let us investigate.

Activity 15.11

Take a glass prism. Allow a narrow beam of sunlight through a small hole in the
window of a dark room to fall on one face of the prism. Let the light coming out of the
other face of the prism fall on
Paheli wants to tell you that you can see a rainbow only when your back is towards the sun.

Fig.30A prism splits sunlight into seven colours

a white sheet of paper or on a white wall. What do you observe? Do you see colours
similar to those in a rainbow (Fig.30)? This shows that the sunlight consists of seven
colours. The sunlight is said to be white light. This means that the white light consists
of seven colours. Try to identify these colours and write their names in your notebook.
Can we mix these colours to get white light? Let us try.
Activity 15.12

Take a circular cardboard disc of about 10 cm diameter. Divide this disc into seven
segments. Paint the seven rainbow colours on these segments as shown in Fig.31 (a).
You can also paste, coloured papers on these segments. Make a small hole at the centre
of the disc. Fix the disc loosely on the tip of a refill of a ball pen. Ensure that the disc
rotates freely [Fig.31 (a)]. Rotate the disc in the daylight. When the disc is rotated fast,
the colours get mixed together and the disc appears to be whitish [Fig.31 (b)]. Such a
disc is popularly known as Newtons disc.

Fig.31(a) A disc with seven colours (b) It appears white on rotating

Paheli has a brilliant idea! Shehas prepared a small top with a small circular disc with
seven rainbow colours painted on it (Fig.32). When the top rotates it appears nearly
white.

Fig.32 A top with seven colours

Keywords

Concave lens
Concave mirror
Convex lens
Convex mirror
Erect image
Magnified image

Magnifying glass
Prism
Rainbow
Real image
Rear view mirror
Side mirror
Spherical mirror
Virtual image

What you have learnt

Light travels along straight lines.

Any polished or a shining surface acts as a mirror.
An image which can be obtained on a screen is called a real image.
An image which cannot be obtained on a screen is called a virtual image.
The image formed by a plane mirror is erect. It is virtual and is of the same size as the object.
The image is at the same distance behind the mirror as the object is in front of it.
In an image formed by a mirror, the left side of the object is seen on the right side in the
image, and right side of the object appears to be on the left side in the image.
A concave mirror can form a real and inverted image. When the object is placed very close to
the mirror, the image formed is virtual, erect and magnified.
Image formed by a convex mirror is erect, virtual and smaller in size than the object.
A convex lens can forms real and inverted image. When the object is placed very close to the
lens, the image formed is virtual, erect and magnified. When used to see objects magnified,
the convex lens is called a magnifying glass.
A concave lens always forms erect, virtual and smaller image than the object.
White light is composed of seven colours.

EXERCISE
1. Fill in the blanks:
o

An image that cannot be obtained on a screen is called

Image formed by a convex

An image formed by a

An image which can be obtained on a screen is called a

is always virtual and smaller in size

mirror is always of the same size as that of the object
image

An image formed by a concave

cannot be obtained on a screen.
2. Mark T if the statement is true and F if it is false:

S.No

a.

b.

Option

We can obtain an enlarged and erect image by a convex

mirror.

A concave lens always form a virtual image.

Ture/False

True
False
True
False

We can obtain a real, enlarged and inverted image by a

concave mirror.

c.

d.

A real image cannot be obtained on a screen.

True
False
True
False

e.

A concave mirror always form a real image.

True
False

Show Result

3. Match the items given in Column I with one or more items of Column II.

4.

Column I

Column II

(a) A plane mirror

(i)

Used as a magnifying glass

A convex
mirror

(ii)

Can form image of objects spread over a

large area.

(c) A convex lens

(iii)

Used by dentists to see enlarged image of

teeth.

(iv)

The image is always inverted and

magnified.

(b)

(d)

A concave
mirror

(e) A concave lens (v)

The image is erect and of the same size as

the object.

(vi)

The image is erect and smaller in size than

the object.

5. State the characteristics of the image formed by a plane mirror.

6. Find out the letters of English alphabet or any other language known to you in which the
image formed in a plane mirror appears exactly like the letter itself. Discuss your findings.
7. What is a virtual image? Give one situation where a virtual image is formed.
8. State two differences between a convex and a concave lens.
9. Give one use each of a concave and a convex mirror.
10. Which type of mirror can form a real image?
11. Which type of lens forms always a virtual image?

Choose the correct option in questions 1113

12. A virtual image larger than the object can be produced by a

Option

S.No
a.

concave lens

b.

concave mirror

c.

convex mirror

d.

plane mirror

13. David is observing his image in a plane mirror. The distance between the mirror and his image
is 4 m. If he moves 1 m towards the mirror,then the distance between David and his image
will be

Option

S.No
a.

3m

b.

5m

c.

6m

d.

8m

14. The rear view mirror of a car is a plane mirror. A driver is reversing his car at a speed of 2 m/s.
The driver sees in his rear view mirror the image of a truck parked behind his car. The speed
at which the image of the truck appears to approach the driver will be

Option

S.No
a.

1 m/s

b.

2 m/s

c.

4 m/s

d.

8 m/s

Extended Learning Activities and Projects

1. Play with a mirror
Write your name with a sketch pen on a thin sheet of paper, polythene or glass. Read your
name on the sheet while standing in front of a plane mirror. Now look at your image in the
mirror.
2. A burning candle in water
Take a shoe box, open on one side. Place a small lighted candle in it. Place a clear glass sheet
(roughly 25 cm x 25 cm) infront of this candle (Fig.33). Try to locate the image of the candle
behind

Fig.33 Candle burning in water

the glass sheet. Place a glass of water at its position. Ask your friends to look at the image of
the candle through the sheet of glass. Ensure that candle is not visible to your friends. Your
friends will be surprised to see the candle burning in water. Try to explain the reason.
3. Make a rainbow
Try to make your own rainbow. You can try this project in the morning or in the evening.
Stand with your back towards the sun. Take a hosepipe or a water pipe used in the garden.
Make a fine spray in front of you. You can see different colours of rainbow in the spray.
4. Visit a laughing gallery in some science centre or a science park or a village mela. You will find
some large mirrors there. You can see your distorted and funny images in these mirrors. Try
to find out the kind of mirrors used there.

5. Visit a nearby hospital. You can also visit the clinic of an ENT specialist, or a dentist.Request
the doctor to show you the mirrors used for examining ear, nose, throat and teeth. Can you
recognise the kind of mirror used in these instruments?
6. Role play
Here is a game that a group of children can play. One child will be chosen to act as object and
another will act as the image of the object. The object and the image will sit opposite to each
other. The object will make movements, such as raising a hand, touching an ear, etc. The
image will have to make the correct movement following the movement of the object. The
rest of the group will watch the movements of the image. If the image fails to make the
correct movement, she/he will be retired. Another child will take her/his place and the game
will continue. A scoring scheme can be introduced. The group that scores the maximum will
be declared the winner.
Did You Know?

The mirrors can be used as weapons. Archimedes, a Greek scientist, is said to have
done just that more than two thousand years ago. When the Romans attacked Syracuse,
a coastal city-state in Greece, Archimedes used mirrors arranged as shown in Fig. 34.
The mirrors could be moved in any direction. They were positioned such that they
reflected the sunlight on the Roman soldiers. The soldiers were dazzled by the sunlight.
They did not know what was happening. They got confused and ran away. This was an
example of triumph of ideas over military might.

Fig.34 Archimedes mirrors

A biconvex lens.

Lenses can be used to focus light.

A lens is a transmissive optical device which affects the focusing of a light

beam through refraction. A simple lens consists of a single piece of material, while a compound
lens consists of several simple lenses (elements), usually along a common axis. Lenses are
made from transparent materials such as glass, ground and polished to a desired shape. A lens
can be used to focus light to form animage, unlike a prism which refracts light without focusing.
Devices which similarly refract radiation other than visible light are also called lenses, such
as microwave lenses or acoustic lenses.
The variant spelling lense is sometimes seen. While it is listed as an alternative spelling in some
dictionaries, most mainstream dictionaries do not list it as acceptable.[1][2]

History[edit]
This section
requires expansionwith: history
after 1758. (January 2012)

See also: History of optics and Camera lens

The Nimrud lens

The word lens comes from the Latin name of the lentil, because a double-convex lens is lentilshaped. The genus of the lentil plant isLens, and the most commonly eaten species is Lens
culinaris. The lentil plant also gives its name to a geometric figure.
The oldest lens artifact is the Nimrud lens, dating back 2700 years to ancient Assyria.[3][4] David
Brewster proposed that it may have been used as a magnifying glass, or as a burning-glass to
start fires by concentrating sunlight.[3][5] Another early reference to magnificationdates back
to ancient Egyptian hieroglyphs in the 8th century BC, which depict "simple glass meniscal
lenses".[6][verification needed]
The earliest written records of lenses date to Ancient Greece, with Aristophanes' play The
Clouds (424 BC) mentioning a burning-glass (abiconvex lens used to focus the sun's rays to
produce fire). Some scholars argue that the archeological evidence indicates that there was
widespread use of lenses in antiquity, spanning several millennia.[7] Such lenses were used by
artisans for fine work, and for authenticating seal impressions. The writings of Pliny the
Elder (2379) show that burning-glasses were known to the Roman Empire,[8]and mentions what

is arguably the earliest written reference to a corrective lens: Nero was said to watch
the gladiatorial games using anemerald (presumably concave to correct for nearsightedness,
though the reference is vague).[9] Both Pliny and Seneca the Younger (3 BC65) described the
magnifying effect of a glass globe filled with water.
Excavations at the Viking harbour town of Frjel, Gotland, Sweden discovered in 1999 the rock
crystal Visby lenses, produced by turning on pole lathes at Frjel in the 11th to 12th century, with
an imaging quality comparable to that of 1950s aspheric lenses. The Viking lenses were capable
of concentrating enough sunlight to ignite fires.[10]
Between the 11th and 13th century "reading stones" were invented. Often used by monks to
assist in illuminating manuscripts, these were primitive plano-convex lenses initially made by
cutting a glass sphere in half. As the stones were experimented with, it was slowly understood
that shallower lenses magnified more effectively.
Lenses came into widespread use in Europe with the invention of spectacles, probably in Italy in
the 1280s.[11] This was the start of the optical industry of grinding and polishing lenses for
spectacles, first in Venice and Florence in the thirteenth century,[12] and later in the spectaclemaking centres in both the Netherlands and Germany.[13] Spectacle makers created improved
types of lenses for the correction of vision based more on empirical knowledge gained from
observing the effects of the lenses (probably without the knowledge of the rudimentary optical
theory of the day).[14][15] The practical development and experimentation with lenses led to the
invention of the compound optical microscope around 1595, and the refracting telescope in 1608,
both of which appeared in the spectacle-making centres in the Netherlands.[16][17]
With the invention of the telescope and microscope there was a great deal of experimentation
with lens shapes in the 17th and early 18th centuries trying to correct chromatic errors seen in
lenses. Opticians tried to construct lenses of varying forms of curvature, wrongly assuming errors
arose from defects in the spherical figure of their surfaces.[18]Optical theory on refraction and
experimentation was showing no single-element lens could bring all colours to a focus. This led
to the invention of the compound achromatic lensby Chester Moore Hall in England in 1733, an
invention also claimed by fellow Englishman John Dollond in a 1758 patent.

Construction of simple lenses[edit]

Most lenses are spherical lenses: their two surfaces are parts of the surfaces of spheres. Each
surface can be convex (bulging outwards from the lens), concave (depressed into the lens),
or planar (flat). The line joining the centres of the spheres making up the lens surfaces is called
the axis of the lens. Typically the lens axis passes through the physical centre of the lens,
because of the way they are manufactured. Lenses may be cut or ground after manufacturing to
give them a different shape or size. The lens axis may then not pass through the physical centre
of the lens.
Toric or sphero-cylindrical lenses have surfaces with two different radii of curvature in two
orthogonal planes. They have a different focal power in different meridians. This forms

an astigmatic lens. An example is eyeglass lenses that are used used to correct astigmatism in
someone's eye.
More complex are aspheric lenses. These are lenses where one or both surfaces have a shape
that is neither spherical nor cylindrical. The more complicated shapes allow such lenses to form
images with less aberration than standard simple lenses, but they are more difficult and
expensive to produce.

Types of simple lenses[edit]

Lenses are classified by the curvature of the two optical surfaces. A lens is biconvex (or double
convex, or just convex) if both surfaces are convex. If both surfaces have the same radius of
curvature, the lens isequiconvex. A lens with two concave surfaces is biconcave (or
just concave). If one of the surfaces is flat, the lens is plano-convex or plano-concave depending
on the curvature of the other surface. A lens with one convex and one concave side is convexconcave or meniscus. It is this type of lens that is most commonly used in corrective lenses.
If the lens is biconvex or plano-convex, a collimated beam of light passing through the lens will
be converged (or focused) to a spot behind the lens. In this case, the lens is called
a positive or converginglens. The distance from the lens to the spot is the focal length of the lens,
which is commonly abbreviatedf in diagrams and equations.

If the lens is biconcave or plano-concave, a collimated beam of light passing through the lens is
diverged (spread); the lens is thus called a negative or diverging lens. The beam after passing
through the lens appears to be emanating from a particular point on the axis in front of the lens;
the distance from this point to the lens is also known as the focal length, although it is negative
with respect to the focal length of a converging lens.

Convex-concave (meniscus) lenses can be either positive or negative, depending on the relative
curvatures of the two surfaces. A negative meniscus lens has a steeper concave surface and will
be thinner at the centre than at the periphery. Conversely, a positive meniscus lens has a
steeper convex surface and will be thicker at the centre than at the periphery. An ideal thin
lens with two surfaces of equal curvature would have zero optical power, meaning that it would
neither converge nor diverge light. All real lenses have nonzero thickness, however, which
causes a real lens with identical curved surfaces to be slightly positive. To obtain exactly zero
optical power, a meniscus lens must have slightly unequal curvatures to account for the effect of
the lens' thickness.

Lensmaker's equation[edit]
The focal length of a lens in air can be calculated from the lensmaker's equation:[19]

where
is the focal length of the lens,
is the refractive index of the lens material,
is the radius of curvature (with sign, see below) of the lens surface closest to the light
source,

is the radius of curvature of the lens surface farthest from the light source, and
is the thickness of the lens (the distance along the lens axis between the two surface
vertices).
The focal length f is positive for converging lenses, and negative for
diverging lenses. The reciprocal of the focal length, 1/f, is the optical
power of the lens. If the focal length is in metres, this gives the optical
power in dioptres (inverse metres).
Lenses have the same focal length when light travels from the back to
the front as when light goes from the front to the back. Other properties
of the lens, such as the aberrationsare not the same in both directions.
Sign convention for radii of curvature R1 and R2[edit]
Main article: Radius of curvature (optics)
The signs of the lens' radii of curvature indicate whether the
corresponding surfaces are convex or concave. The sign
convention used to represent this varies, but in this article
apositive R indicates a surface's center of curvature is further along in
the direction of the ray travel (right, in the accompanying diagrams),
while negative R means that rays reaching the surface have already
passed the center of curvature. Consequently, for external lens surfaces
as diagrammed above, R1 > 0 and R2 < 0 indicate convex surfaces
(used to converge light in a positive lens), while R1 < 0 and R2 >
0 indicate concave surfaces. The reciprocal of the radius of curvature is
called the curvature. A flat surface has zero curvature, and its radius of
curvature is infinity.
Thin lens approximation[edit]
If d is small compared to R1 and R2, then the thin lens approximation can
be made. For a lens in air, f is then given by

[20]

Imaging properties[edit]
As mentioned above, a positive or converging lens in air will focus a
collimated beam travelling along the lens axis to a spot (known as
the focal point) at a distance f from the lens. Conversely, a point
source of light placed at the focal point will be converted into a
collimated beam by the lens. These two cases are examples
of image formation in lenses. In the former case, an object at an
infinite distance (as represented by a collimated beam of waves) is

focused to an image at the focal point of the lens. In the latter, an

object at the focal length distance from the lens is imaged at infinity.
The plane perpendicular to the lens axis situated at a
distance f from the lens is called the focal plane.
If the distances from the object to the lens and from the lens to the
image are S1 and S2 respectively, for a lens of negligible thickness,
in air, the distances are related by the thin lens formula:

.
This can also be put into the "Newtonian" form:
[21]

where

and

A camera lens forms a real image of a distant object.

Therefore if an object is placed at a distance S1 > f from a

positive lens of focal length f, we will find an image
distance S2 according to this formula. If a screen is placed
at a distance S2 on the opposite side of the lens, an image
will be formed on it. This sort of image, which can be
projected onto a screen or image sensor, is known as a real
image.

Virtual image formation using a positive lens as a magnifying glass.

This is the principle of the camera, and of the human eye.

The focusing adjustment of a camera adjusts S2, as using
an image distance different from that required by this
formula produces a defocused (fuzzy) image for an object
at a distance of S1 from the camera. Put another way,
modifying S2 causes objects at a different S1 to come into
perfect focus.
In some cases S2 is negative, indicating that the image is
formed on the opposite side of the lens from where those
rays are being considered. Since the diverging light rays
emanating from the lens never come into focus, and those
rays are not physically present at the point where
they appear to form an image, this is called a virtual image.
Unlike real images, a virtual image cannot be projected on
a screen, but appears to an observer looking through the
lens as if it were a real object at the location of that virtual
image. Likewise, it appears to a subsequent lens as if it
were an object at that location, so that second lens could
again focus that light into a real image, S1 then being
measured from the virtual image location behind the first
lens to the second lens. This is exactly what the eye does
when looking through a magnifying glass. The magnifying
glass creates a (magnified) virtual image behind the
magnifying glass, but those rays are then re-imaged by
the lens of the eye to create a real image on the retina.

A negative lens produces a demagnified virtual image.

A Barlow lens (B) reimages a virtual object (focus of red ray path) into
a magnified real image (green rays at focus)

Using a positive lens of focal length f, a virtual image will

result when S1 < f, the lens thus being used a magnifying
glass (rather than if S1 >> f as for a camera). Using a
negative lens (f < 0) with a real object (S1 > 0) can only
produce a virtual image (S2 < 0), according to the above
formula. It is also possible for the object distance S1to be
negative, in which case the lens sees a so-called virtual
object. This happens when the lens is inserted into a
converging beam (being focused by a previous
lens) before the location of its real image. In that case even
a negative lens can project a real image, as is done by
a Barlow lens.

Real image of a lamp is projected onto a screen (inverted).

Reflections of the lamp from both surfaces of the biconvex lens are
visible.

A convex lens (f << S1) forming a real, inverted image rather than the
upright, virtual image as seen in a magnifying glass

For a thin lens, the distances S1 and S2 are measured from

the object and image to the position of the lens, as
described above. When the thickness of the lens is not
much smaller than S1 and S2 or there are multiple lens
elements (a compound lens), one must instead measure
from the object and image to the principal planes of the
lens. If distances S1 or S2 pass through a medium other
than air or vacuum a more complicated analysis is required.

Magnification[edit]
The linear magnification of an imaging system using a
single lens is given by

,
where M is the magnification factor defined as the ratio
of the size of an image compared to the size of the
object. The sign convention here dictates that if M is
negative, as it is for real images, the image is upsidedown with respect to the object. For virtual images M is
positive, so the image is upright.
Linear magnification M is not always the most useful
measure of magnifying power. For instance, when
characterizing a visual telescope or binoculars which
produce only a virtual image, one would be more
concerned with the angular magnification which

expresses how much larger a distant object appears

through the telescope compared to the naked eye. In
the case of a camera one would quote the plate scale,
which compares the apparent (angular) size of a distant
object to the size of the real image produced at the
focus. The plate scale is the reciprocal of the focal
length of the camera lens; lenses are categorized
as long-focus lenses or wide-angle lenses according to
their focal lengths.
Using an inappropriate measurement of magnification
can be formally correct but yield a meaningless
number. For instance, using a magnifying glass of 5 cm
focal length, held 20 cm from the eye and 5 cm from
the object, produces a virtual image at infinity of infinite
linear size: M = . But the angular magnification is 5,
meaning that the object appears 5 times larger to the
eye than without the lens. When taking a picture of
the moon using a camera with a 50 mm lens, one is not
concerned with the linear
magnificationM 50 mm / 380000 km = 1.31010. R
ather, the plate scale of the camera is about 1/mm,
from which one can conclude that the 0.5 mm image on
the film corresponds to an angular size of the moon
seen from earth of about 0.5.
In the extreme case where an object is an infinite
distance away, S1 = , S2 = f and M = f/= 0,
indicating that the object would be imaged to a single
point in the focal plane. In fact, the diameter of the
projected spot is not actually zero,
since diffraction places a lower limit on the size of
the point spread function. This is called the diffraction
limit.

Images of black letters in a thin convex lens of focal length f are

shown in red. Selected rays are shown for letters E, I and K in
blue, green and orange, respectively. Note that E (at 2f) has an
equal-size, real and inverted image; I (at f) has its image
at infinity; and K (at f/2) has a double-size, virtual and upright
image.

Aberrations[edit]

Optical aberration

Distortion

Spherical aberration
Coma
Astigmatism
Petzval field curvature
Chromatic aberration
Defocus

Tilt

Main article: Optical aberration

Lenses do not form perfect images, and there is always
some degree of distortion or aberration introduced by
the lens which causes the image to be an imperfect
replica of the object. Careful design of the lens system
for a particular application ensures that the aberration is
minimized. There are several different types of
aberration which can affect image quality.

Spherical aberration[edit]
Main article: Spherical aberration
Spherical aberration occurs because spherical surfaces
are not the ideal shape with which to make a lens, but
they are by far the simplest shape to which glass can
be ground and polished and so are often used.
Spherical aberration causes beams parallel to, but
distant from, the lens axis to be focused in a slightly
different place than beams close to the axis. This
manifests itself as a blurring of the image. Lenses in
which closer-to-ideal, non-spherical surfaces are used
are called aspheric lenses. These were formerly
complex to make and often extremely expensive, but
advances in technology have greatly reduced the
manufacturing cost for such lenses. Spherical
aberration can be minimised by careful choice of the
curvature of the surfaces for a particular application: for
instance, a plano-convex lens which is used to focus a
collimated beam produces a sharper focal spot when
used with the convex side towards the beam source.

Coma[edit]
Main article: Coma (optics)
Another type of aberration is coma, which derives its
name from the comet-like appearance of the aberrated
image. Coma occurs when an object off the optical axis
of the lens is imaged, where rays pass through the lens
at an angle to the axis . Rays which pass through the
centre of the lens of focal length f are focused at a point
with distance f tan from the axis. Rays passing
through the outer margins of the lens are focused at
different points, either further from the axis (positive
coma) or closer to the axis (negative coma). In general,
a bundle of parallel rays passing through the lens at a
fixed distance from the centre of the lens are focused to
a ring-shaped image in the focal plane, known as
acomatic circle. The sum of all these circles results in a
V-shaped or comet-like flare. As with spherical
aberration, coma can be minimised (and in some cases
eliminated) by choosing the curvature of the two lens
surfaces to match the application. Lenses in which both
spherical aberration and coma are minimised are
called bestform lenses.

Chromatic aberration[edit]
Main article: Chromatic aberration
Chromatic aberration is caused by the dispersion of the
lens materialthe variation of its refractive index, n,
with the wavelength of light. Since, from the formulae
above, f is dependent upon n, it follows that different
wavelengths of light will be focused to different
positions. Chromatic aberration of a lens is seen as
fringes of colour around the image. It can be minimised
by using an achromatic doublet (or achromat) in which
two materials with differing dispersion are bonded
together to form a single lens. This reduces the amount
of chromatic aberration over a certain range of
wavelengths, though it does not produce perfect
correction. The use of achromats was an important step
in the development of the optical microscope.
An apochromat is a lens or lens system which has even
better correction of chromatic aberration, combined with
improved correction of spherical aberration.
Apochromats are much more expensive than
achromats.
Different lens materials may also be used to minimise
chromatic aberration, such as specialised coatings or
lenses made from the crystal fluorite. This naturally
occurring substance has the highest known Abbe
number, indicating that the material has low dispersion.

Other types of aberration[edit]

Other kinds of aberration include field
curvature, barrel and pincushion distortion,
and astigmatism.

Aperture diffraction[edit]
Even if a lens is designed to minimize or eliminate the
aberrations described above, the image quality is still
limited by the diffraction of light passing through the
lens' finiteaperture. A diffraction-limited lens is one in
which aberrations have been reduced to the point
where the image quality is primarily limited by
diffraction under the design conditions.

Compound lenses[edit]
See also: Photographic lens, Doublet
(lens) and Achromat

Simple lenses are subject to the optical

aberrations discussed above. In many cases these
aberrations can be compensated for to a great extent
by using a combination of simple lenses with
complementary aberrations. A compound lens is a
collection of simple lenses of different shapes and
made of materials of different refractive indices,
arranged one after the other with a common axis.
The simplest case is where lenses are placed in
contact: if the lenses of focal lengths f1 and f2 are "thin",
the combined focal length f of the lenses is given by

Since 1/f is the power of a lens, it can be seen that

the powers of thin lenses in contact are additive.
If two thin lenses are separated in air by some
distance d, the focal length for the combined
system is given by

The distance from the front focal point of the

combined lenses to the first lens is called
the front focal length (FFL):

[22]

Similarly, the distance from the second

lens to the rear focal point of the combined
system is the back focal length (BFL):

As d tends to zero, the focal lengths

tend to the value of f given for thin
lenses in contact.
If the separation distance is equal to
the sum of the focal lengths (d = f1+f2),
the FFL and BFL are infinite. This

corresponds to a pair of lenses that

transform a parallel (collimated) beam
into another collimated beam. This
type of system is called an afocal
system, since it produces no net
convergence or divergence of the
beam. Two lenses at this separation
form the simplest type of optical
telescope. Although the system does
not alter the divergence of a collimated
beam, it does alter the width of the
beam. The magnification of such a
telescope is given by

which is the ratio of the output

beam width to the input beam
width. Note the sign convention: a
telescope with two convex lenses
(f1 > 0, f2 > 0) produces a negative
magnification, indicating an
inverted image. A convex plus a
concave lens (f1 > 0 > f2) produces
a positive magnification and the
image is upright.

Other types[edit]
Cylindrical lenses have curvature
in only one direction. They are
used to focus light into a line, or to
convert the elliptical light from
a laser diode into a round beam.

Close-up view of a flat Fresnel lens.

A Fresnel lens has its optical

surface broken up into narrow
rings, allowing the lens to be much
thinner and lighter than
conventional lenses. Durable
Fresnel lenses can be molded
from plastic and are inexpensive.
Lenticular lenses are arrays
of microlenses that are used
in lenticular printing to make
images that have an illusion of
depth or that change when viewed
from different angles.
A gradient index lens has flat
optical surfaces, but has a radial or
axial variation in index of refraction
that causes light passing through
the lens to be focused.
An axicon has a conical optical
surface. It images a point
source into a line along the optic
axis, or transforms a laser beam
into a ring.[23]
Superlenses are made
from negative index
metamaterials and claim to
produce images at spatial
resolutions exceeding
the diffraction limit.[24] The first
superlenses were made in 2004
using such a metamaterial for
microwaves.[24] Improved versions
have been made by other
researchers.[25][26]As of 2014 the
superlens has not yet been
demonstrated at visible or nearinfrared wavelengths.[27]

Uses[edit]
A single convex lens mounted in a
frame with a handle or stand is
a magnifying glass.
Lenses are used as prosthetics for
the correction of visual
impairments such
as myopia, hyperopia, presbyopia,
and astigmatism. (See corrective
lens, contact lens, eyeglasses.)
Most lenses used for other
purposes have strict axial
symmetry; eyeglass lenses are
only approximately symmetric.
They are usually shaped to fit in a
roughly oval, not circular, frame;
the optical centres are placed over
the eyeballs; their curvature may
not be axially symmetric to correct
for astigmatism. Sunglasses'
lenses are designed to attenuate
light; sunglass lenses that also
correct visual impairments can be
custom made.
Other uses are in imaging systems
such
as monoculars, binoculars, telesco
pes, microscopes, cameras and pr
ojectors. Some of these
instruments produce a virtual
image when applied to the human
eye; others produce a real
image which can be captured
on photographic film or an optical
sensor, or can be viewed on a
screen. In these devices lenses
are sometimes paired up
with curved mirrors to make
a catadioptric system where the
lens's spherical aberration corrects

the opposite aberration in the

mirror (such
as Schmidtand meniscus corrector
s).
Convex lenses produce an image
of an object at infinity at their
focus; if the sun is imaged, much
of the visible and infrared light
incident on the lens is
concentrated into the small image.
A large lens will create enough
intensity to burn a flammable
object at the focal point. Since
ignition can be achieved even with
a poorly made lens, lenses have
been used as burning-glasses for
at least 2400 years.[28] A modern
application is the use of relatively
large lenses to concentrate solar
energy on relatively
small photovoltaic cells, harvesting
more energy without the need to
use larger and more expensive
cells.
Radio
astronomy and radar systems
often use dielectric lenses,
commonly called a lens antenna to
refract electromagnetic
radiation into a collector antenna.
Lenses can become scratched and
abraded. Abrasion-resistant
coatings are available to help
control this.[29]

See also[edit]

Anti-fogging treatment of
optical surfaces
Back focal plane
Bokeh

Cardinal point (optics)

Caustic (optics)
Eyepiece
F-number
Gravitational lens
Lens (anatomy)
List of lens designs
Numerical aperture
Optical coatings
Optical lens design
Photochromic lens
Prism (optics)
Ray tracing
Ray transfer matrix analysis

References[edit]
1. Jump up^ Brians, Paul
(2003). Common Errors in
English. Franklin, Beedle &
Associates. p. 125.ISBN 1887902-89-9. Retrieved 28
June 2009. Reports "lense"
as listed in some
dictionaries, but not
generally considered
acceptable.
2. Jump up^ MerriamWebster's Medical
Dictionary. MerriamWebster. 1995.
p. 368. ISBN 0-87779-9148. Lists "lense" as an
acceptable alternate
spelling.
3. ^ Jump up
to:a b Whitehouse, David (1
July 1999). "World's oldest
telescope?". BBC News.
Retrieved 10 May 2008.
4. Jump up^ "The Nimrud
lens/The Layard
lens". Collection database.
The British Museum.
Retrieved 25
November 2012.
5. Jump up^ D. Brewster
(1852). "On an account of a
rock-crystal lens and
decomposed glass found in
Niniveh". Die Fortschritte
der Physik (in German)
(Deutsche Physikalische
Gesellschaft).

6. Jump up^ Kriss, Timothy

C.; Kriss, Vesna Martich
(April 1998). "History of the
Operating Microscope:
From Magnifying Glass to
Microneurosurgery". Neuro
surgery 42 (4): 899
907.doi:10.1097/0000612319980400000116. PMID 9574655.
7. Jump up^ Sines, George;
Sakellarakis, Yannis A.
(1987). "Lenses in
antiquity". American Journal
of Archaeology 91 (2): 191
196. doi:10.2307/505216. J
STOR 505216.
8. Jump up^ Pliny the
Elder, The Natural
History (trans. John
Bostock) Book XXXVII,
Chap. 10.
9. Jump up^ Pliny the
Elder, The Natural
History (trans. John
Bostock) Book XXXVII,
Chap. 16
10. Jump up^ Tilton, Buck
(2005). The Complete Book
of Fire: Building Campfires
for Warmth, Light, Cooking,
and Survival. Menasha
Ridge Press. p. 25. ISBN 089732-633-4.
11. Jump up^ Glick, Thomas
F.; Steven John Livesey,
Faith Wallis
(2005). Medieval science,
technology, and medicine:
an encyclopedia.
Routledge.
p. 167. ISBN 978-0-41596930-7. Retrieved 24
April 2011.
12. Jump up^ Al Van
Helden. '''The Galileo
Project > Science > The
Telescope. Galileo.rice.edu.
Retrieved on 6 June 2012.
13. Jump up^ Henry C. King
(28 September 2003). The
History of the Telescope.
Courier Dover Publications.
p. 27. ISBN 978-0-48643265-6. Retrieved 6
June 2012.

14. Jump up^ Paul S. Agutter;

Denys N. Wheatley (12
December 2008). Thinking
about Life: The History and
Philosophy of Biology and
Other Sciences. Springer.
p. 17. ISBN 978-1-40208865-0. Retrieved 6
June 2012.
15. Jump up^ Vincent Ilardi
(2007). Renaissance Vision
from Spectacles to
Telescopes. American
Philosophical Society.
p. 210. ISBN 978-0-87169259-7. Retrieved 6
June 2012.
16. Jump up^ Microscopes:
Time Line, Nobel
Foundation. Retrieved 3
April 2009
17. Jump up^ Fred Watson (1
October 2007). Stargazer:
The Life and Times of the
Telescope. Allen & Unwin.
p. 55. ISBN 978-1-74175383-7. Retrieved 6
June 2012.
18. Jump up^ This paragraph
is adapted from the 1888
edition of the Encyclopdia
Britannica.
19. Jump up^ Greivenkamp
2004, p. 14
Hecht 1987, 6.1
20. Jump up^ Hecht 1987,
5.2.3.
21. Jump up^ Hecht 2002,
p. 120.
22. Jump up^ Hecht 2002,
p. 168.
23. Jump up^ Proteep Mallik
(2005). "The Axicon".
Retrieved 22
November 2007.
24. ^ Jump up to:a b Grbic, A.;
Eleftheriades, G. V. (2004).
"Overcoming the Diffraction
Limit with a Planar Lefthanded Transmission-line
Lens". Physical Review
Letters 92 (11):
117403.Bibcode:2004PhRv
L..92k7403G. doi:10.1103/P
hysRevLett.92.117403.PMI
D 15089166.

25. Jump up^ Valentine, J. et

al. (2008). "Threedimensional optical
metamaterial with a
negative refractive
index". Nature 455 (7211):
376
9. Bibcode:2008Natur.455..
376V.doi:10.1038/nature07
247. PMID 18690249.
26. Jump up^ Yao, J. et al.
(2008). "Optical Negative
Refraction in Bulk
Metamaterials of
Nanowires".Science 321 (5
891):
930. Bibcode:2008Sci...321
..930Y. doi:10.1126/science
.1157566.PMID 18703734.
27. Jump up^ Nielsen, R. B.;
Thoreson, M. D.; Chen, W.;
Kristensen, A.; Hvam, J. M.;
Shalaev, V. M.; Boltasseva,
A. (2010). "Toward
superlensing with metal
dielectric composites and
multilayers" (Free PDF
download). Applied Physics
B 100:
93.Bibcode:2010ApPhB.10
0...93N. doi:10.1007/s0034
0-010-4065-z.
28. Jump
up^ Aristophanes (424
BC). "The Clouds". Check
date values
in: |date= (help)
29. Jump up^ Schottner, G
(May 2003). "Scratch and
Abrasion Resistant
Coatings on Plastic
LensesState of the Art,
Current Developments and
Perspectives". Journal of
Sol-Gel Science and
Technology. pp. 7179.
Retrieved 28
December 2009.

Bibliography[edit]

Hecht, Eugene
(1987). Optics (2nd ed.).
Addison Wesley. ISBN 0-20111609-X. Chapters 5 & 6.

Hecht, Eugene
(2002). Optics (4th ed.).
Addison Wesley. ISBN 0-32118878-0.

Greivenkamp, John E.
(2004). Field Guide to
Geometrical Optics. SPIE
Field Guides vol. FG01.
SPIE. ISBN 0-8194-5294-7.

External links[edit]
Wikimedia Commons has
media related to Lens.

Thin lens simulation

Applied Photographic Optics:

Lenses and Optical Systems
for Photography, Film, Video,
Electronic and Digital
Imaging at Google Books

The Properties of Optical

Glass at Google Books

Handbook of Ceramics,
Glasses, and Diamonds,
Volume 34 at Google Books

Basic Optics and Optical

Instruments at Google Books

History of Optics (audio

mp3) by Simon Schaffer,
Professor in History and
Philosophy of Science at
the University of Cambridge,
Jim Bennett, Director of the

Museum of the History of

Science at the University of
Oxford and Emily Winterburn,
Curator of Astronomy at
the National Maritime
Museum (recorded by
the BBC).

a chapter from an online

textbook on refraction and
lenses

Thin Spherical
Lenses on Project PHYSNET.

Lens article
at digitalartform.com

Article on Ancient Egyptian

lenses

picture of the Ninive rock

crystal lens

Do Sensors Outresolve
Lenses?; on lens and sensor
resolution interaction.

Fundamental optics

FDTD Animation of
Electromagnetic Propagation
through Convex Lens (on- and
off-axis) Video on YouTube

The Use of Magnifying Lenses

in the Classical World

Simulations[edit]

Learning by Simulations
Concave and Convex Lenses

OpticalRayTracer Open
source lens simulator
(downloadable java)

Video with a simulation of light

while it passes a convex lens
Video on YouTube

Animations demonstrating
lens by QED

LIGHT
Light

POINTS

1.

TO

Light

travels

REMEMBER

in

straight

line.

2. Mirror:A smooth shining surface, which rebounces the light back in same
or

in

different

directions

is

called

mirror.

3. Reflection of light:Scattering back of the light by shining, and smooth

surfaces

is

called

Reflection.

4. Lateral inversion:Phenomenon of changing left to right and right to left

by

the

mirror

while

forming

images

is

called

lateral

inversion.

5. Diffused reflection:The light reflected from non-polished surfaces is not

in a well-defined direction. It spreads out in all directions. This is called
diffused

reflection.

6. The incident ray:A ray of light from a source striking a given surface is
called

the

incident

ray.

7. The point of incidence:The point at which the incident ray strikes the
surface

is

called

the

point

of

incidence.

8. Normal:The perpendicular to the surface at the point of incidence is

called

normal.

9. The angle of incidence:The angle between the normal and the incident
ray

is

called

the

angle

of

incidence.

10. The angle of reflection:The angle between the normal and the reflected
ray

is

called

the

angle

of

reflection.

11.The two laws of reflection are as follows:

1.

The incident ray, the normal at the point of incidence and the reflected ray
are lie on the same plane

2.

The angle of reflection is equal to the angle of incidence.(

i=

r)

12. Plane of incidence:The plane that contains both the incident ray and the
normal

to

the

plane

is

called

the

plane

of

incidence.

13. Kaleidoscope:This is an interesting device based on the principle of

multiple

reflections

in

inclined

mirrors.

It

is

called

Kaleidoscope.

14. Periscope:It is a device which is used to see objects, which are not in
the

direct

line

of

sight.

15. Real image:It is formed if two or more reflected rays actually meet.
16. Virtual image:It is formed if two or more reflected rays appear to meet.
17.Real

image

18.Virtual

can

image

be

can

obtained

not

be

on

obtained

a
on

screen.
a

screen.

19. Lens:Lenses are widely used in spectacles, telescopes and microscopes.

Lenses

are
(a)

of

Convex

lens

two
and

(b)

types:
Concave

lens.

20. Spherical mirror:Mirrors having curved surfaces are known as spherical

mirrors.
21.

Concave

22.

Convex

mirror:Its
mirror:Its

reflecting
reflecting

surface
surface

is
is

in

curving.

bulged

out.

23. Erect image:If the direction of image and object are same is called erect
image.
24. Magnifying glass:Any object viewed through a convex lens is seen as
magnified.
It

is

used

for

observing

small

or

minute

object.

25. Magnified image:If the size of the image is larger than the object it is
called

magnified

image.

26. Prism:It is a transparent object triangular in shape that separates white

light

into

different

colors.

27. Rainbow:A big arch of a band of seven colors is formed in the sky in the
direction opposite to the location of the sun. We identify seven colors in a

rainbow

as

Violet,

Indigo,

Blue,

Green,

Yellow,

Orange

and

Red.

28. Rear view mirror:Convex mirror are widely used as rear view mirrors in
cars and other vehicles. In rear view mirror, a virtual, upright and
diminished

image

is

seen.

29. Side mirror:Rear view mirror is also used as side mirror in vehicles.

Q.1. Fill in the blanks:

1.
2.
3.

An image that cannot be obtained on a screen is called .. .

Image formed by a convex ................. is always virtual and smaller in size.
An image formed by a mirror is always of the same size as that of
the object.

4.
5.

An image which can be obtained on a screen is called a .. image.

An image formed by a concave cannot be obtained on a screen.
Ans.

(a)

virtual
(d)

image

(b)

mirror

real

(c)
(e)

plane
lens.

Q.2. Mark T if the statement is true and F if it is false:

1.
2.
3.

We can obtain an enlarged and erect image by a convex mirror. (T/F)

A concave lens always form a virtual image. (T/F)
We can obtain a real, enlarged and inverted image by a concave mirror.
(T/F)

4.
5.

A real image cannot be obtained on a screen. (T/F)

A concave mirror always form a real image. (T/F)
Ans. (a)

(b)
(d)

(c)
(e)

T
F.

Q.3. Match the item given in Column I with one or more item of Column II.
Column I
Column II

a. A plane mirror
b. A convex mirror
c. A convex lens
d. A concave mirror
e. A concave lens

1. Used as a magnifying glass.

2. Can form image of object spread over a
large area.
3. Used by dentists to see enlarged image of
teeth.
4. The image is always inverted and
magnified.
5. The image is erect and of the same size
as the object.
6. The image is erect and smaller in size
than the object.

Ans.
Column I

Column

a. A plane mirror

5. The image is erect and of the same size

as the object.
2. Can form image of object spread over a
large area.
1. Used as a magnifying glass.
3. Used by dentists to see enlarged image
of teeth.
The image is erect and smaller in size
than the object.

b.
A convex mirror
c. A convex lens
d. A concave mirror
e. A concave lens

Q.4. State the characteristics of the image formed by a plane mirror.

Ans.Image formed by a mirror (flat) has following features:

1.
2.
3.
4.

Image in virtual and of same size.

Reflected image retains the color of the object.
Image is erected but laterally inverted.
Lateral inversion.Right side of the object appears as left side in the image
formed by a plane mirror. For example if we show our right hand, image in
the mirror will show it's left hand.

Fig.15.1.Lateral

inversion

by

plane

mirror

Q.5. Find out the letters of English alphabet or any other language known to
you in which the image formed in a plane mirror appears exactly like the

letter

itself.

Ans.

A,

H,

Discuss

I,

M,

your

O,

T,

U,

findings.

V,

W,

X,

Y.

Q.6. What is a virtual image? Give one situation where a virtual image is
formed.
Ans.A virtual image is formed when two reflected (or refracted) rays do not
meet actually. A virtual image cannot be obtained on a screen. Image
formed

by

Fig.15.2.The

plane

image

mirror

formed

by

is

always

plane

mirror

virtual

is

always

image.

virtual

Q.7. State two differences between a convex and a concave lens.

Ans.
Convex lens

Concave lens

1. Feel thicker in the middle than at the 1. Feel thinner in the middle than at the
edges.
edges.
2. Converges the light falling on it.
2. Diverges the light falling on it.
3. Can form real and inverted image also 3. Always forms erect, virtual and smaller
form virtual and erect image.
image.
Q.8.

Give

Ans.Use

one

use

each
of

of

concave

and

concave

convex

mirror.
mirror:

Doctors use concave mirrors for examining eyes, ears, nose, throat

and

teeth.

Fig.15.3.A
Use

dentist
of

examining
convex

patient
mirror:

Convex mirror is used as a side view mirror in motor vehicles.

Fig.15.4.Convex
Q.9.
Ans.

Which
A

mirror
type

concave

of

as
mirror

mirror

side
can

can

form
form

view
a
a

real
real

mirror
image?
image.

Fig.15.5.
Q.10.

concave

Which

type

mirror
of

Ans.A
Choose

lens

forms

forms

real
always

image
a

of

virtual

concave
the

correct

option

the

sun

image?
lens

in

questions

11-13:

Q.11. A virtual image larger than the object can be produced bya

1.
2.

concave lens

ii. concave mirror

convex mirror
Ans. ii.

iv. plane mirror

Concave

mirror

Q.12. David is observing his image in a plane mirror. The distance between
the mirror and his image is 4 m. If he moves I m towards the mirror, then
the distance between David and his image will be:

1.
2.

3m

ii. 5 m

6m

iv. 8 m

Ans.iii.

Q.13. The rear view mirror of a car is a plane mirror. A driver is reversing
his car at a speed of 2 m/s. The driver sees in his rear view mirror the
image of a truck parked behind his car. The speed at which the image of the
truck appears to approach the driver will be:

1.
2.

1 m/s

ii. 2 m/s

4 m/s
Ans.iii.

iv. 8 m/s
4

m/s

ADDITIONAL
Q.1.

IMPORTANT

What

is

rectilinear

QUESTIONS

propagation

of

light?

Ans.Light travels in a straight line, it is called rectilinear propagation of

light.
Q.2.

What

is

regular

reflection?

Ans.When light falls on polished surfaces they change the direction of light
in

well

define

manner.

Q.3.

This

is

called

regular

reflection.

Define

Mirror.

Ans.A smooth shining surface, which rebounces the light back in same or in
different

direction

is

called

mirror.

Q.4. How many reflected ray can there be for a given single incident ray
falling

on

Ans.For

one

incident

Q.5.

ray,

plane

there

Define

is

only

mirror?

one

reflected

lateral

ray.

inversion.

Ans.Phenomenon of changing left to right and right to left by the mirror

while

forming

Q.6.

State

images

is

two

called

lateral

of

concave

uses

inversion.
mirror.

Ans. i. Concave mirrors are used in head lights of the cars, buses, etc.
ii.
Q.7.

What

Used

type

of

by

image

dentists

can

be

obtained

and
by

doctors.

convex

mirror?

Ans.A convex mirror always produces the virtual, erect and smaller images.
Q.8.

Why

should

we

not

look

at

the

sun

through

convex

lens?

Ans.As the light after passing through a convex lens becomes concentrated
at
Q.9.

point
Why

and

can

we

need

do

damage
a

our

shiny

eyes

surface

for

permanently.
reflection?

Ans.The extent of reflection depends upon the shine and smoothness of the
surface. More is the shine and smoothness of the surface, more will be the
reflection. That is why, mirrors reflect most of the light falling on it. Hence
for
Q.10.

reflection,

shiny
What

surfaces
is

are

required.
reflection?

Ans.When a ray of light falls on a smooth and shiny surface, the whole of
light is sent back in the same direction. It is calledreflection (Fig. 15.6).
Mirrors do not allow even a small amount of light to pass through them.

Mirrors

show

regular

and

Fig.15.6.Reflection

complete

of

reflection.

light

Q.11. Can you guess how light would be reflected from a mirror if the angle
of

incidence

is

90

degree.

Ans.Incident ray is striking at an angle of 90 degree (perpendicular to the

mirror). According to the laws of reflection, the angle of reflection will be
90 degree. The ray of light will be reflected back along the same line.
Q.12. While standing before a plane mirror, if you move your right hand,
which

hand

does

your

image

move?

Ans.If we move our right hand, our image will move left hand. It is because
in a plane mirror our "left appears right" and "right appears left". This is
called lateral inversion. Hence we can say that the plane mirror forms
laterally

inverted

images.

Fig.15.7.Left

hand

appears

on

the

right

side

in

the

image

Q.13. Explain the incident ray, point of incidence and normal in brief.
Ans.A ray of light from a source when strikes to a given surface is called the
incident

ray.

The point at which the incident ray strikes the surface is called the
point of incidence. Whereas, the perpendicular to the surface at the point of
incidence
Q.14.

Differentiate

is
between

called
real

image

and

normal.
the

Ans.Difference between Real image and Virtual image:

virtual

image.

Real Image

Virtual Image

1. It cannot be obtained on a screen.

2. It is always erect.
3. It is formed where the reflected rays
appear to meet virtually.
4. It is always behind the mirror.

1. It can be obtained on a screen.

2. It is inverted.
3. It is formed at the point where the
reflected rays actually meet.
4. It is on the same side of the mirror where
the object is present.
1. Size of the image varies according to the
5. Size of the image depends upon the
mirror used, i.e. image is of same size in
distance of the object from the mirror.
plane mirror, larger in concave mirror and
smaller in convex mirror
Q.15.

What

are

spherical

mirrors?

Give

their

types.

Ans.Mirrors having curved surfaces are known as spherical mirrors. Their

name is so, because they are considered as a part of a hollow sphere.
Mirrors

are
concave
(i) Concave
(ii) Convex

mainly
mirrors
mirror. Its
mirror. Its

of
and
reflecting
reflecting

two

types:

convex

mirrors:

surface
surface

is
is

in

curving.

bulged

out.

Fig.15.8.Convex

and

Concave

Mirrors

Q.16. Here are given capital letters of English Alphabet encircle the letters
which

wi

ll

not

show

lateral

inversion

on

facing

plane

mirror.

Ans.

Q.17. Why a convex mirror is used as a rear view mirror in cars and other
vehicles?
Ans.Convex mirror has a wider field of view than a plane or a concave
mirror. So it can well be used to see what is behind us rather well. Hence
drivers

use

convex

mirror

to

see

the

traffic

following

him.

Q.18. Draw a ray diagram to explain the formation of a virtual image of a

point
Ans.See

source

of

Fig.

light
15.2

in

plane

on

page

mirror.
210.

Q.19. In Fig. 15.9, complete the image of the coin after reflection at the
surfaces

of

both

the

mirrors.

Ans.

Fig.

Q.20.
in

15.9

Explain

why

the

word

'AMBULANCE'
in

is

written

as

figure?

Fig.15.10.An

ambulance

Ans. When the driver of a vehicle ahead of an ambulance looks in his/her

rear view mirror, she/he can read `AMBULANCE' written on it and give way
to it. It is the duty of every one of us to allow ambulance to pass without
blocking
Q.21.

its
Explain

Ans.Lenses

the

two

are

of

way.
types

of
two

lenses.
types:

1. Convex lens.Those lenses which feel thicker in the middle than at

the

edges

are

convex

lenses.

2. Concave lens.Those lenses which feel thinner in the middle than at

the

edges

are

concave

lenses.

(a)
Fig.15.11.(a)
Q.

22.

convex

What

are

lens

(b)

and

(b)

converging

and

concave

diverging

lens
lens?

Ans.A convex lens converges (bends inwards) the light falling on it.
Therefore, it is called a converging lens. On the other hand, a concave lens
diverges (bends outward) the light and is called a diverging lens.
Q.23.

How

many

colors

are

found

in

rainbow?

Ans.There are seven colors in a rainbow, though it may not be easy to

distinguish all of them. They are as VIBGYOR, and the colors are red,
orange,

yellow,

green,

blue,

indigo

and

violet.

Q.24. Give an activity to show that seven colors can be mixed to get white
light.
Ans.Take a circular cardboard disc of about 10 cm diameter. Divide this disc
into seven segments. Paint each segment with the seven rainbow colors, as
shown in the following figure. Make a small hole at the centre of the disc.
Fix

the

disc

loosely

on

the

tip

of

refill

(a)

(b)

Fig.15.12.(a) A disc with seven colors (b) It appears white on rotating

of a ball pen. Rotate the disc in the day light when the disc will rotate fast,
the colors get mixed together and the disc appears to be whitish. Such a
disc

is

Q.25.

popularily
State

Ans.Laws

known
the

laws

of

as

Newton's
of

disc.
reflection.

reflection

are:

(i) The incident ray, the reflected ray and the normal all lie in the
same

plane

at

the

point

of

incidence.

(Fig.

15.13).

Fig.15.13.Reflection

of

light

(ii) The angle of incidence is always equal to the angle of reflection.

i

Q.26. Observe the figure (15.14) and fill in the blanks:

1.
2.

Size of your friend is . to the size of image.

Distance between mirror and image is . to the distance between
your friend and mirror.

3.
4.

Image of your friend is . .

Image of your friend is . inverted.

Fig.

15.14

Ans. (a)

equal
(c)

(b)

erect

equal

(d)

laterally.

Q.27. Write the properties of the images formed by a plane, concave and
convex

mirror

and

also

concave

and

convex

lenses.

Ans. (i) Plane Mirror. The image formed by a plane mirror is always erect.
It is virtual and is of the same size as the object. The image is at the same
distance

behind

the

mirror

as

the

object

is

in

front

of

it.

In an image formed by a mirror, the left side of the object is seen on the
right side in the image, and right side of the object appears to be on the left
side

in

the

image.

(ii) Concave Mirror. A concave mirror can form a real and inverted
image. When the object is placed very close to the mirror, the image formed
is

virtual,

erect

and

magnified.

(iii) Convex Mirror. Image formed by a convex mirror is erect, virtual

and

smaller

in

size

than

the

object.

(iv) Convex Lens. A convex lens can form real and inverted image.
When the object is placed very close to the lens, the image formed is
virtual, erect and magnified. When used to see objects magnified, the
convex

lens

is

called

magnifying

glass.

(v) Concave Lens. A concave lens always forms erect, virtual and
smaller

image

than

the

object.

Q.28. Explain the uses of concave and convex mirror and also concave and
convex

lenses.

Ans.
(a) Concave

Mirror

(i) Doctors use concave mirror for examining eyes, ears, nose and
throat.
(ii) Concave mirrors are also used by dentists to see an enlarged image
of

the

teeth.

(iii) The reflectors of torches, headlights of cars and scooters are concave
in

shape.

Fig.15.15.Reflector

of

torch

(b) Convex

Mirror

(i) Convex mirror is used as a side view mirror. These help the drivers
to

see

the

traffic

behind

them.

(c) Convex

Lens

(i) It is used as a magnifying glass, microscopes, telescopes etc.

(ii)

Used

in

spectacles

to

correct

far

sightedness.

(d) Concave
(i)

Can

OBJECTIVE

Lens
be

used

to

correct

short

sightedness

in

TYPE

spectacles.

QUESTIONS

Q.1. Match the items given in Column I with those given in Column II:
Column I
Column II

1.
1. Light travels in
2. Angle between normal and the incident 2.
ray
3. Device which is used to see objects
1.
4. Rear view mirror
2.
5. Reflecting surface in curving
3.
6. Transparent object triangular as shape 4.

Angle of incidence
Periscope
side mirror
Prism
Concave mirror
straight line

Q.2. Fill in the blank space in the following statements.

1.
2.
3.
4.

Uneven surfaces show reflection.

Incident ray, the reflected ray and lie on the same .. .
Laws of . is applicable in playing back shots in the carroms.
Changing of right side to left is called .. .
Q.3. Choose the true and false statements from the following:

1.
2.

Concave mirror is converging in nature.

Convex mirror is diverging in nature.

3.
4.
5.
6.
7.

Plane mirror forms virtual image.

Concave mirror has a virtual focus.
Spherical mirrors do not obey laws of reflection.
During lateral inversion, the image becomes inverted.
Angle between incident ray and reflected ray is double that of the angle of
incidence.
Q. 4. Choose the correct option in the following:

1.

The path of the light is

(a)

always

straight

line

(c) a zig-zag line

1.

(b)

Plane

mirror

(b)

Convex

mirror

(d) All of these

Image formed by a plane mirror is always

(a)

Virtual

and

erect

(b)

(c) Virtual and inverted

Real

and

erect

(d) Real and inverted

An image which can be obtained on a screen is called

(a)

Erect

(b)

(c) Real

1.

line

(d) depends on the medium

(c) Concave mirror

1.

curved

Which one shows lateral inversion?

(a)

1.

Inverted

(d) Virtual

Image formed by a convex mirror is

(a) Erect, virtual and smaller

(b) Inverted, virtual and

smaller
(c) Erect, real and smaller

(d) Erect, virtual and

magnified

1.

Which is used as side view mirror?

(a)

Plane

mirror

(b)

(c) Convex mirror

1.

Concave

mirror

(d) None of these

A concave lens always forms

(a)

Erect,

(b)

Erect,

(c)

virtual
virtual

Erect,

real

and

smaller

image

and

magnified

image

and

smaller

image

(b)

colors

(b) Inverted, virtual, and smaller image

1.

White light is composed of

(a)

Seven

colors

(c) Five colors

1.

Convex

(c) Plane

(b)

Concave

(d) Both (a) and (b)

The ratio of the size of the image to the size of the object is called
(a)

magnification

(c) transformation ratio

1.

(d) Eight colors

The mirror has a wide field of view must be

(a)

1.

Three

The laws of reflection of light are valid for

(b)
(d) focal length

power

(a)

Plane

mirrors

only

(b)

(c) Convex mirrors only

1.

only

(d) All reflecting surfaces

cm

(b)

(c) dioptre

cm-1

(d) m

The splitting of white light into its seven constituent colors is called
(a)

refraction

(b)

(c) deviation

1.

mirrors

The power of a lens is measured in

(a)

1.

Concave

dispersion

(d) reflection

A convex lens
(a)

has

(b)

has

(c)

is

always

two

always

thinner

in

two

the

middle

convex

surfaces

spherical

surfaces

than

at

the

edges

(d) is thicker in the middle than at the edges.

1.

During the reflection of light angle of reflection is

(a) equal to incidence angle

(b) smaller than incidence angle

(c) bigger than incidence angle

ANSWERS

TO

(d) equal to incident ray

OBJECTIVE

TYPE

QUESTION

Q.1. Match the items given in Column I with those given in Column II:
Column I
Column II
Straight line
Angle of incidence

1.
1. Light travels in
2. Angle between normal and the incident 2.
ray
3. Device which is used to see objects
1.
4. Rear view mirror
2.
5. Reflecting surface in curving
3.
6. Transparent object triangular as shape 4.

Periscope
side mirror
Concave mirror
Prism

Q.2. Fill in the blanks:

1.
2.

irregular

ii. Normal, plane

Reflection

iv. Lateral inversion.

Q.3. True/False

1.
2.

True

ii. True

False

vii. True.

Q.4.

iii. True

Choose

the

iv. False

correct

v. False

option:

i.

(a)

ii. (a)

iii. (a)

iv. (c)

v. (a)

vi.

(c)

vii. (a)

viii. (a)

ix. (b)

x. (a)

xi. (d)

xii. (c)

xiii. (b)

xiv. (d)

xv. (a).

Now consider parallel rays travelling towards the convex lens. After emerging they get converged
at the focus. Won't this lead to interference between light rays? Practically it should but I would
like to know why this does not happen.

Look at the focus in the above image. The rays get converged and shouldn't that lead to
interference. Similar phenomenon should occur with a concave mirror at its focus.

2. Answer
Yes you get interference - but a well constructed lens has introduced just enough phase shift in
the wave front at every point that the interference is constructive. Because the lens is finite in
size there will be some interference pattern observed at the focus - something known as "Airy's
rings"
In fact - the way a lens works is precisely by creating a phase shift between light rays traveling
along different paths, and after the phase shift the ray changes direction because that is the
direction in which the interference is constructive.
The following diagram tries to explain this - I am using the conventional Huyghens construction to
show that every point on a wave front can be considered a source of a wavefront that travels in
all directions - with the final wave front continuing in the direction where all of these interfere
constructively. The blue wedge is a prism - a very small piece of a lens. Inside the prism, the
wavelength of the light is shorter (because of the refractive index of the lens), so the wave fronts
(little circles) that represent a wavelength are closer together. You can think of a spherical lens
as being made up of many prisms - each acting in the same manner (although the phase
difference will change depending on the thickness of the lens). Note that in my drawing, the
upper ray has exactly one wavelength inside the prism and two outside, while the lower ray has
two wavelengths inside and only one outside. In both cases, the line connecting the wave fronts
corresponds to exactly three wavelengths after the entrance plane of the prism. There are of
course infinitely many rays between these two - if there were not, you would have something akin
to a Young's Slits experiment setup, and would see interference patterns (several directions in
which constructive interference can occur).

Incidentally - the picture you show in your question is very misleading. The rays don't "magically
change direction" at the center of the lens - instead, they are refracted both at the entrance face
and exit face of the lens. The following shows what I mean (in reality the angles are not quite as
drawn - there is a thing called "spherical aberration" that is ignored here - but I hope you get the
idea. I drew just the top few rays inside the lens in red; obviously the same thing is true for the
bottom half):

UPDATE to explain how this works for a concave mirror:

If you take an arbitrary ray traveling parallel to the horizontal axis in this image:

You can compute its length as

length=Dy+h2+(fy)2
Now if we want to set the length to a constant value regardless of h, we can say

y+lengthDy+C(y+C)2y2+2Cy+C22(C+f)y+C2+f2y=h2+(fy)2=h2+(f
y)2=h2+(fy)2=h2+f22fy+y2=h2=h22(C+f)C2f2
Which describes y as a parabolic function of h. In other words - in a parabolic (convex) mirror,
the path length for all rays to the focal point is the same. So once again, there will
be constructive interference at the focal point.

Its from
http://physics.stackexchange.com/

SCIENCE form 4 all topics (not a ringkas)

http://allspmnotes.blogspot.in/2012/12/science-form-4-alltopics-nota-ringkas.html

Method of Scientific Investigation

Scientific investigation method

A scientific method is a series of systematic steps which a scientist practises

when conducting an investigation.

The steps of a scientific investigation are as follows:

Identifying the problem

Identifying the variables

Making a hypothesis

Planning the investigation

Carrying out the experiment

Collecting and recording data

Analysing and interpreting data

Making a conclusion

Writing a report

Making a hypothesis

Making hypothesis is the process of forming a general statement about the

relationship between the variable that is manipulated and the responding variable.

a hypothesis is also a statement of a scientific concept or principle made

as a solution to the problem.

Planning investigation
then planning of an investigation often involves the following:

determining the apparatus and materials

determining the procedures

determining the observation to be made and measurements

determining the correct and safe techniques

determining the set of apparatus of control experiments

identifying the variables

Carrying out the investigation

the apparatus, materials and procedures must be handled correctly and

safely when carrying out investigations.

The variebles must be determined accurately

The observations must be made accurately and objectively.

Collecting and recording data
Data collected by measurement in digits are called quantitative data.

Data collected by more observation and do not involve accurate

measurements are known as qualitative data.An assessment of the characteristics of an
observation is also part of the qualitative data.

The data collected can be recorded in the form of:

Table

Graph

Pie chart

Diagram

Histogram

Bar chart

Analysing and interpreting data

Analysing and interpreting data

Making a conclusion

Writing a report

A scientist must have scientific attitudes and noble values such asa being curious in
stating a problem statement, being honest and accurate in recordibg and validating data,
being responsible for the safety of oneself, others and the environment when conducting
an experiment, being critical and analytical thinking when proposing a hypothesis and
being objective when making a conclusion.
The scientific attitudes and noble values ned to be practised when conducting a scientific
investigation to ensure a better understanding and interpretation of a scientific
investigation.A scientist must have scientific attitudes and noble values such asa being
curious in stating a problem statement, being honest and accurate in recordibg and
validating data, being responsible for the safety of oneself, others and the environment
when conducting an experiment, being critical and analytical thinking when proposing a
hypothesis and being objective when making a conclusion.

Body Coordination

Body coordination is a life process that involves harmonious fuctioning of

interrelated organs and parts in the body to produce a coordinated response

Two body systems that control and regulate coordination are:

The nervous system

The endocrine system

A stimulus is a detectable change in the internal or external environment.It

evokes a response.

Response is an action or movement as a result of a stimulus.

The nervous system handles fast and short responses which involve the
transmission of electrical impulses

The Human Nervous System

The human nervous system can be divided into:

cord.

The central nervous system (CNS) which consists of the brain and spinal

The peripheral nervous system (PNS) which consists of cranial nerves and
spinal nerves.

nervous system

A neurone is a nerve cell which is the basic functional unit of the nervous system

The central nernous system consists of the brain and spinal cord

The peripheral nervous system consists of cranial nerves and spinal nerves.

The brain is an organ that is the centre of control and coordination in the nervous
system

The spinal cord controls reflex action

The peripheral nervous system is the network of nerves which connect the
central nervous system with other parts of the body.

Cranial nerves composed of 12 pairs of nerves which orogonate from the brain
and are connected to sense organs in the head and neck, and also to effectors such as
the muscles or glands in the body cavity.

Spinal nerves are composed of 31 pairs of nerves which originate from spinal cord
and are connected to sense organs and effectors in the whole body including hands and
legs.
Neurones

A neurone is a nerve cell.It is the basic functional unit of the nervous system

The cell body contains many projections

cell body

Dendrons - projections from the cytoplasm that point outward from the

Dendrites - smaller projections that branch from dendrons or axons

Axons - another type of projection


Dendrans and dendrites receive messages from other cells and trnasmit the
message to the cell body

Axons conduct messages away from the cell body

Some axons in certain neurones are covered by myelin sheath.The sheath breaks
up at intervals along the dendrons or axons.This enables impulses to jump from one
node to another, shortening the time impulses travel along the surface of the axons or
dendrons.

Besides this, the meylin sheath is important because:

It acts as an electrical insulator

it is a source of food for axons and dendrons

it also protects axons and dendrons from physical injury.

Types of neurones

There are three types of neurones

sensory neurones

motor neurones

interneurones (relay neurones)

Nervous Coordination
Receptors and effectors

Any changes which occur inside and outside of the human body are known
as stimuli

Receptors are sensory cells that detect and receive stimuli and turn them into
electrical impulses

Effectors are muscles or glands which produce responses due to stimuli.They

respond to stimuli by:

contraction

gland secretion

Figure above shows how the human nervous system works.

Nerve Impulses

are messages conveyed along the nerve in the form of weak electrical pulse

An impulse moves only in one direction as shown in figure.

Impulses move in one direction

Reflex action

A reflex action is a rapid,automatic unlearned response to a stimulus.This action

is involuntary and cannot be controlled by the brain

A reflex action does not require conscious thought or decision by the brain

The components involved in a reflex action are:

The receptors

The effectors

Sensory neurones

Relay neurones

Motor neurones

Reflex arc

A reflex arc is a sequence of pathways taken by the impulses from receptors to

effectors in a reflex action

The pathway of impulses in a reflex arc are as follow:

Pathway of impulses
Proprioceptors

Proprioceptors are sense organs which are connected to sensory

neurones.Humans are able to determine the position of their legs, arms, head and other
parts, along with the orientation of the body as a whole with this type of receptors

Proprioceptors are found in all skeletal muscles, tendons, ligaments and

joints.They provide information to the brain regarding adjustment in posture and

movement.Therefore, adjusments may be made to maintain body posture or to carry out

a particular body movement.
Kinaesthesis

Kinaesthesis is the ability to sense the position, location, orientation and

movement of the body and its part without looking at ourselves.

The Human Brain and Its Complexity

Structure of the brain

The human brain is the most complex organs in the human body.It is also the
most complex brain among all mammals.

The brain is the centre that contols and coordinates our responses as shown in
above

The human brain has an external layer which is white in colour.

The grey-coloured layer is made up of closely packed neurone cell bodies

which form the grey matter of the brain

The white-coloured layer is made up of nerve fibres which form the white
matter of the brain

The human brain can be divided into three main parts:

Cerebrum

Cerebellum

Medulla oblongata

Human Brain

Cerebrum

The cerebrum is the largest part of the human brain.It makes up about 80%
of the mass of the human brain.

The cerebrum can be divided into two hemispheres.

Right hemisphere

Left hemisphere

Nerve impulses from the left side of the body will be received by the right
hemisphere whereas nerve impulses from the right side of the body will be received by
the left hemisphere

Functions of the cerebrum are:

It controls voluntary and highest intellectual functions such as thinking,

learning and problem solving.

It regulates emotion and memory through the limbic system.

It controls human behavior.

Receives and interpets impulses from sensory organs

Cerebellum

The cerebellum is located below and behind the cerebrum

The function of the cerebellum are:

Controlling and maintaining posture and balance of the body

Controlling and coordinating muscular activities

Medulla oblongata

Medulla oblongata is the lower most portion of the brain and is continuos with the
spinal cord.It is the smallest component of the brain

Medulla oblongata relays nerve signals between the brain and spinal cord.

Medulla oblongata controlsn automatic functions

Voluntary and involuntary actions

Human respond to a stimulus through voluntary actions and involuntary actions

Effect of injuries to specific parts of the human brain

Hormonal Coordination in the Body

Hormones

are chemicals secreted by endocrine glands.Hormone produced are secreted

directly into the bloodstream and carried by blood to tissues or organs without the need
of any ducts.They are usually secreted is small amounts

The hormones have a specific effect only on the tissue or an organ designed to
receive its message .This tissue or organ is called target tissueor target organ.This is
because only this specifictissue or organ will respond to them.

Important roles of hormones are:

causing physical and physiological changes.

Controlling the rate of body process

Influencing growth

The endocrine system

Chemical coordination involves the endocrine glands and their secretion

Endocrine system consists of endocrine glands and their secretion

Endocrine glands do not have ducts.Thus it is also called ductless glands.

Pituitary gland

is located at the base of the brain just beneath the hypothalamus

The anterior lobe regulates the activity of several glands.Among these are
thyroid,adrenals and reproductive glands.

It produces hormones such as:

Corticotropin - stimulates the adrenal gland to produce certain hormones.

Growth hormone - stimulates the growth of bones, muscles and other

body organs.Plays a role in the handling of nutriens and minerals in the human body.

Prolactin - promotes the development of glandular tissue in the female

breast during pregnancy.Stimulates milk production in women who are breastfeeding.

Thyrotropin - stimulates the thyroid gland to produce thyroxine hormones.

The posterior lobe of the pituitary gland releases antidiuretic hormones

(ADH).This hormone acts on the kidneys to regulate water content and write
output.Oxytocin is also released by the posterior lobe.Oxytocin triggers the contraction
of the uterus during labour.It also stimulates the ejection of milk from the lactating
breast.

Thyroid gland

The thyroid gland is located in the front of the lower neck.

Hormone thyroxine produced by the thyroid gland has the following functions:

Controls metabolic rate

Controls skeletal growth

Controls mental development

PancreasPancreas produces two important hormones

Insulin - insulin decreases blood glucose concentration by stimulating the

conversion of glucose into glycogen in the liver.

Glucagon - glucagon increases blood glucose concentration by stimulating the

conversion of glycogen to glucose in the liver.

Insulin and glucagon work together to maintain a steady level of

glucose in the blood.This is important to produce and maintain
stores of energy.

Adrenal gland

is located on top of each kidney.

The adrenal glands have two parts; the internal part is the adrenal cortex and the
inner part is name adrenal medulla

Adrenal cortex produces hormones called corticosteroids.Corticosteroids influence

or regulate salt and water balance in the body, the body's response to
stress,metanolism,the immune system and sexual development abd function.

Adrenal medulla produces catecholamines such as adrenaline.

Ovary

are located in the female reproductive system

Ovaries produce two groups of female sex hormones.

Oestrogen

Progesterone

Oestrogen is involved in the development of secondary sexual characteristics in

female such as:

The development of breasts

The accumulation of body fat aroundthe hips and thighs.

Maturation of reproductive organs such as the uterus and vagina.

Progesterone prepare the uterus lining for pregnancy

Testis

is located in the male reproductives system

testis secretes hormones called androgens

The most important androgen hormone is testosterone.

Coordination between the Nervous System and the Endocrine System

The two types of coordination work together at certain times.The human digestive
system is a good example.When food is served,the mouth will start to salivate and this
response is coordinated by the nervous system.Gastrin a type of hormone is secreted
when the half-digested food goes into the stomach.Gastrin causes the stomach wall to
produce hydrochloric acid and other emzymes to carry out further digestion.

Effects of Drug Abuse on Body Coordination and Health

Definition of drugs

Drugs are chemical or biological substances which affect the function of the
nerveous system,especially the brain,causing changes in behaviour and personality.They
change the way the body works.

Types of drugs

The four main types of drugs are:

Stimulants

Depressants

Hallucinogens

Opiates

Drug abuse

is the misuse or overuse of any medication or drug

Reasons of drug abuse include:

use drugs because they are thrill-seekers

use drugs out of curiosity or because their friends do it

use drugs in order to cope with unpleasant emotions and difficulties in life

Effects of Excessive Consumption of Alcohol on Body Coordination and

Health

Ethanol commonly known as alcohol is found in most alcoholic drinks.It is a

strong psychoactive substance with a depressing effect.

Ethanol is produced in a process call fermentation.Fermantation is a process that

uses yeast or bacteria to change the glucose in the food into ethanol.

Yeast + glucose > ethanol + carbon

dioxide + energy
Effect of excessive consumption of alcohol on body
coordination

Alcohol is a depressant.This means it slows down the function of the central

nervous system.

When alcohol is consumed, it is absorbed into the bloodstream rapidly and travels
around the body to the brain.

Effect of excessive consumption

Alcohol is broken down into acetaldehyde by the enzyme, alcohol
dehydrogenase in the liver.The acetaldehyde is then broken down into acetic
acid by the enzyme acetaldehyde dehydrogenase.Next acetic acid is converted
into fats or carbon dioxide and water.Fatty acids build up as plaques in the
capillaries around liver cells.Liver cells begin to die.This leads to the liver disease
called cirrhosis.As we know the liver is damaged,certain toxins build up.This
leads to sympthoms of jaundice.

Foetal alcohol syndrome is another one consequence of excessive

consumption of alcohol use.

Foetal alcohol syndrome:

a foetus is fed through the placenta inside the mother.Since alcohol

passes easily through the placenta,the developing foetus gets a dose of alcohol
when the mother drinks alcohol.

UNDERSTANDING PROCESS CELL DIVISION

We know that our bodies built from millions Tues In this cell there is a center of activity known as the
nucleus. There are chromosomes in the nucleus that contains genes. Gen, this is the nature of our control. For
example it controls whether our hair curly or not.

Genes are genes that carry material genetic information.

Gene located in chromosome. If viewed through a microscope, chromosomes are structures in the nucleus
stranded Tues

Humans can grow and reproduce because the cell can divide. Two types of cell division is Mitosis and
Meiosis. Mitosis occurs in the entire body and cause each day we grow. The number of chromosomes that results
remain the same as the original genes [sometimes called the 'master gene']. Meiosis also occurs in the testes or
ovaries to produce sperm or ovum. Number of chromosomes in sperm is half the number of cells holding. Human
chromosome 23 has a half from Stem cell chromosomes (46 chromosomes).

There are many differences between Mitosis and Meiosis

SUCCESSION CHARACTERISTICS

Scientists already know that organisms typically have a pair of chromosomes that carry a pair of genes.
Genes may be different or the same. There are two types of genes and gene dominant gene resesif.

Gene dominant gene is a strong and able to highlight features in the organism. Resesif genes are genes that
weak. It can not be met if the features highlight a dominant gene. Gen.

resesif can only highlight the features if he came to the same pair resesif genes.Dominant gene will result in
a dominant nature. Based on several examples of genetic research scientist dominant nature of human nature is such
as wavy hair and the ability to roll tongue. [the ability to roll his tongue].Resesif properties are properties such as hair
is straight and can not roll tongue. How these properties can be handed down from parents to children?.

Human cell has 46 chromosomes (23 pairs of genes). Sperm and ovum that results from Meiosis only contain
only 23 chromosomes. If the sperm carrying genes that control the nature of curly hair (dominant) ovum mix that
brings nature hair straight, then the resulting child will be curly-haired.

Chromosome structure in gamet:

Chromosomes X and Y chromosome known as the "sex chromosome". This chromosome determines gender
of a person.

SEX DETERMINATION AND THE OCCURRENCE OF TWINS

Sex Choromosomes

22 pairs of choromosomes are known as autosomes.The largest of the autosomes is referred to as

chromosome 1,the next largest as chromosomes 2, and so on, down to the smallest autosomes , which are
chromosomes 21 and 22.The 23rd pair of the last two chromosomes are known as sex chromosomes.Sex
choromosomes are responsible for determining gender.There are two types of sex chromosomes:

X chromosomes
Y chromosomes

Sex determination

Male chromosomes

and Y

The human male will have a genetic make up of pairs of autosomes and two types of sex choromosomes X

Female chromosomes

The human female will have a genetic make up of 22 pairs of autosomes and only one type of sex
chromosomes, XX.
Formation of twins

Under normal circumstances, one ovum is released in one menstrual cycle.During fertilision, one ovum will
be fertilised by one sperm to produce one zygote.Therefore, a single baby will be born,

There are two types of twins:

Non- identical twins
Identical twins

Non-identical twins

More than one ovum is produced in expectional cases.Each ovum will be fertilised by different sperms,
developing into zygotes

Formation of non-identical twins

Identical twins

Sometimes, one ovum is fertilised and then divides immediately into two or more zygotes through division,
resulting in twins.

The zygotes then develop into two embryos.Both embryos share one placenta with separate amniotic
sacs.Babies born in this wy are known as identical twins

Formation of non-idential twins

Formation of idential twins

Siamese twin

In certain cases identical twins are born joined at identical sides.This happens because the zygote failed to
divide completely into two separate embryos.
Mutation

definition of mutation - Human traits can be altered by sudden changes in chromosomes or genes.This is
known as mutation

Mutation can happen in somatic or reproductive cells.The difference is mutation in somatic cells cannot be
inherited by the next generation.

Mutation that happens in either the sperm or ovum may be inherited by the next generation although the
parents do not possess these traits.
Type of mutationThere are two types of mutation:

Chromosome mutation occurs when changes take place in the structure of the chromosome or to the number
of choromosomes.

Gene mutation occurs when there is a change in the chemocal structure of a gene.

Examples of mutation:

Klinefelter's syndrome

Karyotype of an individual with Klinefelter's syndrome

turner's syndrome

down's syndrome

Karyotype of an individual with turner's syndrome

Karyotype of an individual with down's syndrome

Non-disjunction in meiosis I and meiosis II

Albinism

is a condition where there is an absence of the melanin pigment in the skin, hair and iris in human.This
condition is caused by a recessive gene taht affects the production of melanin.
Colour blindness

Colour blindness is a condition that arises from the mutation of the gene for colour vision.This causes a
person to be unable to differentiate between the colour green and red.The mutation produces a recessive gene.

Haemophilia

is a disease where the blood fails to clot.As a result severe sufferers can bleed to
death without treatment .Even if with treatment, internal bleeding in the joints is the
most problematic complication since it leads to paintful arthritis.This disease is an
example of a sex-linked disease which is caused by a recessive allele on the X
chromosome.

Haemophoilia man married to a normal female

A normal man married to a carrier female

Causes of mutation

Some mutations are induced and others are spontaneous.

Mutation is more likely to occur as a result of exposure to mutagens.Mutagens

are factors that cause mutation.Among the known mutgens are nuclear
radiations,harmful rays and certain chemicals called carcinogens.

Nuclear radiations will penetrate the nucleus of the cell and change the structure
of the genes and chromosomes in the nucleus.

Harmful rays are also mutagens


Chemical - There are many hundreds of known chemical mutagens such as
benzene,fungicides,herbicides,insecticides,pesticides and dioxins

Advantages and disadvantages of mutation

Advantages of mutation

mutation is one of the sources for the creation of new species.

mutation may lead to variation .Variation is the difference in traits between

individual of the same species.

If no mutation occurs,evolution could not have taken place.In other words

mutation is a precursor of the evolution process.
Disadvantages of mutation

The disadvantages of mutation to humans can be grouped into:

Physical deformities - is a type of physical deformity as a result of

mutation.Suffers have extra fingers or toes on both hands or feet.

Genetic diseases - Gene mutation many cause genetic diseases such as

colour-blindness and albanism.

Effects of Genetic Research on Human Life

Distributions of gebe

Amniocentesis is a test perfomed between 16 and 18 weeks of a woman's

pregnancy.The drawn fluid is then analysed.This fluid can be tested not only to check for
genetic problems but also to determine the sex of an unborn baby.

In gene therapy, a detective gene in unhealthy cells will be replaced with a new
and healthy gene by using a type of virus called retrovirus.

Selective breeding

Selective breeding is a technique which involves the choosing and breeding of

animals or plants with desirable traits to ensure that these traits are inherited by the
next generation.

Oil palm is the highest yielding oil crop.Selective breeding between the oil palm
species Pisifera and Dura to produce a new species called Tenera is a good example.This
is shown in Figure 3.32.The oil palm is continually being improved through breeding.

Table shows comparison between Pisifera, Dura and Tenera

Advantages and disadvantages of genetic research

Advantages

Vaccines and better medicines are produced in medicine and healthcare through
genetic research.

The quality of crops and livestock have been improved by genetic research.

Crops can be affected by many different diseases.Transgenic plants which are

resistant to certain diseases are produced to solve this problem
Disadvantages

Genetic research may lead to exitinction of species since new varieties replace
them.

Cloning oe genetic engineering, especially on human beings may give rise to

moral,ethical and religious problems.

Genetically modified food may be harmful to human health.

Ecosystem can also be threatened by genetic technology.

Variation Among Living Things

Definition of variation


Variation is the difference in trais of an organism of the same species which can
be passed on from one generation to another.
Variation in humans

Human differ from each other in terms of

Physical characteristics

Physiologically

There are two types of variation

Continuous variation - differences in traits which are not very distict or

discrete.This type of variation tend to be quantitative. controlled by genetic factors and
is often significantly affected by environmental influences.

Discontinuous variation - is variation which deals with clear-cut differences

in traits.Discontinuous variation is completely controlled by genetic factors and is not
effected at all by environmental factors.
Factors that cause variation

There are two factors that lead to variation:

Genetic factors

variation that is controlled by genetic factors can be

inherited.Crossing-over occurs at the start of Prophase I during meiosis.

Chromosome separate randomly in gamete formation

Random fertilisation

Environmental factors

environmental factors which cause variation include climate.light,

moisture,oxygen,pressure,soil fertility,temperature,type of food and lifestyle.
The importantace of variation

The emergence of traits which can adapt well to changes in the environment
enables the organism to survive,breed and inherit new characteristics.

Variation ensures the survival of a species.Variation may encourage the formation

of new species,a process called speciation

There will be no diversity in organisms without variation.

Family tree

Pedigree analysis is another term for the construction of a family tree.

Pedigree analysis is a schematic chart that shows the flow of a certain trait from
parents to the next generation and other related members in a family through
inheritance.

Table shows a a list of symbols commonly used in a human pedigree analysis.

Changes in States of Matter

All things wheather living or non-living things in the world consist of

matter.Matter is any living or non-living thing that has mass and occupies space.Matter
is made up of tiny and discrete particles


The kinetic Theory of Matter states that matter is mae up of tiny and discrete
particles which are always moving in random motion
States of matter

Matter exists in three states which are solid,liquid and the gaseous states.

All matter whether solid, liquid or in the gaseous state, have the following
characteristics:

Made up of tiny particles

Particles always vibrate and are sometimes moving

has space between the particles

In the solid state, particules:

are arranged in a regular pattern

are tightly packed

have fixed positions

do not move freely

only vibrate and rotate around their fixed positions.

In the liquid state,particles:

are not arranged in a regular pattern

are further apart

do not have fixed positions

move freely around one another

In the gaseous state,particles:

are not arranged in a regular pattern

are widely spaced

do not have fixed positions

Sublimation

process where solid changes to gas or gas to solid without going htrough the
liquid

e.g. iodine, dry ice, ammonium chloride and naphthalene

Diffusion

can occur because particles move into the space in between the particles of
solids, liquids and gases

Eg: when 50 cm3 of ethanol and 50 cm3 of distilled water are mixed,only
3
98cm of mixture are obtained.This is because the ethanol and water particles occupy
each other spaces between the particles.
Brownian motion

is random movement example shown by smoke particles or pollen grains when

knocked about by air particles

Changes in the state of matter

Impurities like common salt can

increase the boiling point of distilled water (102oc)

lower the freezing point of distilled water (-2oc)

Atom ( a basic unit all matter)

all matter consists of tiny units called atoms

a neutral atom is the number of protons equal to the number of electron (Number of
proton = number of electron)
Ion are atoms which have charge:

Positive ion = atom which losses of electron

Negative ion = atom which receives more electron

Proton number = numner of protons = number of electrons

Nucleon number = total number of protons and neutrons
Isotopes = atoms that posses the same number of proton but different number of
neutrons
= same proton number (chemical properties) but different nucleon number
(physical properties)

The periodic table is important in the systematic and methodical study of elements.

Classification of elements in periodic table are arranged orderly and systematically of

increasing proton number from left to right based on the number of protons.

Characteristic or Properties of Metals and Non-Metals

Pure substances

Distilled water is pure water because it does not contain any dissolve substance
or forein matter.

The boiling point of pure water is 100oc and melting point is 0oc


However impurities such as salt can increase the boiling point to 102 oc and lower
the melting points to -3oc
Purifying substances

Distillation

liquid

is the process of boiling the liquid and condensing the vapour into pure

Crystallisation

Is forming of pure crystal from a hot saturated of a salt when it is cooled

E.g mining salt from sea water

Preparing crystals

5.1 physical and chemical changes.

two types of changes involved in matter:

*physical changes

*Chemical changes

Physical Changes

1.

physical change are defined as the changes that only affect the
physical properties of substances.
2. the characteristics of physical change are:

involves only physical changes such as shape or size of a substance.

involves changes in the state of matter;solid,liquid and gas.

chemicals composition and chemical properties of substances remain

unchanged so that no new substances is formed.

less energy is needed.

the changes are reversible.

3.physical changes in our daily life are:

(a) *Melting of ice:

*Melting of chocolate.

(b)Freezing:

(C) *Evaporation of water:

*evaporation of alcohol or evaporation of petrol.

(d)Natural water cycle.

(e)Condensation:

(f)Dissolving salt and sugar in water.

(g)Formation of dew on the grass.

4.Physical changes being studied in a laboratary are:

(a)Sublimation:

~CHEMICAL CHANGES~

1.

Defined as the changes that affect the chemical composition and

chemical properties of the substances.
2. the characteristics of chemical change are:

new substances known as products.

chemical composition and chemical properties of the new substances are
different from the original substance which is known as reactant.

is usually fixed and irreversible.

needs large amount of energy.

3.chemical changes in our daily life are:

respiration:

burning of paper or fossil fuels produces carbon dioxide and ash.

digestion of food.
washing dishes with detergent or washing hair using shampoo.
Change in colour of peeled apple when exposed to air.
decomposition of animal carcasses.
making bread from wheat flour.
photosynthesis.

4.examples of chemical changes being studied in a laboratary are:

Respiration

Oxygen + glucose --------> carbon dioxide + water vapour + energy

neutralisation:

Acid + alkali + -------> salt = water

electrolysis of water.

~COMPARING AND CONTRASTING PHYSICAL AND CHEMICAL CHANGES~

~5.2 HEAT CHANGE IN CHEMICAL REACTIONS~

CHEMICAL REACTION INVOLVES HEAT CHANGE

- chemical reactions involves changes in energy in the form of heat energy.

- chemical reactions,

energy is aborded to break bonds in the reactants.

energy is released when new bonds sre formed in the products.

-chemical reaction that absorbs energy is dissolving ammonium chloride in

water.when ammonium chloride(Salt) is put into a beaker of
water
which is held with our hands,we can feel that the temperature of water
falls.this is because the reaction in the beaker absorbs
energy from the
water and our hands.

-Chemical reactions that releases energy is dissolving sodium hydroxide in water.When sodium hydroxide(SOAP) is
put into a pail of water
and stirred using our hands,we can feel that the soap solution becomes hot.this is
because the reaction releases heat into the
surroundings.

REACTION INVOLVING HEAT LOSS AND HEAT GAIN.

Chemical reactions can be classified into two groups:

exothermic reactions.
endothermic reactions

~Exothermic reactions~

1.

exothermic reactions is defined as a reaction which releases energy

in the form of heat into the surrounding (heat loss),and causes the
surrounding temparature to increase.
2. the characteristics of exothermic reactions are:

heat is released into the surroundings.

Energy is released when bonds are formed because the energy needed to
break the bond in the reactants is less than the energy released when new
bonds are formed in the products.

surrounding temperature increases due to the release of energy but the

temperature of mixture decreases.

Energy content of the reactant(s)

Higher energy content of the product(s)

~Endothermic reactions~

1.~absorb energy or gain heat.

~surrounding temperature to decrease.

2.The characteristics of exothermic reaction are:

heat is absorbed.
Energy is aborded.

surrounding temperature decreases and temperature of the mixture

increases.

energy content of the reactant(s) is lower than energy content of the

product(s)

3.endothermic reactions are:

boiling water.

heating copper sulphate crystals.

melting wax.

dissolving ammonium chloride in water.

photosynthesis.

decomposition of mercury oxide by heat and decomposition of copper

carbonate by heat.
HEAT CHANGES IN INDUSTRIAL CHEMICAL REACTIONS

Haber process
contact process

haber process

ammonia is produced by the haber process on a large scale.

catalyst(iron)at atemparature of 450-500C and a pressure of 200

atmospheres.

the process is reversible.

heat is released in the forward reaction (exothermic).

5.3 The reactivity of metals .

Activity a chemical reaction.

the reactions metals with water.

The reactivity of metals with water.

Highly reactive metals.

less reactive metals

The reactivity of metals with oxygen.

metal+oxygen=metal oxide

the metal oxide produced a different colour compared to the original metal
as shown in table 5.6.

TABLE 5.6
COMPARING AND CONTRASTING THE REACTIVITY OF METALS WITH WATER,ACIDS AND OXYGEN.

The reaction of metals with water,dilute acids and oxygen will

individually produce different chemical substances.

table 5.8 shows the comparison of the reactivity of metals with water,dilute
acids and oxygen:

table 5.8
Reactivity series of metals.

The reactivity series order of reactivity with oxygen

Table 5.9 shows the reactivity series of metals .

TABLE 5.9

THE POSITION OF CARBON IN THE REACTIVITY SERIES OF METALS.

The raectivity series of metals shows the inclination of a metal to react

with oxygen.

The operatinal definition of this experiment is carbon reduces a metal

oxide to its metal if carbon is more reactive than the metal.

on the the other hand, carbon does not react with a metal oxide if it is less
reactive than the metal.
5.4 APPLICATION OF THE REACTIVITY SERIES OF METALS

RELATING THE POSITION OF METALS IN THE REACTIVITY SERIES TO THE METHOD OF EXTRACTION OF
METALS FROM THEIR ORES.

Table 5.12 shows some common ores.

TABLE 5.12

Two methods of extraction of metals from their ores:

Electrolysis of the molten more.

reducation of metal ore using carbon

A Suitable method to extract a metal from its ore is based on the position of the metal in the reactivity
series of metals as shown in table 5.13.

Table 5.13

The importance of the reactivity series are:

Determine the method of extracting the metal.

Predict the reactivity of a particular metal.
Predict whether a particular metal can remove oxygen from another metal oxide.

The extraction of metals from their ores through reduction using carbon.


Metal which are located below carbon in the reactivity series are extracted
through the reduction method by carbon.

Pure metals which can be extracted using carbon include tin,zinc,copper,iron and
lead.

Tin extraction

Flotation.
Tin extraction Process is carried out in two main stages as follows:
impurities,Removed
mixed with coke (carbon) and limestone (Calcium carbonate)

Electrolysis

Decomposition of an electrolyte using electricity.

Electrical energy is changed into chemical energy.

Electrolyte

electrolyte is a compound in molten form or aqueous solution which contains ions.

Positive ions (cations) and Negative ions (anions).

Electrodes

Eloctrode Conductor.
Carbon rods.
anode.
Cathode.

Electrical Source

Electrical source is the source which generates electrical energy.

Ammeter

Ammeter measure the flow of current.

Electrolysis of an electrolyte using carbon electrodes.

Electrolysis process is based on the type of electrolyte decomposed and the

movement of the ions.

Uses of electrolysis in industry

Extraction of metals
Purification of metals
Electroplating of metals

Extraction of metals

Electrolysis
Extraction of metals.
Extraction of aluminium:

bauxite
melted
Mixed with cryolite
Cathode
Anode

Purification of metals

Pure metal electrolysis.

Impure metal as the anode
Pure metal as the cathode
A salt solution as the electrolyte.

Electroplating of metals

Electroplating coating of a thin layer of less reactive metal on the surface of

another more reactive metal electrolysis.

Electroplating a coin with copper.

Electroplating an iron nail with copper.

Electroplating costume jewellery with gold.

Tin plating to produce food cans

Silver plating.

Electroplating iron nails with zinc.

Prevent a metal object from rusting.

Make metal look nicer,shiny and attractive.

5.6 The production of electrical energy from chemicals reactions

Chemical energy can change into electrical energy.

A simple cell is used hoe electrical energy id produced by chemical reaction.

Simple cell.

Two different metal plates or carbon plate and a metal plate as electrodes.

A dilute acid,an alkali or a salt solution as an electrolyte.

The less reactive metal or carbon forms the positive electrode known as the
anode

Various types of cells and their uses

Production of electrical energy from a simple cell to produce electrical energy.

5.7 Chemical reactions that occur in the presence of light.

Chemical reaction which require light.

Some reactions need light energy to start a chemical reaction.

Photosynthesis.
Photographic film.
Silver chloride.

Photosynthesis


Green plants synthesise food using chlorophyll pigment,light energy,water and
carbon dioxide.

Hydrogen and oxygen as photolysis of water.

Dark reaction;

Food or glucose.

Effect of light on photosensitive chemicals

Is sensitive to Light is known as a photosensitive chemical.

Photosensitive chemical are:
Silver chloride.

silver bromide.

Silver iodide.

chlorine water.

hypochlorite solution

silver nitrate

5.8 Innovative efforts in the design of equipments using chemical reactions as sources of energy

Electrical energy
using ellectrical energy efficiently.

6.1 Radioctive substances

Unstable nucleus.
Radioactive substances are:

Uranium
Polonium
Radium
Radioactive isotopes or radioisotopes.
Examples of radioisotopes:

Uranium-235,uranium-238
Radium-226

Polonium-212
Carbon-14
Cobalt-60
Phosporus-32
Sodium-24
Hydrogen-2,hydrogen-3

Radioactive decay

Nuclei energy is produced.

Three types of radiations:

alpha()
beta()
Gamma()

The uses of radioactive substances

Agriculture
Medicine
Archaeology;

Carbon Dating.
Industry
Food preservation

6.2 Production of Nuclear Energy and Its Uses

Nuclear energy is released

Radio active decay and nuclear reaction
Two types of nuclear reactions:

Nuclear fission
nuclear fusion

Nuclear fission

nuclei.

An unstable nucleus is bombarded by high-speed neutrons,Form more stable

Nuclear energy produced by nuclear fission is used to generate electricity.
Nucleus of uranium -235 is bombarded with high-speed neutrons.
Nucleus will absorb the neutron and split in two nuclei.
Two nuclei are radioactive barium-141 nucleus and krypton-92 nucleus.
Three new high-speed neutrons are produced.
a large amount of nuclear energy is released.

Nuclear fusion

Two light nuclei combine to form a heavier nucleus.

Nuclear energy.

Nuclear fusion of hydrogen isotopes:

Very high temperature and pressure,hydrogen-2 and hydrogen-3 isotopes fuse

and form a helium nucleus.

Total mass after nuclear fusion is slightly lower than the mass before nuclear
fusion.

Loss in mass is converted into large amount of nuclear energy and a neutron is
released.

The uses of nuclear energy.

Used to propel vessels such as submarine and aircrafts which allow them to
operate for one or two years without having to refuel.

Besides solar energy,Nuclear energy is the major source of energy that enables
the satellites to operate for years.

Nuclear energy is mainly used to generate electricity.

Process of generating electricity from nuclear energy.

Uranium rods,Radioactive substances.

graphite rods,control the rate of chain reactions.
Heat energy ,boil water.
Steam rotates the turbine,produce electricity
Condenser,Condense steam.

The effect of nuclear energy production

table 6.2
6.3 The Need Proper Handling of Radioactive Substances

In 1986,a fire in a nuclear power plant in cherynobyl,Russia.This incident

caused:

The death of thousands of people.

About 24 000 people will die of cancer in the next 70 years.

Farm and diary products in europe were polluted with radioactive

substances .

The city was completely destroyed.

Proper safety measures should be taken when handling radioactive

substances in order to prevent:

Nuclear disaster such as in chernobyl,Russia.

Radioactive contamination.
Health problem such as cancer.
genetic mutations .

Effect of radioactive radiations on living things can be categorised into

short and long term as shown in table 6.3:

Table 6.3

Correct ways of handling radioactive substances and radioactive wastes.

Symbol represent radioactive substances:

Figure 6.6
Low-level wastes
Intermediate-level wastes
High-level waste

7.1 Formation of images by plane mirrors and lenses.

Formation of images by plane mirrors.

Virtual.

upright.
Laterally inverted
Same size.
Distance image behind the screen same as the distances of the object.

Characteritics of images formed by convex and concave lenses.

A lens transparent material glass or plastic.

Convex lens.
concave lens.

Table 7.2

Table 7.4 shows the comparison of images formed by a convex and

a concave lens .

Table 7.4

Ray diagram

A ray diagram shows the path of light rays passing through a lens.

A ray diagram is drawn using two rays from a point on the object as
shown in table 7.5:


The ray diagram and the characteristic of images formed by convex lens is
different according to the object distances as shown in table 7.6.

Focal length.

Focal length is defined as the distance between the focal point and the
optical centre.

The symbol for local length is 'f '.

7.2 Formation of images by optical instruments

Identifying parts of optical instruments involved in image formation

Periscope:

Figure 7.5 Periscope

Virtual
upright
The same size as the object.
Image distance.
same object distance.

Telescope.

Two convex lenses.

Virtual
Inverted.
Bigger.

Figure 7.6(a) Telescope

Magnifying glass

Virtual
Upright
Larger

Figure 7.7(a)Magnifying glass.

Pinhole camera

Figure 7.8 Pinhole Camera

camera.

Real and inverted.

Size of the image dependent on the object distance in front of the pinhole
Number of image dependent on the number of pinholes.

Camera

Lens.

Diaphragm.

Aperture.

Focus adjustor.

shutter.

Film.

Nearby object,lens is adjusted away from the film.Distance between the

lens and the film is increased.

Distant object,Lens is adjusted towards the film.The distance between the

lens and film is decreased.

diaphragm control the amount of light entering the lens.Aperture focal

length of the camera lens.

Shutter.

Table 7.9 shows effect of the light condition due to the size of the

diaphragm opening and the speed of the shutter opening.

Table 7.9

Film capture the image of the object.

Real,inverted and smaller.

The human eye as an optical instrument.

Figure 7.10 structure of the human eye.

Retina

Image are formed here.It contains thousands of light sensitive cells which
send nerve impulses when they receive light.

Optic nerves

Carries nerve impulse to the brain to be processed.

Lens

The thickness of the lens can be altered to control the focus of the eye.

Pupil

Light enters the eye through this opening,it appears black.

Cornea

through it.

Helps to focus light onto the retina by refracting light rays that pass

Iris

Control the size of the pupil.

Table 7.10 Function of main parts of the human eye.

Ability of the eye lens to change its focal length accommodation.

Dim lights

Radial muscles contract,circular muscles relax.

Size of the pupil bigger.

Bright light

Radial muscles relax.

circular muscles contract.
Size of the pupil smaller.

Comparing the human eye with a camera.

The structure and function of various parts of human eye using the camera as an anology.

Table 7.12 shows the analogy between the structure and function of the eye and a camera.

7.3 Dispersion of light.

Dispersion of light.

Dispersion of light by a prism

glass prism.

Light dispersion light is split colour consituents Spectrum passes through a

Red,Orange,yellow,green,blue,indigo and violet.

Formation of the rainbow

Dispersion of light.
Two refraction.
One reflaction.
Primary rainbow.
Two refraction.
Two reflaction.
Secondary rainbow.

7.4 Scattering of light.

Wavelength of the light.

Shorter more scattered.

Scattering of light in natural phenomena.

At noon:

Short wavelength scattered more.

sky blue.
Eyes more sensitive to blue light.

At dawn or dusk:

Short wavelength scattered more..

Long wavelength Scattered less.
Sun reddish if polluted with dust.

7.5 Addition and substraction of coloured light.

Primary colours;

Red
Blue
Green

Secondary colours;

Yellow
Magenta
cyan

Addition of coloured light.

Process two primary coloured lights overlap.

Table 7.14

Subtraction of coloured lights by coloured filters.

Enables a particular coloured light to pass through it.

Primary filter.

Red,green,and blue filters.

Allows lights of the same colours to pass.

Secondary filter.

Yellow,magenta and cyan filters.

allows lights of the same colours and primary colours that from them.

Table 7.29

7.6 Using the principle of substraction of coloured lights to explain the appearance of coloured objects.

Primary coloured reflect its own colour.

Secondary coloured reflect its own colour and the colours that form it.

Table 7.16 shows the summary of the principle of subtraction of coloured lights in the appearance of an object.

Table 7.16

Function of rod and cone cells in the eye.

Rod cells:

Sensitive to low intensity light.

Red
Green
Blue
Cone cells:

Sensitive to coloured light.

7.7 The Effects of Mixing Pigments.

Pigments.

Substract and reflects certain colours in light.

Living things such as plants and animals.

Uses of pigments.

Textile industry
Food industry
Cosmetics industry
Printing industry
Painting industry
Natural world

Effects of mixing pigments.

Primary colours:
Red
blue
Yellow
Except white.

Mixing of coloured pigment produces colours as shown in table 7.17.

Table 7.17

Coloured lights reflected by different coloured pigments in white lights as shown in table 7.18.

Table 7.18

Comparison between the coloured pigments and coloured light from different aspects as shown in table 7.19.

Table 7.19

7.8 The importance of colour in daily life.

Colour printing.
Electrical wiring.
Traffic lights.
Symbols and signals.
Survival of living things.
Colour television.

Colour printing

Yellow,magenta,cyan,and black.
Colour separation.
Printing plates.
Black ink to sharper clearer.

Electrical wiring

Brown for live wires.

Blue for neutral wires.
Yellow and green stripes for earth wires.

Figure 7.35

Traffic lights

Red.
Yellow.
Green.

Figure 7.36

Symbols and signals.

permitted.

of the road.

green flag is

Two white lines in the middle of the road indicate that no overtaking is
Yellow line painted side of the road ,Cars cannot be parked along the side
Yellow box painted with yellow stripes,Cannot stop inside the box.
Small red flag is raised when an event is being is being prepared,Small
raised when the event is ready to begin.
Ambulance red light indicates an emergency.

7.9 Appreciating the benefits of various types of optical instruments of to mankind.

Table 7.20 shows optical instuments and their uses.

Table 7.20

8.1 Properties of alloys and Their uses in industry.

Alloys

Homogenuos mixture pure metal another pure metal or Non metal.

Alloying mixing other elements to the pure metal.
Alloying process is carried out as follow:

A pure metal is melted

some metal and non-metal are then added to the molten

metal

The mixture is the cooled

Table 8.1

Alloying Changes the properties of metals.

Weakness and structure of a pure metal are improved by alloying.

Pure metals become more resistant to corrosion,shinier,more attractive

appearance and harder.

Prevents corrosion of metals.

Alloying.

Improves the appearance of metals.

Copper has dull brown surface after being oxidised.

Alloying prevents rust,most alloys,nice shiny surface.
Examples:

A little nickel is added to copper to produce copper nickel

alloy.

Increases the hardness and strength of metals.

Metal such as magnesium,aluminium are soft and light.

Problem can overcome by alloying.Alloys are harder and stronger.
For example:

Magnesium is mixed with aluminium to produce

magnalium.Magnalium is an alloys are hard but it still retains the lightness of
both these pure metals.

Arrangement of particles in alloys and the uses of alloys

121.

Atoms of pure metals are arranged very closely and orderly as shown in

figure 8.1.

Figure 8.1

2.The layers of atoms slide easily over one another when a force is applied.as a
result,it becomes ductile as shown in figure 8.2.

Figure 8.2 Ductile property of metal.

3.Ability of the layers metal atoms to slide easily also makes it malleable and easily
shaped when a forced is applied as shown in figure 8.3.

Figure 8.3
In an alloy,substances added which are smaller or bigger fill the shapes between the
pure metal atoms and the new arrangement is formed as shown in figure 8.4.

another.

Figure 8.4 Alloy with smaller atoms.

Prevents the layers of pure metal atoms from sliding over one

Table 8.2 shows the comparison between a pure metal and alloy.

Table 8.2
The importance of alloys in industry.

corrosion.

Carbon steel.
Stainless steel resistant to

Supercondutor alloys.

Differences ordinary conductor(Normal conductor) and superconductor.

Figure 8.5
Table 8.3 shows uses of superconductor alloys in industry and daily life.

Table 8.3
8.2 Production and uses of ammonia in industry.
Ammonia.

Pungent smell,colourless and very soluble in water.

ammonium hydroxide.

Uses of ammonia and its compound in daily life.

Table 8.4 shows uses of ammonia and its compounds in daily life.

Table 8.4
Production of ammonia in industry.

cracking oil.

Haber process produce ammonia.

Nitrogen and hydrogen.
Hydrogen is produced by reacting methane with steam or from the

Iron powder is added as a catalyst.Booster like aluminium oxide.

The following shows the reaction in producing ammonia.

Reversible.

Figure 8.6 The haber Process

Factor influencing the production of ammonia:

Pressure 200-500 atmospheres.

Temperature Exothermic 450-500C

Catalyst increase the rate of a chemical reaction boosters

activate the catalyst.

Uses of ammonia in industry.

Ammonia is also used in large quantities to produce Nitric acid.

Production of ammonium fertilisers.

Natural fertiliser.
Synthetic fertiliser.

Production of ammonium salt fertilisers.

Ammonium nitrate

Ammonium sulphate

Ammonium phosphate

follows:

The preparation of ammonium salt fertiliser in the science laboratory is as

Production of urea.

Urea is produce through the following processes:

Heated 200C and pressure of 200 atmospheres.

Separated
dried

The reaction between chemicals which produce urea is shown below.

8.3 Effects of industrial waste disposal on the environment.

Poisonous and harmful industrial activities causes the quality of the

environment to be on the decline.

the two main pollution-causing industrial activities are:

The burning of fossil fuels.

the direct disposal of industrial wastes from facrtories.

Sources of pollution from manufacturing activities and the effects of imporer industrial waste disposal .

Burning of fossil fuels.

Fossil fuels such as diesel,oil and natural gas are burned in factories and
electric power stations to generate heat energy and electrical power.

Gases such as carbon dioxide,carbon monoxide,sulphur dioxide,and

nitrogen dioxide are released.because fossil fuels have high contents of carbon and
sulphur.
Greenhouse effect.

Earth receives most of its energy from the sun.Energy is used to heat up
the Earth's surface.Heat produced is in the form of infrared radiation.It reflects heat back
into the atmosphere.70% of the sun's energy is radiated back into space.Earth is kept
warm enough to support life.


Increase Earth's temperature by trapped heat in the atmosphere as shown
in figure 8.8.

Figure 8.8 the green house

effect
The greenhouse effect also causes other problems such as:

The weather becomes warmer.

The melting of ice.

desert areas bigger.

Global warming.
Figure 8.9 shows the contribution of different types of greenhouse gases towards global
warming.
Greenhouse gases that contribute
towards global warming

figure 8.9
Acid rain

Figure 8.10 Formation of acid rain

sulphur dioxide contributes to acid rain

Oxides of nitrogen contribute to acid rain.

Figure 8.11

The effects of acid rain:

Disturbs the equilibrium of nature

Acid rain affects lakes,streams,rivers,bays,ponds and other sources by

increasing their acidity.This leads to the death aquatic organisms and plants.

Destroys plants and trees as the soil becomes too acidic.

Chemical industry.

Toxic chemicals,oils and untreated waste.

Pollutants also affect quantity of dissolved oxygen,affecting aquatic

animals and plants.

Nuclear power stations and research institutions.

Radioactive produced nuclear research centres,nuclear reactors and

manufactring products contain radioactive substances.

Radioactive radiations released by these sources into the surrounding.

Agriculture industry.

Oil palm industry

Oil palm industry are stalks of fruit branches,fibre wastes

and oil spill.

Oil palm wastes are disposed off by burning them or leaving

them to rot.

Rubber industry

Rubber wastes are made up of phospate salt,ammonia and

rubber protein.

These wastes encourage the growth of bacteria.

Table 8.5 shows the types of pollutants,their sources and effects on living
organisms.

Table 8.5

Method of controlling industrial waste disposal.

Several ways to control the disposal of industrial wastes such as:

Law enforcement

Environmental Quality (scheduled wastes)Regulation,1989

Environmental quality (Clean air)Regulation,1979

Recycling wastes

Variety of industrial wastes recycled for use as products.

Particulars industry can also be used by other industries if
that industries if that industrial waste is suitable for them.

Education

Technology

Public need to be educated about the importance of

environmental cleanliness and the harmful effects of environmental pollution.

The mass media and schools plays important roles in

spreading environmental awareness to the public.

Biogas technology
direct burning
Disposal drums
Using electrostatic precipitator
Using a scrubber

Biogas technology

Process agricultural wastes naturally through digestion by microorganisms.

Anaerobic microorganisms.
Inside a digester drum called the Digester unit.
Temperature 30 C - 40 C
Biogas.

Figure 8.12 biogas digester

The separated methane is sent to houses for cooking purposes or to

factories for Heating purpose.

Electrical energy.

Direct burning

Agricultural wastes are directly burned in a heating furnace.

Figure 8.13 shows the system which is used to burn agricultural wastes.

Figure 8.13 Component of the direct burning system.

Disposal drum

Radioactive waste is radioactive material which may be left after a

commercial or laboratory process has been carried out.

Radioactive wastes disposal drums which are made of strontium.

Disposal drums placed 200 metres below the soil surface.

Using electrostatic precipitor.

Electrostatic precipitator two collection plates:

Positive plate
Negative plate

Using a scrubber.

Scrubber is used to filter the poisonous gases by sparing a liquid onto the
poisonous gases.

The toxic-free gas is then released.

figure 8.14 shows an air scrubber.

Figure 8.14 Air scrubber.

8.4 Preservation and Conservation of the Environment.

Preservation Environment refers to steps taken to maitain the

environment as close to its Natural state as possible.

Conservation refers continuos managment of the environment to minimise

damage to the environment.
Consequences of uncontrolled and haphazard disposal of industrial wastes.

Earth is in real danger.This can be proven through headlines in

newspapers about the uncontrolled and haphazard disposal of industrial wastes.

Indusrtrial wastes can pollute water sources.Water sources become

unsuitable for human consumption.Water pollution also threatens aquatic lives.

The importance of practising responsiblity in disposing wastes.

Humans must practice responsibility.

All wastes produced by industries must be stored,transported and

disposed off properly.

A pollution-prevention hierarcy which emphasies on reducing the amount

of toxic waste produced as shown in figure 8.15 must be implemented .stratergies
involved include:

Reduce the amount of pollution at the source.

Recycle wastes wherever possible.

Treat wastes to minimise their hazards.
Disposal of wastes on land is carried out only as a last resort.

Figure 8.15 the pollution-prevention hieracy

Several ways to preserve and conserve the environment which include:

Control by authorities.
Education.
Use of technology.

Control by authorities.

The following laws are used to control the disposal of industrial wastes:

The Environmental Quality act 1974(Amendment 1985).

The Factory and machinery Act 1976(Revised 1983).
The pest Poison Act 1874

The government organised and participated in international conferences to

discuss environmental world issues.There are:

The langkawi declaration (october 1991).

The Earth summit conferences (1992).

The agreements made in this conferences include:

Reducing the emission of carbon dioxide gas that causes

global warming.

The protection of animals and plants to ensure they do not

become extinct.

The Earth summit resulted in the following documents:

Educating the public.

Agenda 21
convention on biological diversity
Forest principles
Rio declaration on Environment and development.


Every citizen has a responsibility in looking after the cleanliness and purity
of the environment.

The preservation and conservation Environment can be spread through

campaigns,mass media and the school syllabus.

Use of technology.

Pollution reduced by using modern technology.

Factories reduce pollutants in the air by installing filters.