10-3-4 Optics Lenses and Dispersion My NC Notes
10-3-4 Optics Lenses and Dispersion My NC Notes
10-3-4 Optics Lenses and Dispersion My NC Notes
10.3 LENSES
What is a Lens?
A concave lens (a.k.a. diverging lens) is thinner in the middle than at the edges.
A concave lens causes light rays to diverge (spread out). If the rays are traced
backwards they appear to come from a focal point or principal focus (F).
A concave lens will disperse light and make an image that is always virtual,
upright and smaller than the object.
PICTURE: Light rays passing through a concave lens are spread out
When light rays go through a convex lens the rays are refracted.
For any ray entering the lens that is not along a normal the light will change
direction at both surfaces (see the picture below) where the air meets the glass.
A ray entering along the normal will pass straight through.
The normal for a lens is also called the principal axis
The light ray is often not shown changing direction at both surfaces of the lens
but just changing direction once to give the overall effect.
Sometimes the lens is just shown as a thin straight line instead of a curved
surface. The diagrams below give both ways of showing the same thing. Either
way is acceptable.
What are the Principal Axis and the Focal Point (principal focus) of a Convex
Lens?
The principal axis is a horizontal line going through the centre of a lens along
the normal.
Any light ray parallel to the principal axis will be refracted, change direction
and cross the principal axis at the focal point, F.
The focal point is also called the principal focus, F.
The principal focus (F) is the point at which parallel rays converge when
refracted by a convex lens.
Since light can pass through a lens in either direction, it can be focused on
either side of the lens. Therefore there are two principal foci equidistant from
the optical centre (C), one on either side of the lens. These are represented by
the symbols F and F’.
2F and 2F’ means twice the focal length from the optical centre on either side
of the lens.
What are the optical centre and Focal Length of a Convex Lens?
To draw any ray diagram for a convex lens you only need to know three rules.
1. A ray parallel to the principal axis of a lens is refracted through the focal
point (F).
2. A ray that passes through the focal point is refracted to be parallel to the
principal axis.
3. A ray passing through the optical centre of a lens will go straight
through.
NB. By using a ray diagram, any two of the above rules can be used to
determine where an image lies in relation to the object.
Step 2: From top of object (O), draw the ray parallel to the principal axis.
Step 3: Draw the refracted ray so that it passes through the principal focus.
Step 5: Where the rays cross, that is where the image is.
Step 6: Use the scales to measure the position and size of the image.
State the characteristics/nature of the image. Say whether the image is:
Real or virtual
Upright (erect) or inverted
Same size, magnified or diminished
State the position of the image. Say whether the image position is:
At F (v = f)
Between F and 2F (f < v < 2f)
At 2F (v = 2f)
Beyond 2F (v > 2f)
At infinity (v = ∞)
Further away
Behind object
On the opposite side of lens
On the same side of lens
For example in the diagram above, the nature of the image is as follows:
Real
Inverted
Magnified
On opposite side of lens
Beyond 2F.
It is a good idea to draw your ray diagram on graph paper as the following
ray diagram is.
Follow the six steps outlined previously.
Be careful with your drawing; a small change in the angle of the undeviated
ray can lead to quite a big change in the final position of the image.
And PLEASE... Be a good chap and use a sharp pencil.
The following is a ray diagram on graph paper for an object beyond 2F.
A ray diagram on graph paper for an object between F and optical centre (C)
Real Image:
o Images whereby light actually converges
o Occurs when object is placed outside the focal length
Virtual Image:
o Locations where light appears to have converged
o Occurs when object is placed within the focal length
MAGNIFICATION
Magnification =
m=
Or magnification =
m=
Please note
Worked example
Defect of vision in which the eye can see nearby objects clearly but cannot see
distant objects clearly.
Short sight is a defect in which close objects are seen clearly but distant
objects are blurred.
Close objects are in focus but distant objects are out of focus.
This defect is due to the formation of image of distant object in front of the
retina.
Correction of Myopia
1. What is myopia?
2. How is myopia caused?
3. How can myopia be corrected?
4. Which type of lens is used to correct myopia?
HYPERMETROPIA OR LONGSIGHTEDNESS
Defect of vision in which the eye can see distant (far) objects clearly but
cannot see the nearby objects clearly.
This defect is due the image of nearby object being formed beyond the
retina.
Correction of Hypermetropia
This defect is corrected by using spectacles having suitable convex lenses.
The convex lens converge the light rays, so the image is formed on the
retina.
1. What is hypermetropia?
2. How is hypermetropia caused?
3. How can hypermetropia be corrected?
4. Which type of lens is used to correct hypermetropia?
What is dispersion?
Dispersion is the splitting up of white light into its seven constituent colours on
passing through a glass prism.
Dispersion is the separation of white light into a spectrum of seven colours by
the process of refraction.
The spectrum of white light consists of seven colours which are: Red, Orange,
Yellow, Green, Blue, Indigo and Violet.
Mnemonics: ROYGBIV.
Absorption of light
A ladybird.
We see the red shell of the ladybird as red light is reflected and the other
colours are absorbed.
The green leaf absorbs all the colours except green which it reflects back into
our eyes.
We see a green leaf as green light is reflected and the other colours are
absorbed by the leaf's surface.
What about the black spots of the ladybird? Is black a colour? The black
spots on the ladybird absorb all the colours and no light is reflected. That is
why they appear black.
What about a white object? Why do you think white objects look white? Have a
look at the following diagram for a clue.
White objects absorb all the colours of white light and reflect all of them.
That is why they appear white.
We have already discussed that the white light is a mixture of seven different
colours.
When this white light consisting of seven colours falls on an object, then that
object absorbs all the colours of the white light except one colour, which it
reflects.
And it is the colour of the reflected light which determines the colour of that
object.
For example, a rose (or blood) appears red in sunlight because when white
light falls on rose (or blood), it absorbs all the colours of white light except red
colour, which it reflects. This reflected red light by rose (or blood) enters our
eyes and we feel the sensation of red colour.
In the same way the leaves of plants appear green in sunlight because when
white light falls on leaves, they reflects green colour to our eyes and absorbs
all other colours. This reflected green light enters our eyes and we feel the
sensation of green colour.
However, it is also observed that some objects absorb or reflect all the colours
of white light which falls over them.
If all the colours of white light are absorbed by an object, without reflecting
any colour then such object appears black. For example, a black board appears
black, because it absorbs all the colours of light falling on it.
On the other hand, if all the colours of white light are reflected by an object
without absorbing any colour then such object appears white. For example, the
milk appears white because it reflects all the colour of white light falling on it.