Geometric Optics

J.M. Gabrielse
 Outline
Basics
Reflection
Mirrors
Plane mirrors
Spherical mirrors
Concave mirrors
Convex mirrors
Refraction
Lenses
Concave lenses
Convex lenses J.M. Gabrielse
A ray of light is an extremely narrow
beam of light.

J.M. Gabrielse
All visible objects emit or reflect
light rays in all directions.

J.M. Gabrielse
Our eyes detect light rays.

J.M. Gabrielse
We think we see objects.

We really see images.

J.M. Gabrielse
Images are formed when
light rays converge.

converge: come together

J.M. Gabrielse
 When light rays go straight into our eyes,
we see an image in the same spot as the object.

object
&
image

J.M. Gabrielse
 Mirrors

It is possible to
see images
when
converging image
light rays reflect
off of mirrors.

object
J.M. Gabrielse
 Reflection
(bouncing light)
Reflection is when light normal
changes direction by
bouncing off a surface.

When light is reflected off

a mirror, it hits the mirror
at the same angle (i, the reflected incident
ray
incidence angle) as it ray
reflects off the mirror (r,
the reflection angle). r i
The normal is an
imaginary line which lies
at right angles to the
mirror where the ray hits it. Mirror
J.M. Gabrielse
Mirrors reflect light rays.

J.M. Gabrielse
How do we see images in mirrors?

J.M. Gabrielse
How do we see images in mirrors?

object image

Light from the object

reflects off the mirror
and converges to form an image.

J.M. Gabrielse
 Sight Lines

object image

We perceive all light rays as if they come straight from an object.

The imaginary light rays that we think we see are called sight lines.

J.M. Gabrielse
 Sight Lines

object image

We perceive all light rays as if they come straight from an object.

The imaginary light rays that we think we see are called sight lines.

J.M. Gabrielse
 Image Types

object object image

&
image
window

mirror

Real images are formed by light rays.

Virtual images are formed by sight lines.

J.M. Gabrielse
 Plane (flat) Mirrors

do di

ho hi

object image

Images are virtual (formed by sight lines) and upright

Objects are not magnified: object height (ho) equals image height (hi).
Object distance (do) equals image distance (di).
J.M. Gabrielse
Spherical Mirrors
(concave & convex)

J.M. Gabrielse
 Concave & Convex
(just a part of a sphere)

C F
f

C: the center point of the sphere

r: radius of curvature (just the radius of the sphere)

F: the focal point of the mirror or lens (halfway between C and the sphere)
f: the focal distance, f = r/2 J.M. Gabrielse
 Concave Mirrors
(caved in)

F optical axis

Light rays that come in parallel to the optical axis reflect through the focal point.

J.M. Gabrielse
Concave Mirror
(example)

F optical axis

J.M. Gabrielse
 Concave Mirror
(example)

F optical axis

The first ray comes in parallel to the optical axis and reflects through the focal point.

J.M. Gabrielse
 Concave Mirror
(example)

F optical axis

The first ray comes in parallel to the optical axis and reflects through the focal point.
The second ray comes through the focal point and reflects parallel to the optical axis.
J.M. Gabrielse
 Concave Mirror
(example)

F optical axis

The first ray comes in parallel to the optical axis and reflects through the focal point.
The second ray comes through the focal point and reflects parallel to the optical axis.
A real image forms where the light rays converge. J.M. Gabrielse
Concave Mirror
(example 2)

F optical axis

J.M. Gabrielse
 Concave Mirror
(example 2)

F optical axis

The first ray comes in parallel to the optical axis and reflects through the focal point.

J.M. Gabrielse
 Concave Mirror
(example 2)

F optical axis

The first ray comes in parallel to the optical axis and reflects through the focal point.
The second ray comes through the focal point and reflects parallel to the optical axis.
J.M. Gabrielse
 Concave Mirror
(example 2)

F optical axis

The first ray comes in parallel to the optical axis and reflects through the focal point.
The second ray comes through the focal point and reflects parallel to the optical axis.
The image forms where the rays converge. But they dont seem to converge.
J.M. Gabrielse
 Concave Mirror
(example 2)

F optical axis

The first ray comes in parallel to the optical axis and reflects through the focal point.
The second ray comes through the focal point and reflects parallel to the optical axis.
A virtual image forms where the sight rays converge. J.M. Gabrielse
 Your Turn
(Concave Mirror)

object
F optical axis

concave mirror

Note: mirrors are thin enough that you just draw a line to represent the mirror
Locate the image of the arrow
J.M. Gabrielse
 Your Turn
(Concave Mirror)

object
F optical axis

concave mirror

Note: the mirrors and lenses we use are thin enough that you can just draw a line to
represent the mirror or lens
Locate the image of the arrow J.M. Gabrielse
 Convex Mirrors
(curved out)

F optical axis

Light rays that come in parallel to the optical axis reflect from the focal point.

The focal point is considered virtual since sight lines, not light rays, go through it.
J.M. Gabrielse
Convex Mirror
(example)

F optical axis

J.M. Gabrielse
 Convex Mirror
(example)

F optical axis

The first ray comes in parallel to the optical axis and reflects through the focal point.

J.M. Gabrielse
 Convex Mirror
(example)

F optical axis

The first ray comes in parallel to the optical axis and reflects through the focal point.
The second ray comes through the focal point and reflects parallel to the optical axis.

J.M. Gabrielse
 Convex Mirror
(example)

F optical axis

The first ray comes in parallel to the optical axis and reflects through the focal point.
The second ray comes through the focal point and reflects parallel to the optical axis.
The light rays dont converge, but the sight lines do.
J.M. Gabrielse
 Convex Mirror
(example)

F optical axis

The first ray comes in parallel to the optical axis and reflects through the focal point.
The second ray comes through the focal point and reflects parallel to the optical axis.
The light rays dont converge, but the sight lines do.
A virtual image forms where the sight lines converge. J.M. Gabrielse
 Your Turn
(Convex Mirror)

object
F optical axis

convex mirror

Note: you just draw a line to represent thin mirrors

Locate the image of the arrow
J.M. Gabrielse
 Your Turn
(Convex Mirror)

object image
F optical axis

convex mirror

Note: you just draw a line to represent thin mirrors

Locate the image of the arrow
J.M. Gabrielse
Lens & Mirror Equation

1 1 1

f di do
= focal length
do = object distance
di = image distance

f is negative for diverging mirrors and lenses

di is negative when the image is behind the lens or mirror
J.M. Gabrielse
Magnification Equation

hi di
m
ho do
m = magnification
hi = image height
ho = object height

If height is negative the image is upside down

if the magnification is negative

the image is inverted (upside down)

J.M. Gabrielse
 Refraction
(bending light)
Refraction is when light bends as it normal
passes from one medium into another.

air
i
When light traveling through air
passes into the glass block it is
glass
refracted towards the normal.
block
r
When light passes back out of the i
glass into the air, it is refracted away
from the normal.

Since light refracts when it changes r air

mediums it can be aimed. Lenses are
shaped so light is aimed at a focal normal
point. J.M. Gabrielse
 Lenses
The first telescope, designed and built by Galileo, used lenses to focus light from
faraway objects, into Galileos eye. His telescope consisted of a concave lens and a
convex lens.

light from convex concave

far away lens lens
object

Light rays are always refracted (bent) towards the thickest part of the lens.
J.M. Gabrielse
 Concave Lenses
Concave lenses are thin in the middle and make
light rays diverge (spread out).

F optical axis

If the rays of light are traced back (dotted sight lines),

they all intersect at the focal point (F) behind the lens.
J.M. Gabrielse
 Concave Lenses

F optical axis

Light
Therays
lightthat
rayscome
behave
in parallel
the same to the
wayoptical
if we ignore
axis diverge
the thickness
from the
offocal
the lens.
point.

J.M. Gabrielse
 Concave Lenses

F optical axis

Light rays that come in parallel to the optical axis still diverge from the focal point.

J.M. Gabrielse
 Concave Lens
(example)

F optical axis

The first ray comes in parallel to the optical axis and refracts from the focal point.

J.M. Gabrielse
 Concave Lens
(example)

F optical axis

The first ray comes in parallel to the optical axis and refracts from the focal point.
The second ray goes straight through the center of the lens.

J.M. Gabrielse
 Concave Lens
(example)

F optical axis

The first ray comes in parallel to the optical axis and refracts from the focal point.
The second ray goes straight through the center of the lens.
The light rays dont converge, but the sight lines do.
J.M. Gabrielse
 Concave Lens
(example)

F optical axis

The first ray comes in parallel to the optical axis and refracts from the focal point.
The second ray goes straight through the center of the lens.
The light rays dont converge, but the sight lines do.
A virtual image forms where the sight lines converge. J.M. Gabrielse
 Your Turn
(Concave Lens)

object
F optical axis

concave lens

Note: lenses are thin enough that you just draw a line to represent the lens.
Locate the image of the arrow.
J.M. Gabrielse
 Your Turn
(Concave Lens)

object image
F optical axis

concave lens

Note: lenses are thin enough that you just draw a line to represent the lens.
Locate the image of the arrow.
J.M. Gabrielse
 Convex Lenses
Convex lenses are thicker in the middle and focus light rays to a focal point in front of
the lens.

The focal length of the lens is the distance between the center of the lens and the
point where the light rays are focused.
J.M. Gabrielse
Convex Lenses

optical axis F

J.M. Gabrielse
 Convex Lenses

optical axis F

Light rays that come in parallel to the optical axis converge at the focal point.

J.M. Gabrielse
 Convex Lens
(example)

optical axis F

The first ray comes in parallel to the optical axis and refracts through the focal point.

J.M. Gabrielse
 Convex Lens
(example)

optical axis F

The first ray comes in parallel to the optical axis and refracts through the focal point.
The second ray goes straight through the center of the lens.

J.M. Gabrielse
 Convex Lens
(example)

optical axis F

The first ray comes in parallel to the optical axis and refracts through the focal point.
The second ray goes straight through the center of the lens.
The light rays dont converge, but the sight lines do.
J.M. Gabrielse
 Convex Lens
(example)

optical axis F

The first ray comes in parallel to the optical axis and refracts through the focal point.
The second ray goes straight through the center of the lens.
The light rays dont converge, but the sight lines do.
A virtual image forms where the sight lines converge. J.M. Gabrielse
 Your Turn
(Convex Lens)

optical axis

object
F

convex lens

Note: lenses are thin enough that you just draw a line to represent the lens.
Locate the image of the arrow.
J.M. Gabrielse
 Your Turn
(Convex Lens)

optical axis
image
object
F

convex lens

Note: lenses are thin enough that you just draw a line to represent the lens.
Locate the image of the arrow.
J.M. Gabrielse
 Thanks/Further Info
Faulkes Telescope Project: Light & Optics by Sarah
Roberts
Fundamentals of Optics: An Introduction for Beginners by
Jenny Reinhard
PHET Geometric Optics (Flash Simulator)
Thin Lens & Mirror (Java Simulator) by Fu-Kwun Hwang

J.M. Gabrielse