1

Geometric optics

Light reflects on interface of two media, following the law of reflection:

ir

Incident light

Normal of the interface

Reflected light

with respect to the normal of the interface.

with respect to the normal of the interface.

2

Planar mirror

The image of an object in front of a planar (flat) mirror: On the other side of the mirror. The image distance di equals the object distance do.

The image has the same height as the object, right side up and virtual.

Concept question: when you look into a flat mirror at your image, it seems that your left and right are reversed (you raise your right hand, your image seems to raise its left hand), but not up and down (your image is still up right). If you rotate the mirror about the plane’s normal direction, your image does not rotate at all. It seems that the plane mirror has an axial symmetry about its normal direction. Then why the mirror treat left/right differently than up/down? Class discussion.

3

Planar mirror

The full length mirror question asked again: Asked: what is the minimum length of this mirror for the penguin to see her full height? Asked again: what is the minimum length of this mirror for you to the penguin of her full height

in the mirror?

4

Spherical mirror

Focal point and focal length with respect to the sphere center and its radius

Concave mirror Convex mirror2

Rf

2

Rf

A

V

12

3

Prove: 1 = 2 = 3, so CF = FA. When A is very close to the principle axis, CF + FA ≈ CA = R.So CF ≈ 0.5R, or FV = f = 0.5R

R

Discussion: in a sunny day, you are given a concave mirror and a tape measure by your mean physics professor and asked to find out the focal length of this mirror. What do you plan to do in order to survive this test?

5

Spherical mirror

The object (height to the principal axis, distance to the midpoint of the mirror) and image (height, distance) relationship: The mirror equation (for both concave and convex mirrors):

fdd oi

111

o

i

o

i

d

d

h

hm Together with this: One can analytically solve

many problems.

6

Spherical mirror

The object (height to the principal axis, distance to the midpoint of the mirror) and image (height, distance) relationship: The sign conventions:

Concave mirrorconverges

Convex mirrordiverges

Converge, real, upright “+”Diverge, virtual, inverted “–”

7

Ray diagram with concave mirror

C F

Object distance: do > 2f

do

di

ho

hi

f

From the ray diagram: the image is up-side-down, real and shrinked.

From the mirror equation:fdd io

111

fd

fd

dfd o

o

oi

111

fd,ff

f

fd

f

d

d,fd,

fd

fdd o

oo

io

o

oi 21

2or0

So: 1and0 m,d

d

h

hm

o

i

o

i We get the same conclusion: the image is up-side-down, real and smaller than the object.

8

Ray diagram with concave mirror

C F

Object distance: do = 2f

do

di

ho

hi

f

From the ray diagram: the image is up-side-down, real and the same size.

From the mirror equation:fdd io

111

fd

fd

dfd o

o

oi

111

12

or222

2

ff

f

d

d,fd,f

ff

ff

fd

fdd

o

io

o

oi

So: 1and1 m,d

d

h

hm

o

i

o

i We get the same conclusion: the image is up-side-down, real and the same size as the object.

9

Ray diagram with concave mirror

CF

Object distance: f < do < 2f

do

diho

hi

f

From the mirror equation: what conclusion can you work out? fdd io

111

fd

fd

dfd o

o

oi

111

fd,fd

f

d

d,df,

fd

fdd o

oo

io

o

oi 21or0

So: 1and0 m,d

d

h

hm

o

i

o

i We get the same conclusion: the image is up-side-down, real and larger than the object.

From the ray diagram: the image is up-side-down, real and larger

10

Ray diagram with concave mirror

C F

Object distance: do = f

do

diho

hi

f

From the mirror equation: what conclusion can you work out? fdd io

111

0111

fd

fd

dfd o

o

oi

,d

d,d

o

ii or

So: m,d

d

h

hm

o

i

o

i andWe get the same conclusion: There is no image, or the image is infinitely far away.

From the ray diagram: the image seems to be far away.

11

Ray diagram with concave mirror

C F

Object distance do < f

do

di

ho

hi

f

From the mirror equation: what conclusion can you work out? fdd io

111

fd

fd

dfd o

o

oi

111

fd,fd

f

d

d,

fd

fdd o

oo

i

o

oi

1and0

So: 1and0 m,d

d

h

hm

o

i

o

i We get the same conclusion: the image is up-side-down, virtual and larger than the object.

From the ray diagram: the image is upright, virtual and larger

12

Ray diagram with convex mirror

Before we move to all those diagrams for convex mirror, how about this problem:

Use the mirror equation to prove that in the case of a convex mirror, the image is always virtual, upright and smaller than the object.

fdd io

111Mirror equation:

So: 1and0 m,d

d

h

hm

o

i

o

i

fd

fd

dfd o

o

oi

111Solve for 0and00

o

o

oi df,

fd

fdd , or

0remember1, and0

ffd

f

d

d,

fd

f

d

d

oo

i

oo

iso

Need to prove that and0id 1m

13

Ray diagram with convex mirror

C

Fdodi

hohi

f

14

example

You place a candle 75 cm in front of a concave spherical mirror with the candle sit upright on the principal axis. The mirror is part of a sphere with a radius of R = 50 cm. You use a small while screen to find an up-side-down image of the size of 0.5 cm. What is the size of the candle?

fdd io

111Mirror equation: And:

o

i

o

i

d

d

h

hm

What are given: down)side(upcm50cm252

cm75 .h,R

f,d io

A real, up-side-down image.

fd

fd

dfd o

o

oi

111Solve for cm537cm

2575

2575.

fd

fdd

o

oi

, or

The fromo

i

o

i

d

d

h

hm

cm1cm537

75)50(

.

.

d

dh

m

hh

i

oiioThe result

15

telescope

You have two concave spherical mirrors. The first mirror is large and has a spherical radius R = 50 cm. The second mirror is small and has a spherical radius r = 5 cm. You want to construct a telescope that has a magnification of 1000 to look at the moon. State one possible design.