Geometric Optics

Light What is light? Waves or particles?

Geometric optics: light travels in straight-line paths called rays

This is true if typical distances are much larger than the wavelength

Geometric Optics

both

2

What it is about Phenomena addressed by geometric optics:

Propagation: light goes in straight lines

Reflection: angle of incidence = angle of reflection

Refraction: Snell’s law

Phenomena not addressed by geometric optics:

Polarization

Diffraction

Interference

Photoelectric effect

Geometric Optics 3

Electromagnetic theory

Quantum mechanics

Reflection and Refraction

Geometric Optics

a

r

ba

r

b

incident angle

reflection angle

refraction angle

medium a (e.g. air)

medium b (e.g. glass)

4

The incident, reflected, and refracted rays, and the normal to the surface, all lie in the same plane

Specular and Diffusive Reflection

Geometric Optics

specular reflection: smooth interface, definite reflection angle

diffusive reflection: rough interface, scattered reflection

we’ll discuss this one

5

Image

Geometric Optics

P 'P

mirror

object point image point

Object point: where the rays actually come from Image point: where the rays appear to come from

s

s: object distance s’: image distance

's

here outgoing rays do not actually come from P’ image is virtual if they did, the image would be real

6

Sign Rules for Distances

Geometric Optics

P 'P mirror

object point image point

0s 0's Object distance: when the object is on the same side as the incoming light, s>0, otherwise, s<0

Image distance: when the image is on the same side as the outgoing light, s’>0, otherwise, s’<0

7

Sign Rules for Distances

Geometric Optics

P 'Pobject point image point

0s

0's

Object distance: when the object is on the same side as the incoming light, s>0, otherwise, s<0

Image distance: when the image is on the same side as the outgoing light, s’>0, otherwise, s’<0

refracting interface

8

Lateral Magnification

Geometric Optics

mirror:

object image

s 's

y 'yP 'P

Q 'Q

need at least two points (P,Q) to figure it out

y

ym

'

1

'

m

ss

9

Inverted and Reversed Images Image can be erect (right side up) or inverted (upside

down)

Image can be reversed (“mirror-image” – left hand looks like right and vice versa)

Geometric Optics

hole

mirror camera obscura

a plain mirror image is virtual, erect, and reversed

10

Reflection in a Sphere

Geometric Optics

P 'PC

B

R

h

s

h

s

h

tan

'tan

tan

's

R

h

s

Equations are involved

s’ depends on α

V

11

Reflection in a Sphere

Geometric Optics

P 'PC

B

R

h

s

h

s

h

tan

'tan

tan

's

R

h

s

Use paraxial approximation

V

12

Spherical Mirror Reflection

Geometric Optics

P 'P

Rss

2

'

11

no α dependence!

's

s

13

Focal Point

Geometric Optics

P

F

fR

s

Rs

2'

2

'

11

focal length

object is far away to the left

14

Focal Point

Geometric Optics

F

fR

s

Rs

2

211

works in both ways

object is placed in the focal point

These things are approximately true for spherical mirrors. They are exactly true for parabolic mirrors.

15

Spherical Mirror: s>f

Geometric Optics

P 'P

fss

1

'

11

f

s

's

F

0'

s

fs

16

Spherical Mirror: s<f

Geometric Optics

P 'P

fss

1

'

11

f

s

's

F

0'

s

fsimage is virtual

17

Spherical Mirror Magnification

Geometric Optics

P C

's

R

s

Q

'QV

'Py

'y

s

s

y

ym

''

because triangles PQV and P’Q’V are similar

s’>0: image is real and inverted (m<0) s’<0: image is virtual and erect (m>0)

18

P 'P

Convex Spherical Mirror convex = curving out

All is exactly the same except that f (and R) is negative

Geometric Optics

'ss

P 'P

'ss

convex concave

19

Focal Point of Convex Mirror

Geometric Optics

F

focus is virtual

provided s>0, a convex mirror always forms a virtual, erect, reversed image (same as the plain mirror) m=1 for plain mirror m<1 for convex mirror

20

Principal rays Need them to find image position and magnification

Geometric Optics Geometric Optics

P C

Q

V'P

'Q

F

B

A

QBQ’: ray parallel to the axis reflects through focal point

QAQ’: ray through focal point reflects parallel to the axis

QCQ’: ray through the center reflects back

QVQ’: ray to the vertex forms equal angles with the axis

this construction neglects aberrations

21

Snell’s law

Geometric Optics 22

bbaa nn sinsin a b

medium a (e.g. air)

medium b (e.g. glass)

This is the basic law of refraction

angle of incidence not equal to angle of refraction!

n: index of refraction what is this?

bnan

Index of Refraction = ratio of the speed of light in the material to that in

vacuum

Geometric Optics

v

cn

n>1: light travels slower in the material than in vacuum

What changes when the light passes from one medium to another? * Frequency ? No, it would imply creating/destroying waves * Speed? Yes, because the media have different n * Wavelength? Yes, because λ=v/f

23

Total Internal Reflection Snell’s law may give sinθ>1 – what does it mean?

Geometric Optics 24

Cba nn sin

critical angle

can only happen if ba nn

There are always two rays: reflected and refracted

At some angle, the refracted ray disappears

bnan

Fiber Optics Light can be transmitted along a fiber with almost no

loss due to total internal reflection

Due to impurity of glass, the signal eventually degrades (typical rates are ~50%/km)

Geometric Optics 25

Widely used in communications – much higher frequency than for regular wires, therefore can transmit much more data

Refraction at a Sphere

Geometric Optics

P

B

R

h

s

h

s

h

b

a

tan

'tan

tan

's

h

s

V C

a

b

26

Refraction at a Sphere

Geometric Optics

P

B

R

h

s

h

s

h

b

a

tan

'tan

tan

's

h

s

V C

a

b

27

Refraction at a Sphere Use Snell’s law

Geometric Optics

)()(

ba

b

a

nn

R

nn

s

n

s

n abba

'

sn

snm

b

a 'magnification:

28

bbaa nn sinsin

Thin Lens Lens = an optical system with two refracting surfaces

Geometric Optics

P 'P

1s

'2s

'1s2s

Thin lens:

'12 ss

bnan

1R

2R

29

Thin Lens Equation

Geometric Optics

222111 ',

' R

nn

s

n

s

n

R

nn

s

n

s

n baababba

',,1 12 ssnnn ba assumptions:

fRRn

ss

111)1(

'

11

2121

30

Lens Types

Geometric Optics

021 RR02

1

R

R12 0 RR 021 RR

02

1

R

R21 0 RR

31

Graphical Methods for Lenses Be careful with the focal length sign!

Geometric Optics 32

Graphical Methods for Lenses

Geometric Optics 33