Speed of light• Galileo – “Its fast”• Roemer (~1700) – Period of Jupiter’s moon

– “Its fast, but finite”

• Michelson (1880-1920) – First experimental measurement of the speed of light.

Speed of light in materials

o o

1v c

k

For free space (vacuum) we showed

We expect in any other material

material Material

1v

Speed of light in materials (dielectrics)

For a dielectric material we showed oK

o We observe

o o o o

1 1 1 cv

K K K

dielectricv c

Index of refraction

c cv

nK

cn K

v

We will see later that n varies with frequency of light

Material n

Vacuum 1Air (STP) 1.0003Water 1.33Ethyl alcohol 1.36Glass

Fused quartz 1.46Crown glass 1.52

Light flint 1.58Lucite or Pexiglass 1.51Sodium chloride 1.53Diamond 2.42

Ray model of light

i r

t

ni

nt n̂

Incident Ray Reflected Ray

Transmitted RayRays are a construct to showthe direction the wave is traveling

Rays are generally perpendicularto the surfaces of equal phase (wave fronts).

The Laws that are Empirically Observed

• Law of reflection.

• Snell’s Law of Refraction.

i r

sin sini i t tn n

Reflection Definitions

• External

• Internal

• Specular - Reflection off a smooth surface

• Diffuse - Reflection off a rough surface

i tn n

i tn ne.g. air to glass

e.g. glass to air

Plane Mirrors

ir

Virtual ImageidThe image is the same size as the object

o id dod

How big does your bathroom mirror have to be?

hoy

2oyh

Shift your observation point to a top view and observe the right-left inversion of an image in a

plane mirror.

Corner Reflectors

• The reflected light ray is always parallel to the incident ray.

• Implication for stealth technology.

A More Physical View of the Law of Reflection

A

B C

D

i r

BD ACBD AC

AD AD

i r

sin sini r

i r

ni

nt

A More Physical View of the Law of Reflection

A

B C

D

i r

BD AC

BD AC

AD AD

i r

sin sini r

i r

ni

nt

Paraxial rays

Refraction• The bending of a light ray at the boundary

between two media.

1 1 2 2n sin n sin Snell’s Law:

Refraction Basics

• Incident, reflected, and refracted rays are all in the plane of incidence.

• A ray entering a higher index medium bends toward the normal.

• A ray entering a lower index medium bends away from the normal.

• Relative index of refraction• Vacuum wavelength

sin

sint i

tii t

nn

n

0v c

n n

Example

• A light ray is incident on a water surface at an angle of 30 degrees w.r.t. the normal to the surface. What is the angle of the refracted ray relative to the normal to the surface?

• Does the frequency of the light change at the water boundary?

• Does the wave length change in the water?• How much?

Fermat’s Principle• The actual path between two points taken by a

beam of light is the one that is traversed in the least time.

i

t

ni

nt

S

O

P

h

b

a

x

a-x

222 2

i t i t

b a xSO OP h xt

v v v v

2 2 22

0i t

a xt x

x v h x v b a x

sin sini t

i tv v

sin sini ti tn nc c

sin sini i t tn n

Total Internal Reflection

sin sini i t tn n i tn n

There will always be an angle such that sin

sin 1i it

t

n

n

We define a critical angle for the limiting case:

(even though it can’t be physically)

sin1i i

t

n

n

sin tc ti

i

nn

n

Fiberoptics

it

90 t

c2c t

1 f

nnsin sin 90

n n

nc

nf

How big can be? i

sin sini i t tn n

ni

cladn 1.44

fibern 1.46

Fiberoptics

it

90 t

2sin sin 90 cos 1 sint cc t t t

i f

n n

n n

nc

nf

How big can be? i

sin sini i t tn n 2 2

2 2 22 2cos 1 sin 1 sinc i

t t i

f f

n n

n n

2 22

2 2sin f ci

i i

n n

n n

2 22 2

2 2

1sin f c

iMax f cii i

n nn n

nn n

ni

Dispersion• Difference in wave speed (n) in a material due to frequency

(or wavelength)