Speed of light

1
Speed of light

• Galileo Its fast
• Roemer (1700) Period of Jupiters moon
• Its fast, but finite
• Michelson (1880-1920) First experimental
  measurement of the speed of light.

2
Speed of light in materials
For free space (vacuum) we showed
We expect in any other material
3
Speed of light in materials (dielectrics)
For a dielectric material we showed
We observe
4
Index of refraction
We will see later that n varies with frequency of
light
5
Ray model of light
Incident Ray
Reflected Ray
ni
nt
Transmitted Ray
Rays are a construct to show the direction the
wave is traveling
Rays are generally perpendicular to the surfaces
of equal phase (wave fronts).
6
The Laws that are Empirically Observed

• Law of reflection.
• Snells Law of Refraction.

7
Reflection Definitions

• External
• Internal
• Specular - Reflection off a smooth surface
• Diffuse - Reflection off a rough surface

e.g. air to glass
e.g. glass to air
8
Plane Mirrors
Virtual Image
9
How big does your bathroom mirror have to be?
h
Shift your observation point to a top view and
observe the right-left inversion of an image in a
plane mirror.
10
Corner Reflectors

• The reflected light ray is always parallel to the
  incident ray.
• Implication for stealth technology.

11
A More Physical View of the Law of Reflection
C
B
ni
A
D
nt
12
A More Physical View of the Law of Reflection
C
B
ni
A
D
nt
13
Paraxial rays
14
Refraction

• The bending of a light ray at the boundary
  between two media.

Snells Law
15
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

16
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?

17
Fermats Principle

• The actual path between two points taken by a
  beam of light is the one that is traversed in the
  least time.

S
h
ni
O
x
nt
b
P
a-x
a
18
Total Internal Reflection
There will always be an angle such that
(even though it cant be physically)
We define a critical angle for the limiting case
19
Fiberoptics
nc
ni
nf
How big can be?
20
Fiberoptics
nc
ni
nf
How big can be?
21
Dispersion

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

(or wavelength)