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 For free space (vacuum) we showed We expect in any other material

Speed of light in materials (dielectrics) For a dielectric material we showed We observe

Index of refraction We will see later that n varies with frequency of light

Ray model of light Incident Ray Reflected Ray ni nt Transmitted Ray Rays are a construct to show the direction the wave is traveling Transmitted Ray Rays are generally perpendicular to the surfaces of equal phase (wave fronts).

The Laws that are Empirically Observed Law of reflection. Snell’s Law of Refraction.

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

Plane Mirrors The image is the same size as the object Virtual Image

How big does your bathroom mirror have to be? 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 B C ni nt A D

A More Physical View of the Law of Reflection B C ni nt A D

Paraxial rays

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

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. S h ni O x nt b P a-x a

Total Internal Reflection There will always be an angle such that (even though it can’t be physically) We define a critical angle for the limiting case:

Fiberoptics nc ni nf How big can be?

Fiberoptics nc ni nf How big can be?

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