W9_parallel_resonance.eps

376 Week 11: Light

Many materials also differentially absorb light and only “reflect” particular wavelengths

and hence colors.

We will assume that the law of reflection holds, more or less perfectly, for shiny smooth

good conducting (e.g. metal) surfaces, such as a polished piece of silver or aluminum.

This in turn will help us understand howmirrorswork to form images of objects next

week.

11.3: Snell’s Law

D

2

θ 1

λ

λ 1

θ 1

θ 2

Figure 144: When light is incident on a transparent dielectric surface, it is partially transmitted and
partially reflected. Since itsspeedchanges, however, the light mustchange directionat the surface
as shown.

Light is incident on a surface that separates two transparent media with different indices

of refractionn 1 andn 2 (where we assume for the moment thatn 1 < n 2 although that

isn’t necessary in the end). This is illustrated in figure 144 above.

It should be fairly obvious that thefrequencyof light in the two media cannot change.

If the same number of wavefronts per second do not pass each point in either medium,

wavefronts must be building up in between. This in turn means that energy (associated

with the wavefronts) must be building up. This simply does not happen.

It should also be less obvious that the wavefronts themselves – theplaces where the waves

reach their maximum amplitudes – should be the same just inside and just outside the

media interface. For it to be otherwise would require a very strangecharge distribution

on the surface itself, one that one cannot easily imagine arising.

Since the wave mustchange speedacross the media interface, and since the speed of the

wave is given by:

v=c

n

=f λ (920)

with the same frequency on both sides, it is clear that the wavelength

λ=

c

nf

(921)

mustalsochange, being longer where the speed of light is greater (andnis smaller).

Simple geometry based on these simple ideas requires that the wave will also change

direction. We can compute this change and direction from the figureabove. If we look

at the top triangle with angleθ 1 and hypotenuseDand the bottom triangle with angle