PHYS212 : Homework

## Homework Assignment 7 (due 3/30)

Reflection and Refraction

1. (a) Use Snell's law and the expression for the reflection coefficient at a planar interface

to show that Brewster's angle, the angle of incidence at which no reflection occurs, is given by

(b) Total internal reflection can occur at a planar interface under certain circumstances. It occurs for angles of incidence greater than the critical angle for which . Use Snell's law to find an expression for .

2. We can reduce the reflections from an interface between two media with impedances and by inserting a layer of a third material with impedance such that . For normal incidence, find an expression for the optimal value of (i.e., the value giving minimal reflection) in terms of and .

3. The average intensity of an acoustic wave is given by

where is the acoustic impedance of the medium.

(a) Use this expression and the reflection and transmission coefficients describing amplitudes we derived in class to find intensity transmission and reflection coefficients

for normal incidence.

(b) Verify that these expressions conserve energy at the boundary. That is, show that

 Copyright © 2003-2009, Lewis A. Riley Updated Tue Apr 14 02:04:45 2009