W9_parallel_resonance.eps

364 Week 10: Maxwell’s Equations and Light

If one considers atipped surface (that still completely absorbs the wave) one has to

compute the flux of the Poynting vector into the surface and reduce the effective force

by the cosine of the angle of incidence:

F~=A

S~

c

cos(θ) (897)

but the force is still exerted in the direction of the incident wave.

If the wave is incident on a tipped surface thatreflectsthe wave, it exertstwicethe force

from the radiation pressure alone, but only along a lineperpendicular to the surface,

much like the homework problem involving beads bouncing on the pan ofa balance in

the Mechanics text. In this case we expect:

F~= 2AS~

c

cos(θ)nˆ (898)

whereˆnis a normal unit vector pointinginto the surface in question. The momentum

density of the incident wave parallel to the surface is unchanged while the momentum

density perpendicular to the surface reverses. As noted above,this is an idealization as

the reflected wave will always have slightly less energy density than the incident one if

the surface itself recoils and gains energy from the wave.

Homework for Week 10

Problem 1.

Physics Concepts

Make this week’s physics concepts summary as you work all of the problems in this week’s

assignment. Be sure to cross-reference each concept in the summary to the problem(s)

they were key to. Do the work carefully enough that you can (after it has been handed

in and graded) punch it and add it to a three ring binder for review andstudy come

finals!

Problem 2.

As always, we need to rederive the principle results of the week on our own for homework

(has it occurred to you yet that this is one of the things we are doing?). So let’s start

by using Maxwell’s equations to show for az-directed plane wave (whereE~andB~are

independent ofxandy) that:

∂Ex

∂z

= −

∂By

∂t

(899)

∂By

∂z

= −μ 0 ǫ 0

∂Ex

∂t

(900)