University of California, Berkeley
Physics 110B Spring 2004 (Strovink)
EXAMINATION 3
Directions: Do all three problems, which have unequal weight. This is a closed-book closed-note
exam except for Griffiths, Pedrotti, a copy of anything posted on the course web site, and anything
in your own original handwriting (not Xeroxed). Calculators are not needed, but you may use one if
you wish. Laptops and palmtops should be turned off. Use a bluebook. Do not use scratch paper –
otherwise you risk losing part credit. Show all your work. Cross out rather than erase any work that
you wish the grader to ignore. Justify what you do. Express your answer in terms of the quantities
specified in the problem. Box or circle your answer.
Problem 1. (30 points)
In a medium with (fixed) conductivity σ, the
ratio of complex fields ˜
H/ ˜
Eis given by the
complex admittance
˜
Z−1=˜
H
˜
E
=
µ1+β2+1
2
1
2+i1+β2−1
2
1
2,
where β≡σ
ω , and the (fixed) dielectric constant
and the (fixed) magnetic permeability µare
due to the effects of bound electrons.
At normal incidence at the interface between
two dissimilar materials 1 and 2, the (complex)
electric field amplitude reflected back into ma-
terial 1 is expressed as a (complex) ratio ˜
Rto
the (complex) incident amplitude. By matching
boundary conditions for the electric and mag-
netic fields, ˜
Ris routinely found to be given by
the standard result
˜
R=˜
Z−1
1−˜
Z−1
2
˜
Z−1
1+˜
Z−1
2
.
Consider the case in which material 1 is an insu-
lator (β= 0) and material 2 is a poor conductor
(β1), with 1/µ1=2/µ2. Calculate the
reflection amplitude ratio ˜
Rto lowest nonvan-
ishing order in β.
Problem 2. (35 points)
An ideal wave plate of thickness Dwith phase
retardation difference
δ≡(ns−nf)ωD
c,
having its slow (ns) axis along the direction
(ˆxcos φ+ˆysin φ), is represented by the Jones
matrix
MW(φ)=
cos δ
2+isin δ
2cos 2φisin δ
2sin 2φ
isin δ
2sin 2φcos δ
2−isin δ
2cos 2φ
A beam of light traveling in the ˆzdirection passes
through a device that consists of the following
ideal components:
•First, a quarter-wave-plate (qwp:δ=π
2)with
slow axis at φ=+45
◦;
•Next, an xpolarizer;
•Finally, a qwp with slow axis at φ=−45◦.
(a.) (10 points)
Calculate the Jones matrix that represents the
effect of this device.
(b.) (15 points)
Given that a beam is observed to emerge from
this device, calculate its state of polarization.
