Phys 375 – Prof. Hall
Homework #4, due October 13&14, 2008
1) A right-elliptically polarized light wave is traveling in the z direction. The major axis
of the ellipse is along the x axis, and has magnitude E0. The minor axis is half as large as
the major axis.
a) (2 points) Draw a diagram of what the electric field vector looks like in the x-y
plane for one oscillation period.
b) (2 points) Write down a vector expression describing the electric field as a
function of
r
r, k
r
, ω, and t.
2) Birefringent crystals have a special axis, known as the optical axis. Light waves which
are polarized parallel the optical axis experience a different index of refraction than light
waves polarized perpendicular to the optical axis. For calcite, n|| = 1.486, while n⊥ =
1.658, at the sodium wavelength of 589.3 nm.
a) (3 points) Show that the difference in time it takes the two polarizations to
cross a calcite crystal of thickness d is ⊥
−=Δ nn
c
d
t|| .
b) (3 points) Show that the phase difference between the two polarization after
crossing the crystal is ⊥
−=Δ nn
d
||
2
λ
πφ
.
c) (3 points) What thickness is needed to create a phase difference of π/2? (A
crystal of this thickness is known as a quarter-wave plate.)
d) (3 points) Show that if a linearly polarized light wave is incident upon a
quarter-wave plate, and the optical axis is 45 degrees from the polarization direction, then
the light emerges as circularly polarized.
2) (6 points) Unpolarized light is incident upon two crossed polarizers, so that no light
is transmitted through the pair. A sample of corn syrup is inserted between the two
polarizers, and then 3% of the unpolarized light incident upon the first polarizer is now
transmitted through the second polarizer. By what angle did the corn syrup rotate the
direction of polarization of the light incident upon it?
3) (5 points) Pedrotti, problem 15-2.
5) (6 points) An ideal polarizer rotates with an angular frequency of ω between a pair of
stationary crossed polarizers. The set of three polarizers is illuminated by unpolarized
light. Show that the intensity of the light transmitted by the entire apparatus as a function
of time is 8/))4cos(1(
0tII
ω
−= , where I0 is the intensity of the unpolarized light.
