University of California, Berkeley
Physics 110B Fall 2003 (Strovink)
FINAL EXAMINATION
Directions: Do all six 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). A table of Fourier transforms is included with the exam.
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)
A point charge etravelling on the zaxis has
position
r(t)=+ˆzβct (t<0)
=−ˆzβct (t>0) ,
where βis a positive constant that is not 1.
That is, the charge reverses direction instanta-
neously at t= 0, while it is at the origin. The
fields that the charge produces are viewed by an
observer at (x, 0,0), where x>0.
(a.) (15 points)
What magnetic field
Bdoes the observer see at
t=0?
(b.) (15 points)
At time tsuch that ct =x(exactly!), what is the
direction of the electric field
Eseen by the ob-
server? (You need consider only the part of the
total electric field which is dominant at exactly
that time.) Justify your answer.
Problem 2. (30 points)
A plane wave of wavelength λis normally inci-
dent on a thin film that is tinted various shades
of gray. The ratio of incident to transmitted
field amplitude is the aperture function g(s),
where s is a vector from the origin (taken on
the downstream surface of the film) to another
point on its downstream surface. This film has
an aperture function
g(s)=e−s2/2d2.
Because this aperture function is cylindrically
symmetric, the outgoing diffraction pattern is
also cylindrically symmetric: it is a function of
θ, the polar angle of the observer relative to the
beam axis. You may make the approximations
θ1
d22λD ,
where Dis the distance from the film to the
observer.
Calculate the irradiance ratio
R(θ)= I(θ)
I(θ=0) .
Problem 3. (35 points)
The irradiance I0of a mystery light beam is at-
tenuated by each of four devices, applied one
at a time: (A) a grey filter passing half the
incident irradiance; (B) an ˆxpolarizer; (C) a
1
√2(ˆx+ˆy) polarizer; and (D) a device consisting
of a quarter-wave plate (qwp) with slow axis at
+45◦to ˆx, followed by an ˆxpolarizer, followed
by a qwp with slow axis at −45◦to ˆx. The at-
tenuated irradiances observed are, respectively,
IA=1
2I0
IB=1
21+ 1
√2I0
IC=1
2I0
ID=1
21+ 1
√2I0.
With devices (A) through (D) no longer in the
picture, device (E) is inserted into the beam. It
is the same as device (D) except that the ˆxpo-
larizer is rotated to become a ˆypolarizer. What
irradiance IEis observed?
