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Unformatted text preview: Physics 4510  Optics Fall 2007 Homework Set #7 — due Thursday' December 13I 200? HW 7 is optional. I recommend you at least sketch out solutions for the problems
because you can expect stuff like it on the final. If you hand it in to my mail box before
Thursday 12l13, I will make an effort to mark it and return it to you by Friday afternoon,
so you can use it to study for the final exam. You can pick up graded homeworks from
my assistant in JILA Room A4060 on Friday. The solution set will be posted online
Friday 12/14 morning. If you do hand the homework in before Thursday night, and you
do reasonably well on it, i will use it to improve some of your score on some other
homework during the year. The formula for doing this will be slightly more complicated
than simply "replacing the lowest score", because not all the homeworks had the same
weight. But in any case handing in HWY will not hurt your overall course grade. 1. (Hecht 8.1, Second Edition) Describe completely the state of polarization of each of
the following waves: A n
a) E=iEocos(zc zw rJonCOS(rczwr) n A b) E=iEosin2 .7 (z/A—w)—jeosin2 7: (2/2..— w)
G) E =IiEosin {w r — K2) +3: E0 sin ((9? —r2— 7r/4)
d) E =’EEO cos {a} r — K2) +350 cos (a) r—KZ + M2) 2. (Hecht 8.11) Suppose than an ideal polarizer is rotated at a rate a: between a similar pair of stationary crossed polarizers. Show that the emergent flux density will be
modulated at four times the rotational frequency. In other words. show that i=2? (lac/039cm?) 3. (Hecht 8.27) Take two ideal polaroids (the first with its axis vertical and the second,
horizontal) and insert between them a stack of 10 halfwave plates, the ﬁrst with its fast
axis rotated rr/40 rad from the vertical, and each subsequent one rotated 3/40 rad from
the previous one. Determine the ratio of the emerging to incident lrradiance. showing
your logic clearly. 4. (Hecht 8.28) Suppose you were originally given only a linear polarizer and a quarter
wave plate. How could you determine which was which? 5. (Hecht 8.32) Imagine thatwe have unpolarized room light incident almost normally
on the glass surface of a radar screen. A portion of it would be specularly reflected
back toward the viewer and would thus tend to obscure the display. Suppose now that we cover the screen with a rightcircular polarizer, as shown in Fig. 8.73. Trace the
incident and reflected beams, indicating their polarization states. What happens to the
reflected beam? Right circular polarizat _ .. ..— Quarterwave plat! ._ 6. Roughly speaking, the theoretical best passive {i.e., without using feedback] stability
you can get in a laser frequency is given roughly by 5v cavity/N, where the numerator is
the linewidth of the cavity. and N is the average number of photons in the cavity at any
time. Suppose you have a relatively short cavity of 1 mm. a relatively low output power
of 0.5 mW. and a relatively low finesse of 10. The lasing wavelength is 820 nm. a) What is 51: cavity/N? b) How much time does a typical photon spend in the cavity before it
escapes? c) How many photons are in the cavity mode at any given time, on
average? d) What's the theoretical limit on passive laser frequency stability? ?. I want to measure the power in a laser beam with freq 400 TH: with about 10 nW of
power. i am required to make my measurement in 1 ms. What is the shotnoise limit on
the fractional precision I can achieve? 8. l arrange for two laser beams to fail on a detector. One has frequency 400 TH: and
10 nW of power. One has frequency 400.001 THz and 10 mW of power. If my detector
has a quantum efficiency of 0.5 (roughly 0.5 electrons come out for every one photon
that falls on the detector), what is the amplitude of the output current at 1 GHz? ...
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 Fall '06
 gustafsson
 Light, Polarization, Hecht

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