more and more optics

more and more optics - Physics 4510 Optics Fall 2007...

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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 z-w rJ-onCOS(rcz-wr) 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 half-wave 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 right-circular 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- _ .. -..— Quarter-wave 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 shot-noise 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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more and more optics - Physics 4510 Optics Fall 2007...

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