# P116B Exam 3 Answers 111507 - PHYSICS 116B - MID-TERM EXAM...

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P HYSICS 116B - M ID -T ERM E XAM 3 A NSWERS - 15 N OVEMBER 2007 I. S HORT - ANSWER QUESTIONS ( M ENTAL S ECURITY C ARDS !) (5 POINTS EACH ) 1. ( 5 points ) You would like to tune in to station KRZY-FM (93.4 MHz) and not hear static from station KBAT-FM (93.1 MHz). The tuning circuit contains a resistor ( R =8 Ω ), an in- ductor ( L =10 -8 H), and a variable capacitor. What value of C should the capacitor have to tune into KRZY-FM? [ Be sure to show your work !] If you are to receive KRZY-FM, you need a receiver with a resonant frequency that is equal to 93.4 MHz. That is related to the natural angular frequency of the inductor and capacitor as f KRZY = " res 2 # = 1 2 1 LC \$ C = 1 L 4 2 f KRZY 2 = 1 10 % 8 2 93.4 10 6 ( ) 2 = 2.90 10 % 10 F 2. ( 5 points ) Maxwell’s equations predict the existence of electromagnetic waves. Is it possible to have a purely electric or purely magnetic wave? Give a reason for your answer. No, because a time-varying magnetic field induces a time-varying electric field (Faraday’s law) and vice versa (the Maxwell-Ampère law). 3. ( 5 points ) To treat myopia , or nearsightedness in one of her patients, an optometrist prescribes a biconcave lens (both surfaces are concave). This means that the image formed by the combination of cornea and lens must be where with respect to the retina? [ Hint : You may find it easiest to sketch a picture.] Biconcave lenses are diverging lenses, so this must mean that the image has been focused at too short a distance (in front of the retina); the diverging lens compensates for the fact that the cornea and lens together focus too strongly. 4. ( 5 points ) A concave cosmetic mirror has a ra- dius of curvature of 1 m. A student checking out the smooth shave provided by his Gillette Fusion razor puts his face 20 cm in front of and to the left of the mirror. Draw a ray-tracing diagram (assuming the student’s face is a plane), and say whether the image he sees is (a) real, inverted, left of the mirror (b) virtual, inverted, left of the mirror (c) real, erect, right of the mirror (d) virtual, erect, right of the mirror

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Physics 116B — Mid-Term Examination 3 — November 14, 2007 — Page 2 of 6 Pages — 5. ( 5 points ) A Mach-Zehnder interferometer, constructed from two identical optical fi- bers as shown in the diagram, has two arms of equal overall length; however, in one one arm a cuvette 3 mm long replaces 3 mm of fiber. An unknown liquid is placed in the cuvette, and light from a HeNe laser ( λ =633 nm) is shined into one end of the in- terferometer. The beam divides at the splitter A into two beams of equal initial amplitude and, of course, with the same initial phase. When the two pulses are combined at B, it is found that the interference pattern is consistent with a phase shift of π /4 between the two beams. What is the index of refraction of the unknown liquid? The index of refraction of glass is 1.5, so the difference in optical path lengths and the phase shift be-
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## This note was uploaded on 04/02/2008 for the course PHYS 116b taught by Professor Haglund during the Fall '07 term at Vanderbilt.

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P116B Exam 3 Answers 111507 - PHYSICS 116B - MID-TERM EXAM...

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