Problem%20Set%208%20Solutions

Problem%20Set%208%20Solutions - 13(a We choose a horizontal...

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approximately equal to 1). Thus, combining these phase differences with λ = 0.600 µ m, we have () 21 2 1 3.50 m 4.00 m 3.50 m 1 1.60 1.40 1 1.40 0.600 m 0.600 m 0.833. LL L nn n µµ λλ −+ −= + = (b) Since the answer in part (a) is closer to an integer than to a half-integer, the interference is more nearly constructive than destructive. 13. (a) We choose a horizontal x axis with its origin at the left edge of the plastic. Between x = 0 and x = L 2 the phase difference is that given by Eq. 35-11 (with L in that equation replaced with L 2 ). Between x = L 2 and x = L 1 the phase difference is given by an expression similar to Eq. 35-11 but with L replaced with L 1 L 2 and n 2 replaced with 1 (since the top ray in Fig. 35-37 is now traveling through air, which has index of refraction
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(b) The slit separation d needs to be decreased. (c) In this case, the 400 nm wavelength in the m = 4 diffraction is to occur at 90°. Thus d new sin θ = m λ d new = (4)(400 nm)/sin(90°) = 1600 nm . This represents a change of | d | = d d new = 200 nm = 0.20 μm. 22. (a) We use Eq. 35-14 to find d : d sin = m λ d = (4)(450 nm)/sin(90°) = 1800 nm . For the third order spectrum, the wavelength that corresponds to = 90° is λ = d sin(90°)/3 = 600 nm . Any wavelength greater than this will not be seen. Thus, 600 nm < 700 nm are absent.
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27. Consider the two waves, one from each slit, that produce the seventh bright fringe in the absence of the mica. They are in phase at the slits and travel different distances to the seventh bright fringe, where they have a phase difference of 2 π m = 14 π . Now a piece of mica with thickness x is placed in front of one of the slits, and an additional phase difference between the waves develops. Specifically, their phases at the slits differ by 222 1 π λ π λ π λ xxx n m −= bg where λ m
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This note was uploaded on 05/04/2010 for the course PHYS 11b taught by Professor Mobius during the Spring '09 term at Harvard.

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Problem%20Set%208%20Solutions - 13(a We choose a horizontal...

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