SM_PDF_chapter27

SM_PDF_chapter27 - Wave Optics CHAPTER OUTLINE 27.1 27.2...

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745 Wave Optics CHAPTER OUTLINE 27.1 Conditions for Interference 27.2 Young’s Double-Slit Experiment 27.3 Light Waves in Interference 27.4 Change of Phase Due to Reflection 27.5 Interference in Thin Films 27.6 Diffraction Patterns 27.7 Resolution of Single-Slit and Circular Apertures 27.8 The Diffraction Grating 27.9 Diffraction of X-Rays by Crystals 27.10 Context Connection Holography ANSWERS TO QUESTIONS Q27.1 (a) Two waves interfere constructively if their path difference is zero, or an integral multiple of the wavelength, according to δ λ = m , with m = 0123 ,,,, K . (b) Two waves interfere destructively if their path difference is a half wavelength, or an odd multiple of 2 , described by δλ =+ F H G I K J m 1 2 , with m = K . Q27.2 The light from the flashlights consists of many different wavelengths (that’s why it’s white) with random time differences between the light waves. There is no coherence between the two sources. The light from the two flashlights does not maintain a constant phase relationship over time. These three equivalent statements mean no possibility of an interference pattern. Q27.3 Every color produces its own pattern, with a spacing between the maxima that is characteristic of the wavelength. With several colors, the patterns are superimposed and it can be difficult to pick out a single maximum. Using monochromatic light can eliminate this problem. Q27.4 Underwater, the wavelength of the light would decrease, water air water = n . Since the positions of light and dark bands are proportional to , (according to Equations 27.2 and 27.3), the underwater fringe separations will decrease. Q27.5 The threads that are woven together to make the cloth have small meshes between them. These bits of space act as pinholes through which the light diffracts. Since the cloth is a grid of such pinholes, an interference pattern is formed, as when you look through a diffraction grating. Q27.6 If the oil film is brightest where it is thinnest, then nnn air oil water << . With this condition, light reflecting from both the top and the bottom surface of the oil film will undergo phase reversal. Then these two beams will be in phase with each other where the film is very thin. This is the condition for constructive interference as the thickness of the oil film decreases toward zero.
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746 Wave Optics Q27.7 As water evaporates from the ‘soap’ bubble, the thickness of the bubble wall approaches zero. Since light reflecting from the front of the water surface is phase-shifted 180° and light reflecting from the back of the soap film is phase-shifted 0°, the reflected light meets the conditions for a minimum. Thus the soap film appears black, as in the illustration accompanying textbook Example 27.4, “Interference in a Wedge-Shaped Film.” Q27.8 If the film is more than a few wavelengths thick, the interference fringes are so close together that you cannot resolve them.
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This note was uploaded on 10/18/2008 for the course PHYS 3Q2341234 taught by Professor Dafsf during the Spring '08 term at UCLA.

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SM_PDF_chapter27 - Wave Optics CHAPTER OUTLINE 27.1 27.2...

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