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Chapter 37

# Chapter 37 - 37 Interference of Light Waves CHAPTER OUTLINE...

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37 CHAPTER OUTLINE 37.1 Conditions for Interference 37.2 Young’s Double-Slit Experiment 37.3 Intensity Distribution of the Double-Slit Interference Pattern 37.4 Phasor Addition of Waves 37.5 Change of Phase Due to Reflection 37.6 Interference in Thin Films 37.7 The Michelson Interferometer Interference of Light Waves ANSWERS TO QUESTIONS Q37.1 (a) Two waves interfere constructively if their path difference is zero, or an integral multiple of the wavelength, according to δλ = m , with m = 0123 ,,,, . (b) Two waves interfere destructively if their path difference is a half wavelength, or an odd multiple of λ 2 , described by =+ F H G I K J m 1 2 , with m = . Q37.2 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. Q37.3 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 37.2 and 37.3), the underwater fringe separations will decrease. Q37.4 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. Q37.5 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. Q37.6 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. 381

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382 Interference of Light Waves Q37.7 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 37.5, “Interference in a Wedge-Shaped Film.” Q37.8 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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Chapter 37 - 37 Interference of Light Waves CHAPTER OUTLINE...

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