SM_chapter38

# SM_chapter38 - 38 Diffraction Patterns and Polarization...

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38 Diffraction Patterns and Polarization CHAPTER OUTLINE 38.1 Introduction to Diffraction Patterns 38.2 Diffraction Patterns from Narrow Slits 38.3 Resolution of Single-Slit and Circular Apertures 38.4 The Diffraction Grating 38.5 Diffraction of X-Rays by Crystals 38.6 Polarization of Light Waves ANSWERS TO QUESTIONS Q38.1 Audible sound has wavelengths on the order of meters or centimeters, while visible light has a wavelength on the order of half a micrometer. In this world of breadbox-sized objects, λ a is large for sound, and sound diffracts around behind walls with doorways. But λ a is a tiny fraction for visible light passing ordinary-size objects or apertures, so light changes its direction by only very small angles when it diffracts. Another way of phrasing the answer: We can see by a small angle around a small obstacle or around the edge of a small opening. The side fringes in Figure 38.1 and the Arago spot in the center of Figure 38.3 show this diffraction. We cannot always hear around corners. Out-of-doors, away from reﬂecting surfaces, have some- one a few meters distant face away from you and whisper. The high-frequency, short-wavelength, information- carrying components of the sound do not diffract around his head enough for you to understand his words. Suppose an opera singer loses the tempo and cannot immediately get it from the orchestra conductor. Then the prompter may make rhythmic kissing noises with her lips and teeth. Try it—you will sound like a birdwatcher trying to lure out a curious bird. This sound is clear on the stage but does not diffract around the prompter’s box enough for the audience to hear it. Q38.2 The wavelength of visible light is extremely small in comparison to the dimensions of your hand, so the diffraction of light around an obstacle the size of your hand is totally negligible. However, sound waves have wavelengths that are comparable to the dimensions of the hand or even larger. Therefore, significant diffraction of sound waves occurs around hand-sized obstacles. *Q38.3 Answer (d). The power of the light coming through the slit decreases, as you would expect. The central maximum increases in width as the width of the slit decreases. In the condition sin θ λ = a for destructive interference on each side of the central maximum, θ increases as a decreases. *Q38.4 We consider the fraction λ L / a . In case (a) and in case (f) it is λ 0 L / a . In case (b) it is 2 λ 0 L /3 a . In case (c) it is 3 λ 0 L /2 a . In case (d) it is l 0 L /2 a . In case (e) it is l 0 2 L / a . The ranking is e > c > a = f > b > d. *Q38.5 Answer (b). The wavelength will be much smaller than with visible light. 379

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380 Chapter 38 *Q38.6 Answer (c). The ability to resolve light sources depends on diffraction, not on intensity. Q38.7 Consider incident light nearly parallel to the horizontal ruler. Suppose it scatters from bumps at distance d apart to produce a diffraction pattern on a vertical wall a distance L away. At a point of height y , where θ = y L gives the scattering angle θ , the character of the interference is determined by the shift δ between beams
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