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Unformatted text preview: Chapter 24 Wave Optics Quick Quizzes 1. (c). The fringes on the screen are equally spaced only at small angles where tan sin θ θ ≈ is a valid approximation. 2. (b). The space between successive bright fringes is proportional to the wavelength of the light. Since the wavelength in water is less than that in air, the bright fringes are closer together in the second experiment. 3. (b). The outer edges of the central maximum occur where sin a θ λ = ± . Thus, as a , the width of the slit, becomes smaller, the width of the central maximum will increase. 4. The compact disc. The tracks of information on a compact disc are much closer together than on a phonograph record. As a result, the diffraction maxima from the compact disc will be farther apart than those from the record. 47 48 CHAPTER 24 Answers to Even Numbered Conceptual Questions 2. The wavelength of light is extremely small in comparison to the dimensions of your hand, so the diffraction of light around obstacles 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. 4. The wavelength of light traveling in water would decrease, since the wavelength of light in a medium is given by n n λ λ = , where λ is the wavelength in vacuum and n is the index of refraction of the medium. Since the positions of the bright and dark fringes are proportional to the wavelength, the fringe separations would decrease. 6. Every color produces its own interference pattern, and we see them superimposed. The central maximum is white. The first maximum is a full spectrum with violet on the inside and red on the outside. The second maximum is also a full spectrum, with red in it overlapping with violet in the third maximum. At larger angles, the light soon starts mixing to white again. 8. (a) Two waves interfere constructively if their path difference is either zero or some integral multiple of the wavelength; that is, if the path difference is m λ , where m is an integer. (b) Two waves interfere destructively if their path difference is an odd multiple of one-half of a wavelength; that is, if the path difference equals ( 29 1 2 1 2 2 m m λ λ + = + . 10. The skin on the tip of a finger has a series of closely spaced ridges and swirls on it. When the finger touches a smooth surface, the oils from the skin will be deposited on the surface in the pattern of the closely spaced ridges. The clear spaces between the lines of deposited oil can serve as the slits in a crude diffraction grating and produce a colored spectrum of the light passing through or reflecting from the glass surface....
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This test prep was uploaded on 04/08/2008 for the course PHY 102 taught by Professor Luo during the Spring '08 term at SUNY Buffalo.
- Spring '08