ch27 - CHAPTER 27 INTERFERENCE AND THE WAVE NATURE OF LIGHT...

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Unformatted text preview: CHAPTER 27 INTERFERENCE AND THE WAVE NATURE OF LIGHT ANSWERS TO FOCUS ON CONCEPTS QUESTIONS 1. (e) The first intensity minimum occurs when the difference in path lengths is 1 2 , the second when the difference is 3 2 , and the third when the difference is 5 2 . 2. (a) The angle that specifies the m th bright fringe is given by sin m d = (Equation 27.1). If sin , then m d = . Thus, if and d are both doubled, the angle does not change. 3. (b) According to the discussion in Section 27.2, the difference in path lengths of the light waves increases by one wavelength as one moves from one bright fringe to the next one farther out. 4. d = 1.1 10- 5 m 5. (d) The wavelength water of the light in water is related to the wavelength vacuum in a vacuum by water vacuum water / n = (Equation 27.3). Since the index of refraction of water n water is greater than one, the wavelength decreases when the apparatus is placed in water. The angle that specifies the m th bright fringe is given by sin m d = (Equation 27.1). When the wavelength decreases, the angle also decreases. 6. (d) The down-and-back distance traveled by the light wave in the film is 2400 nm. The wavelength of the light within the film is (see Equation 27.3) film = vacuum / n film = ( 29 600 nm /1.5 = 400 nm . Thus, the down-and-back distance is equivalent to film film (2400 nm) = 6 400 nm . 7. (c) In drawings 1 and 2, light travels through a material with a smaller refractive index toward a material with a larger refractive index, so the reflection at the boundary occurs with a phase change that is equivalent to one-half a wavelength in the material. In drawings 3 and 4, light travels through a material with a larger refractive index toward a material with a smaller refractive index, so there is no phase change upon reflection at the boundary. 149 INTERFERENCE AND THE WAVE NATURE OF LIGHT 8. (e) In film 4, the reflection at the top surface occurs with a phase change that is equivalent to one-half a wavelength in the film, since light travels from a material with a smaller refractive index ( n air = 1.0) toward a material with a larger refractive index ( n film = 1.5). The reflection at the bottom surface occurs without a phase change, since light travels from a material with a larger refractive index ( n film = 1.5) toward a material with a smaller refractive index ( n air = 1.0). The down-and-back distance traveled by the light is one-half of a wavelength. Therefore, the net phase change is one wavelength, which leads to constructive interference. 9. (b) A bright fringe occurs at a point where the thickness of the air wedge has a certain value. As the thickness of the air wedge becomes smaller, the fringe moves to the right where the air wedge is thicker....
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ch27 - CHAPTER 27 INTERFERENCE AND THE WAVE NATURE OF LIGHT...

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