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chapter22

# chapter22 - Reection and Refraction of Light 285 8 10 The...

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PROBLEM SOLUTIONS 22.1 The total distance the light travels is d D R R = = 2 2 3 center to center Earth Moon .84 10 6 38 10 1 76 10 7 52 10 8 6 6 8 × × × ( ) = × . . . m m Therefore, v = = × = × d t 7 52 10 3 00 10 8 8 . . m 2.51 s m s 22.2 (a) The energy of a photon is E hf hc = = λ , where Planck’s constant is h = × 6 63 10 34 . J s and the speed of light in vacuum is c = × 3 00 10 8 . m s . If λ = × 1 00 10 10 . m , E = × ( ) × ( ) × 6 63 10 3 00 10 10 34 8 . . J s m s 1.00 m 10 = × 1 99 10 15 . J (b) E = × ( ) × = 1 99 10 1 10 1 2 15 . . J eV 1.602 J 19 4 10 4 × eV (c) and (d) For the x-rays to be more penetrating, the photons should be more energetic. Since the energy of a photon is directly proportional to the frequency and inversely proportional to the wavelength, the wavelength should decrease , which is the same as saying the frequency should increase . 22.3 (a) E hf = = × ( ) × ( ) 6 63 10 5 00 10 1 34 17 . . J s Hz eV 1.60 × = × 10 2 07 10 19 3 J eV . (b) E hf hc = = = × ( ) × ( ) × λ 6 63 10 3 00 10 34 8 . . J s m s 3.00 10 1 10 6 63 10 19 2 9 nm nm m J = × . E = × × = 6 63 10 1 10 4 14 19 19 . . J eV 1.60 J e V

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286 Chapter 22 22.4 (a) λ 0 8 7 3 00 10 10 5 50 10 = = × × = × c f . . m s 5.45 Hz m 14 (b) From Table 22.1 the index of refraction for benzene is n = 1 501 . . Thus, the wavelength in benzene is λ λ n n = = × = × 0 7 7 5 50 10 3 67 10 . . m 1.501 m (c) E hf = = × ( ) × ( ) 6 63 10 5 45 10 1 1 60 34 14 . . . J s Hz eV × = 10 2 26 19 J eV . (d) The energy of the photon is proportional to the frequency, which does not change as the light goes from one medium to another. Thus, when the photon enters benzene, the energy does not change . 22.5 The speed of light in a medium with index of refraction n is v = c n , where c is its speed in vacuum. (a) For water, n = 1 333 . , and v = × = × 3 00 10 1 333 2 25 10 8 8 . . . m s m s (b) For crown glass, n = 1 52 . , and v = × = × 3 00 10 1 52 1 97 10 8 8 . . . m s m s (c) For diamond, n = 2 419 . , and v = × = × 3 00 10 2 419 1 24 10 8 8 . . . m s m s 22.6 (a) From λ f c = , the wavelength is given by λ = c f . The energy of a photon is E hf = , so the frequency may be expressed as f E h = , and the wavelength becomes λ = = = c f c E h hc E (b) Higher energy photons have shorter waveleng ths. 22.7 From Snell’s law, n n 2 2 1 1 sin sin θ θ = . Thus, when θ 1 45 = ° and the first medium is air ( n 1 1 00 = . ), we have sin . sin θ 2 2 1 00 45 = ( ) ° n . (a) For quartz, n 2 1 458 = . , and θ 2 1 1 00 45 1 458 29 = ( ) ° = ° sin . sin . (b) For carbon disulfide, n 2 1 628 = . , and θ 2 1 1 00 45 1 628 26 = ( ) ° = ° sin . sin . (c) For water, n 2 1 333 = . , and θ 2 1 1 00 45 1 333 32 = ( ) ° = ° sin . sin .
Reflection and Refraction of Light 287 22.8 (a) From geometry, 1 25 40 0 . sin . m = d ° , so d = 1 94 . m (b) 50 0 . ° above horizontal , or parallel to the incident ray 22.9 n n 1 1 2 2 sin sin θ θ = sin . sin . θ 1 1 333 45 0 = ° sin ( . )( . ) . θ 1 1 333 0 707 0 943 = = θ 1 70 5 = ° . 19 5 . ° above the horizontal 22.10 (a) n c = = × × = v 3 00 10 2 17 10 1 38 8 8 .

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chapter22 - Reection and Refraction of Light 285 8 10 The...

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