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 dD RR =− = 2 23 center to center Earth Moon .84 10 6 38 10 1 76 10 7 52 10 866 8 ×− × () .. . m m ThereFore, v == × d t 752 10 300 10 8 8 . . m 2.51 s ms 22.2 (a) The energy oF a photon is Eh fh c λ , where Planck’s constant is h 663 10 34 . J s and the speed oF light in vacuum is c 8 m s . IF 100 10 10 m , E = ×⋅ ( ) × ( ) × 6 63 10 3 00 10 10 34 8 Js 1.00 m 10 = × 199 10 15 J (b) E × = 1 10 12 15 J eV 1.602 J 19 41 0 4 × eV (c) and (d) ±or 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) f × ( ) × ( ) 6 63 10 5 00 10 1 34 17 H z eV 1.60 × 10 207 10 19 3 J eV . (b) f hc == = ( ) × ( ) × 6 63 10 3 00 10 34 8 3.00 10 1 10 19 29 nm nm m J . E × = 1 10 414 19 19 J eV 1.60 J e V

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286 Chapter 22 22.4 (a) λ 0 8 7 300 10 10 550 10 == × × c f . . ms 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 n n × 0 7 7 367 10 . . m 1.501 m (c) Eh f × ( ) × ( ) 6 63 10 5 45 10 1 160 34 14 .. . Js H z eV × = 10 226 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 = cn , where c is its speed in vacuum. (a) For water, n = 1 333 . , and v = × 1 333 225 10 8 8 . . . (b) For crown glass, n = 152 . , and v = × 197 10 8 8 . . . (c) For diamond, n = 2 419 . , and v = × 2 419 124 10 8 8 . . . 22.6 (a) From fc = , the wavelength is given by = cf . The energy of a photon is f = , so the frequency may be expressed as fE h = , and the wavelength becomes = c f c hc E (b) Higher energy photons have shorter waveleng ths. 22.7 From Snell’s law, nn 22 11 sin sin θθ = . Thus, when θ 1 45 and the ± rst medium is air ( n 1 100 = . ), we have sin . sin 2 2 45 = ( ) ° n . (a) For quartz, n 2 1 458 = . , and 2 1 1 458 29 = () ° sin .s i n . (b) For carbon disul± de, n 2 1 628 = . , and 2 1 1 628 26 = ° sin i n . (c) For water, n 2 1 333 = . , and 2 1 1 333 32 = ° sin i n .
Ref ection and ReFraction oF Light 287 22.8 (a) From geometry, 125 400 .s i n . m = d ° , so d = 194 . m (b) 50 0 . ° above horizontal , or parallel to the incident ray 22.9 nn 11 2 2 sin sin θθ = sin . sin . θ 1 1 333 45 0 sin ( . )( . ) . 1 1 333 0 707 0 943 == 1 70 5 19 5 . ° above the horizontal 22.10 (a) n c × × = v 300 10 217 10 138 8 8 . . . ms (b) From Snell’s law, 22 sin sin = , 2 1 2 1 100 231 = = () ° −− sin sin sin i n . n n 0 284 16 5 1 . sin . . = = ° 22.11 (a) From Snell’s law, n n 2 2 300 19 24 15 ° ° = sin sin i n .

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This note was uploaded on 04/23/2010 for the course DS SAD taught by Professor Asd during the Spring '10 term at A.T. Still University.

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

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