33_InstructorSolutions

33_InstructorSolutions - THE NATURE AND PROPAGATION OF...

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33-1 T HE N ATURE AND P ROPAGATION OF L IGHT 33.1. IDENTIFY: For reflection, ra θ = . SET UP: The desired path of the ray is sketched in Figure 33.1. EXECUTE: 14.0 cm tan 11.5 cm φ = , so 50.6 = ° . 90 39.4 r = −= °° and 39.4 = = ° . EVALUATE: The angle of incidence is measured from the normal to the surface. Figure 33.1 33.2 IDENTIFY: For reflection, = . SET UP: The angles of incidence and reflection at each reflection are shown in Figure 33.2. For the rays to be perpendicular when they cross, 90 α = ° . EXECUTE: (a) 90 += ° and 90 β ° , so = . 90 2 ° and 180 2 = ° . (b) 11 22 (180 ) (180 90 ) 45 =− = ° ° . EVALUATE: As 0 ° , 180 ° . This corresponds to the incident and reflected rays traveling in nearly the same direction. As 90 ° , 0 ° . This corresponds to the incident and reflected rays traveling in nearly opposite directions. Figure 33.2 33

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33-2 Chapter 33 33.3. IDENTIFY and SET UP: Use Eqs.(33.1) and (33.5) to calculate v and . λ EXECUTE: (a) 8 8 2.998 10 m/s so 2.04 10 m/s 1.47 cc nv vn × == = = × (b) 0 650 nm 442 nm 1.47 n = EVALUATE: Light is slower in the liquid than in vacuum. By , vf = when v is smaller, is smaller. 33.4. IDENTIFY: In air, 0 cf = . In glass, 0 n = . SET UP: 8 3.00 10 m/s c EXECUTE: (a) 8 0 14 517 nm 5.80 10 Hz c f × = × (b) 0 517 nm 340 nm 1.52 n = EVALUATE: In glass the light travels slower than in vacuum and the wavelength is smaller. 33.5. IDENTIFY: c n v = . 0 n = , where 0 is the wavelength in vacuum. SET UP: 8 c . n for air is only slightly larger than unity. EXECUTE: (a) 8 8 3.00 10 m/s 1.54. 1.94 10 m/s c n v × = × (b) 77 0 (1.54)(3.55 10 m) 5.47 10 m. n λλ −− × = × EVALUATE: In quartz the speed is lower and the wavelength is smaller than in air. 33.6. IDENTIFY: 0 n = . SET UP: From Table 33.1, water 1.333 n = and benzene 1.501 n = . EXECUTE: (a) water water benzene benzene 0 nn . water benzene water benzene 1.333 (438 nm) 389 nm 1.501 n n ⎛⎞ = ⎜⎟ ⎝⎠ . (b) 0 water water (438 nm)(1.333) 584 nm n = EVALUATE: is smallest in benzene, since n is largest for benzene. 33.7. IDENTIFY: Apply Eqs.(33.2) and (33.4) to calculate and . rb θ The angles in these equations are measured with respect to the normal, not the surface. (a) SET UP: The incident, reflected and refracted rays are shown in Figure 33.7. EXECUTE: 42.5 ra θθ = The reflected ray makes an angle of 90.0 47.5 r °− = ° with the surface of the glass. Figure 33.7 (b) sin sin , aa bb = where the angles are measured from the normal to the interface. sin (1.00)(sin42.5 ) sin 0.4070 1.66 b b n n ° = 24.0 b The refracted ray makes an angle of 90.0 66.0 b = ° with the surface of the glass. EVALUATE: The light is bent toward the normal when the light enters the material of larger refractive index. 33.8. IDENTIFY: Use the distance and time to find the speed of light in the plastic. c n v = . SET UP: 8 c EXECUTE: 8 9 2.50 m 2.17 10 m s 11.5 10 s d v t = × × . 8 8 3.00 10 m/s 1.38 2.17 10 m/s c n v × = × . EVALUATE: In air light travels this same distance in 8 2.50 m 8.3 ns = × .
The Nature and Propagation of Light 33-3 33.9. IDENTIFY and SET UP: Use Snell&s law to find the index of refraction of the plastic and then use Eq.(33.1) to calculate the speed v of light in the plastic.

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This homework help was uploaded on 03/14/2008 for the course MSE 250 taught by Professor Jabbour during the Spring '08 term at University of Arizona- Tucson.

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33_InstructorSolutions - THE NATURE AND PROPAGATION OF...

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