D 5 m l 2 sin u 5 1 1 21 0173 3 10 2 9 m 2 2 1 sin

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d 5 m l 2 sin u 5 1 1 21 0.173 3 10 2 9 m 2 2 1 sin 22.4° 2 5 0.227 nm. m 5 1. m 5 1, 2, 3, c u 2 d sin u 5 m l , 26-10 Chapter 26
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26.50. Set Up: Solve: Same means 26.51. Set Up: The angular size of the object is its height divided by its distance from the eye. Solve: and Diffraction doesn’t play a significant role. 26.52. Set Up: The angular size of the object is its height divided by its distance from the eye. Solve: (a) The angular size of the object is and the object cannot be resolved. (b) and (c) This is very close to the experimental value of 1 min. (d) Diffraction is more important. 26.53. Set Up: Take the width of a typical license plate to be about 30 cm. Solve: The angular size of the object is Setting gives Reflect: A mirror of this diameter (less than one meter) is feasible. 26.54. Set Up: Constructive interference occurs when the path difference from the two sources is Destructive interference occurs when the path difference is Solve: (a) The path difference from the two speakers is a half-integer number of wavelengths and the interference is destructive. (b) The path difference changes by so and (c) The speaker must be moved a distance so the path difference will change by 26.55. Set Up: The interference minima are located by For a liquid with refractive index n , Solve: so and Reflect: In the liquid the wavelength is shorter and gives a smaller than in air, for the same m . u sin u 5 A m 1 1 2 B l d n 5 sin u air sin u liq 5 sin 35.20° sin 19.46° 5 1.730. sin u air l air 5 sin u liq l air / n sin u air l air 5 sin u liq l liq . sin u l 5 A m 1 1 2 B d 5 constant, l liq 5 l air n . d sin u 5 A m 1 1 2 B l . l . l 5 0.796 m, f 5 v l 5 340 m / s 0.796 m 5 427 Hz, l 5 0.796 m. l 2 5 0.398 m l 2 , 6 2, c 6 1, m 5 0, r 2 2 r 1 5 m l , r 2 2 r 1 6 2, c 6 1, m 5 0, r 2 2 r 1 5 m l , r 2 2 r 1 v 5 f l . D 5 1.22 l u 5 1 1.22 21 500 3 10 2 9 m 2 7.5 3 10 2 7 rad 5 81 cm. u res 5 u u 5 0.30 m 400 3 10 3 m 5 7.5 3 10 2 7 rad. u res 5 1.22 l D . u 5 u res 5 3.4 3 10 2 4 rad 5 0.019° 5 1.1 min. y 5 s u res 5 1 25 cm 21 3.4 3 10 2 4 rad 2 5 8.5 3 10 2 3 cm 5 85 m m. u res 5 y s u , u res u res 5 1.22 l D 5 1.22 1 550 3 10 2 9 m 2.0 3 10 2 3 m 2 5 3.4 3 10 2 4 rad. u 5 50 3 10 2 6 m 25 3 10 2 2 m 5 2.0 3 10 2 4 rad. u res 5 1.22 l D . y 5 s u res 5 1 25.0 cm 21 3.36 3 10 2 4 2 5 8.4 3 10 2 3 cm 5 0.084 mm. u res 5 y s u res 5 1.22 1 550 3 10 2 9 m 2.00 3 10 2 3 m 2 5 3.36 3 10 2 4 . u res 5 1.22 l D . D 2 5 D 1 l 2 l 1 5 1 8000 3 10 3 m 2 1 550 3 10 2 9 m 2.0 3 10 2 2 m 2 5 220 m. l 1 D 1 5 l 2 D 2 . u res u res 5 1.22 l D Interference and Diffraction 26-11
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26.56. Set Up: Consider the interference of the rays reflected from each side of the film. At the front of the film light in air reflects off the film and there is a phase shift. At the back of the film light in the film reflects off the glass and there is a phase shift. Therefore, the reflections introduce no net phase shift. The path difference 2 t , where t is the thickness of the film. The wavelength in the film is Solve: (a) Since there is no net phase difference produced by the reflections, the condition for destructive interfer- ence is and the minimum thickness is (b) For destructive interference, and All other values are shorter. The only visible wavelength in air for which there is destructive inter-
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