solutions_chapter26

# Set up the line density in is with d in cm the bright

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Set Up: The line density in is with d in cm. The bright spots are located by Solve: (a) (b) For For 26.37. Set Up: The bright spots are located by The second pair correspond to Solve: (a) and (b) The next bright spots are for and Reflect: and is not small. The approximation is not accurate. 26.38. Set Up: The bright fringes are located at angles of deviation given by The separation d between adjacent slits in the grating is d 5 1.00 3 10 2 2 m 6000 5 1.67 3 10 2 6 m. sin u 5 m l d . sin u < tan u l d 5 471 3 10 2 9 m 1.79 3 10 2 6 m 5 0.263 y 5 R tan u 5 1 42.5 cm 21 tan 52.13° 2 5 54.7 cm. u 5 52.13°. sin u 5 m l d 5 3 1 471 3 10 2 9 m 2 1.79 3 10 2 6 m m 5 6 3. l 5 d sin u m 5 1 1.79 3 10 2 6 m 21 sin 31.75° 2 2 5 471 nm u 5 31.75°. tan u 5 y R 5 26.3 cm 42.5 cm 5 0.6188 y 5 R tan u . d 5 1 5580 lines / cm 5 1.79 3 10 2 4 cm 5 1.79 3 10 2 6 m. m 5 6 2. 6 2, c . 6 1, m 5 0, d sin u 5 m l , u 5 6 66.5°. m 5 6 3, u 5 6 37.7°. m 5 6 2, sin u 5 m l d 5 m 1 632.8 3 10 2 9 m 2.07 3 10 2 6 m 2 5 m 1 0.3057 2 . 1 d 5 4830 lines / cm. d 5 m l sin u 5 1 1 21 632.8 3 10 2 9 m 2 sin 17.8° 5 2.07 3 10 2 6 m 5 2.07 3 10 2 4 cm. 6 2, c . 6 1, m 5 0, d sin u 5 m l , 1 / d , lines / cm u 5 46.1°. 1 m 5 3 2 : 28.7°. u 5 1 m 5 2 2 : u 5 13.9°. 1 m 5 1 2 : sin u 5 m 1 600.0 3 10 2 9 m 2.50 3 10 2 6 m 2 5 m 1 0.240 2 . d 5 1.00 3 10 2 3 m 400.0 5 2.50 3 10 2 6 m. sin u 5 m l d . u u 5 6 32.1°. sin u 5 m l d 5 6 2 1 481 3 10 2 9 m 1.81 3 10 2 6 m 2 5 6 0.531 m 5 6 2. l 5 d sin u m 5 1 1.81 3 10 2 6 m 2 sin 15.4° 1 5 481 nm. d 5 1 5510 cm 5 1.81 3 10 2 4 cm 5 1.86 3 10 2 6 m 5510 lines / cm m 5 6 1. 6 15.4° 6 2, c . 6 1, m 5 0, d sin u 5 m l , l air 5 n l 5 1 1.45 21 438 nm 2 5 635 nm. l 5 a sin u 1 5 1 0.00125 3 10 2 3 m 2 sin 20.5° 1 5 438 nm. 20.5°. u 5 tan u 5 y R 5 11.2 cm 30.0 cm y 5 11.2 cm 26-8 Chapter 26

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Solve: (a) (b) and 26.39. Set Up: The bright fringes are located at angles of deviation given by The separation d between adjacent slits in the grating is Solve: (a) line: and line: and (b) line: and line: and Reflect: Light of longer wavelength is deflected through a larger angle. 26.40. Set Up: Maxima are located by The largest value can have is 1.00. Solve: (a) Set and solve for m : The largest is 3, so there are 7 bright spots . (b) and 26.41. Set Up: The bright spots are located by Third-order means and second-order means Solve: so and Reflect: The third-order line for a particular occurs at a larger angle than the second-order line. In a given order, the lines for violet light (400 nm) occurs at a smaller angle than the line for red light (700 nm). 26.42. Set Up: The visible spectrum ranges between 400 nm and 700 nm. The maxima are located by so the largest is for the largest The problem requires that for and Solve for d . Solve: 26.43. Set Up: The maxima are at angles given by where d is the spacing between adjacent planes in the crystal. Solve: 26.44. Set Up: The maxima are at angles given by where Solve: l 5 2 d sin u 1 5 2 1 0.440 nm 2 sin 39.4° 5 0.559 nm. m 5 1. d 5 0.440 nm. 2 d sin u 5 m l , u d 5 2 l 2 sin u 5 0.0850 nm sin 21.5° 5 0.232 nm m 5 2. 2 d sin u 5 m l , u 1 d 5 7.14 3 10 5 lines / m 5 7140 lines / cm. d 5 m l sin u 5 2 1 700 3 10 2 9 m 2 1.00 5 1.4 3 10 2 6 m.
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