solutions_chapter26

Set up since the values of m are rather large dont

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Set Up: Since the values of m are rather large, don’t use Eq.(26.6). For bright fringes, For dark fringes, For the fifth bright fringe (not counting the central bright spot), and for the eighth dark fringe, Solve: (a) and (b) and 26.7. Set Up: The values of are much smaller than the distance R to the screen, so the approximate expression is accurate. Solve: Reflect: This is a visible wavelength. 26.8. Set Up: The value of is much smaller than R and the approximate expression is accurate. Solve: 26.9. Set Up: Bright fringes are located at when Dark fringes are at and For the third bright fringe (not counting the central bright spot), For the third dark fringe, m 5 2. m 5 3. y 5 R tan u . d sin u 5 A m 1 1 2 B l y m V R . y m 5 R m l d , l 5 c f 5 3.00 3 10 8 m / s 6.32 3 10 14 Hz 5 4.75 3 10 2 7 m. d 5 20 R l y 20 5 1 20 21 1.20 m 21 502 3 10 2 9 m 2 10.6 3 10 2 3 m 5 1.14 3 10 2 3 m 5 1.14 mm y 20 5 10.6 3 10 2 3 m. y m 5 R m l d y 20 l 5 d D y R 5 1 0.460 3 10 2 3 m 21 2.82 3 10 2 3 m 2 2.20 m 5 590 nm D y 5 y m 1 1 2 y m 5 R l d . y m 5 R m l d y m y 5 R tan u 5 7.16 cm. u 5 5.45°. sin u 5 A 7 1 1 2 B 1 l d 2 5 0.0949 y 5 R tan u 5 1 75.0 cm 2 tan 3.63° 5 4.75 cm u 5 3.63°. sin u 5 5 1 l d 2 5 5 1 525 3 10 2 9 m 0.0415 3 10 2 3 m 2 5 0.0633 m 5 7. m 5 5 d sin u 5 A m 1 1 2 B l . d sin u 5 m l . y m 5 R tan u m . l / 2. d 5 l 4 5 1.36 m 4 5 34.0 cm. 2 d 5 l 2 l / 2. d 5 l 2 5 1.36 m 2 5 68.0 cm. 2 d 5 l l . l 5 v f 5 340.0 m / s 250.0 Hz 5 1.36 m 6 2, c . 6 1, m 5 0, path difference 5 A m 1 1 2 B l , 6 2, c . 6 1, m 5 0, path difference 5 m l , 180° r 1 r 2 r 2 2 r 1 d 5 l 2 5 1.36 m 2 5 68.0 cm. 2 d 5 l l . d 5 l 4 5 1.36 m 4 5 34.0 cm. 2 d 5 l 2 l / 2. l 5 v f 5 340.0 m / s 250.0 Hz 5 1.36 m 26-2 Chapter 26

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Solve: (a) (b) and Reflect: The third dark fringe is closer to the center of the screen than the third bright fringe on one side of the cen- tral bright fringe. 26.10. Set Up: At large distances from the antennas the equation gives the angles where maximum intensity is observed and gives the angles where minimum intensity is observed. Solve: (a) (b) 26.11. Set Up: is very small for these dark lines and the approximate expression is accurate. Adjacent dark lines are separated by Solve: 26.12. Set Up: Water has In water the wavelength is is very small for these dark lines and the approximate expression is accurate. Adjacent dark lines are separated by Solve: is smaller in water and the dark lines are closer together when the apparatus is immersed in water. 26.13. Set Up: The largest value can have is 1.00. Bright fringes are located at angles given by Solve: (a) For Therefore, the largest m for fringes on the screen is There are bright fringes, the central one and 19 above and 19 below it. (b) The most distant fringe has and Reflect: For small the spacing between adjacent fringes is constant but this is no longer the case for larger angles. D y u u 5 6 73.3°. sin u 5 m l d 5 6 19 1 5.85 3 10 2 7 m 0.0116 3 10 2 3 m 2 5 6 0.958 m 5 6 19. 2 1 19 2 1 1 5 39 m 5 19. m 5 d l 5 0.0116 3 10 2 3 m 5.85 3 10 2 7 m 5 19.8. sin u 5 1, m 5 d sin u l .

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