oldhw 39 - nguyen (jmn727) oldhomework 39 Turner (59070) 1...

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Unformatted text preview: nguyen (jmn727) oldhomework 39 Turner (59070) 1 This print-out should have 14 questions. Multiple-choice questions may continue on the next column or page find all choices before answering. 001 (part 1 of 2) 10.0 points Light of wavelength 580 nm illuminates two slits of width 0 . 02 mm and separation 0 . 1 mm. How many interference maxima fall within the full width of the central diffraction maxi- mum? Correct answer: 9. Explanation: Let : = 580 nm , d = 0 . 1 mm , and w = 0 . 02 mm . The angle of the first diffraction minimum to the width w of the slits of the diffraction grating is sin 1 = w , and the angle corresponding to the m th inter- ference maxima is sin m = m d . We require 1 = m , so w = m d m = d w . Therefore the number of fringes in the central maximum is N = 2 m- 1 = 2 parenleftbigg d w parenrightbigg- 1 = 2 parenleftbigg . 1 mm . 02 mm parenrightbigg- 1 = 9 . 002 (part 2 of 2) 10.0 points What is the ratio of the intensity of the third interference maximum to the side of the cen- terline (not counting the center interference maximum) to the intensity of the center in- terference maximum? Correct answer: 0 . 254572. Explanation: The phase difference between the lights at centerline and at third interference maximum is = 2 w sin 3 = 2 w 3 d = 6 w d , so the ratio of the intensities is I 3 I = sin 2 2 2 = sin 6 w 2 d 6 w 2 d 2 = sin 3 w d 3 w d 2 = sin 3 (0 . 02 mm) . 1 mm 3 (0 . 02 mm) . 1 mm 2 = . 254572 . 003 10.0 points Using a conventional two-slit apparatus with light of wavelength 593 nm, 31 bright fringes per centimeter are observed on a screen 4 m away. What is the slit separation? Correct answer: 7 . 3532 mm. Explanation: nguyen (jmn727) oldhomework 39 Turner (59070) 2 Let : N = 31 cm 1 = 3100 m 1 , = 593 nm = 5 . 93 10 7 m , and L = 4 m . The distance on the screen to the m th and ( m + 1) th bright fringe is y = ( m + 1) L d- m L d = L d . Then the number of fringes per unit length is N = 1 y = d L and the slit separation is d = L N = (5 . 93 10 7 m) (4 m) (3100 m 1 ) 1000 mm m = 7 . 3532 mm . 004 10.0 points Two coherent microwave sources that produce waves of wavelength 2 cm are in the xy plane, one on the y axis at y = 12 cm and the other at x = 3 cm, y = 10 cm. If the sources are in phase, find the differ- ence in phase between the two waves from these sources at the origin. Correct answer: 280 . 745 . Explanation: Let : vectorx 1 = ( x 1 , y 1 ) = (0 , 12 cm) , vectorx 2 = ( x 2 , y 2 ) = (3 cm , 10 cm) , and = 2 cm ....
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This note was uploaded on 01/21/2010 for the course PHY 303L taught by Professor Turner during the Spring '08 term at University of Texas at Austin.

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oldhw 39 - nguyen (jmn727) oldhomework 39 Turner (59070) 1...

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