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Unformatted text preview: terry (ect328) – oldhomework 39 – Turner – (59130) 1 This printout should have 14 questions. Multiplechoice 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 520 nm illuminates two slits of width 0 . 04 mm and separation . 12 mm. How many interference maxima fall within the full width of the central diffraction maxi mum? Correct answer: 5. Explanation: Let : λ = 520 nm , d = 0 . 12 mm , and w = 0 . 04 mm . The angle of the first diffraction minimum to the width w of the slits of the diffraction grating is sin θ 1 = λ w , and the angle corresponding to the m th inter ference maxima is sin θ m = m λ d . We require θ 1 = θ m , so λ w = m λ 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 . 12 mm . 04 mm parenrightbigg 1 = 5 . 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: 1 . 05556 × 10 − 23 . Explanation: The phase difference between the lights at centerline and at third interference maximum is φ = 2 π λ w sin θ 3 = 2 π λ w 3 λ d = 6 π w d , so the ratio of the intensities is I 3 I = sin φ 2 φ 2 2 = sin 6 π w 2 d 6 π w 2 d 2 = sin 3 π w d 3 π w d 2 = sin 3 π (0 . 04 mm) . 12 mm 3 π (0 . 04 mm) . 12 mm 2 = 1 . 05556 × 10 − 23 . 003 10.0 points Using a conventional twoslit apparatus with light of wavelength 593 nm, 29 bright fringes per centimeter are observed on a screen 4 m away. What is the slit separation? Correct answer: 6 . 8788 mm. terry (ect328) – oldhomework 39 – Turner – (59130) 2 Explanation: Let : N = 29 cm − 1 = 2900 m − 1 , λ = 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 Δ y = ( m + 1) λ L d m λ L d = λ L d . Then the number of fringes per unit length is N = 1 Δ y = d λ L and the slit separation is d = λ L N = (5 . 93 × 10 − 7 m) (4 m) (2900 m − 1 ) × 1000 mm m = 6 . 8788 mm . 004 10.0 points Two coherent microwave sources that produce waves of wavelength 1 . 5 cm are in the xy plane, one on the y axis at y = 15 cm and the other at x = 1 cm, y = 14 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: 231 . 439 ◦ . Explanation: Let : vectorx 1 = ( x 1 , y 1 ) = (0 , 15 cm) , vectorx 2 = ( x 2 , y 2 ) = (1 cm , 14 cm) , and λ = 1 . 5 cm ....
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 Fall '09
 Turner
 Wavelength, Sin, Correct Answer, Terry

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