# OHW 39 - terry(ect328 – oldhomework 39 – Turner...

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Unformatted text preview: terry (ect328) – oldhomework 39 – Turner – (59130) 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 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 two-slit 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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OHW 39 - terry(ect328 – oldhomework 39 – Turner...

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