HW11-solutions-1 - gilbert (amg3448) HW11 tsoi (57210) 1...

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Unformatted text preview: gilbert (amg3448) HW11 tsoi (57210) 1 This print-out should have 18 questions. Multiple-choice questions may continue on the next column or page find all choices before answering. 001 10.0 points Will the light from two very close stars pro- duce an interference pattern? 1. Yes; strong light from the two stars cre- ates very clear interference patterns. 2. No; the light is too strong to produce a discernable interference pattern. 3. No; light from two very close stars is not likely to have the same frequency. correct 4. Yes; if they are very close to each other, the light has large overlapping area. Explanation: Light from a pair of stars will not produce an interference pattern because the waves of light from the two separate sources have dif- ferent frequencies and thus are incoherent; when combined they smudge. Interference occurs when light from a single source divides and recombines. 002 10.0 points A laser beam of wavelength 554 nm is incident on two slits. y 5 . 51 m . 2mm S 1 S 2 viewing screen Approximately how far apart will be the bright interference fringes on the viewing screen? Correct answer: 0 . 0152628 m. Explanation: Let : = 554 nm = 5 . 54 10- 7 m , L = 5 . 51 m , y = 0 . 0152628 m , and d = 0 . 2 mm = 0 . 0002 m . r 2 r 1 y L d S 1 S 2 = ta n- 1 y L viewing screen d sin r 2- r 1 P O S 2 Q S 1 90 Q The condition for constructive interference is d sin = m , where m = 0 , 1 , 2 , , . so the angle be- tween the bright interference fringes measured from the center of the double slits is = arcsin d = arcsin 5 . 54 10- 7 m . 0002 m = 0 . 15871 . Therefore, the distance between the bright interference fringes is y = L tan = (5 . 51 m) tan(0 . 15871 ) = . 0152628 m . 003 10.0 points A screen is illuminated by monochromatic light as shown in the figure below. The distance from the slits to the screen is L . y L d S 1 S 2 viewing screen gilbert (amg3448) HW11 tsoi (57210) 2 Using the small angle approximation ( = sin = tan ) , what is the wave length if the distance from the central bright region to the seventh bright fringe is y . 1. = 1 8 L y d 2. = 2 13 L y d 3. = 1 8 d y L 4. = 2 13 d y L 5. = 1 7 d L y 6. None of these. 7. = 2 13 d L y 8. = 1 8 d L y 9. = 1 7 L y d 10. = 1 7 d y L correct Explanation: Basic Concepts: For bright fringes, we have = d sin = m , and for dark fringes, we have = d sin = m + 1 2 , where m = 0 , 1 , 2 , 3 , . From geometry, we have y = L tan . r 2 r 1 y L d S 1 S 2 = ta n- 1 y L viewing screen d sin r 2- r 1 P O S 2 Q S 1 90 Q r 2 r 1 d S 1 S 2 = ta n- 1 y L d s i n r 2- r 1 S 2 Q S 1 9 Q Solution: The angle from the slits mid- point to the y position on the screen is = arctan y L ....
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This note was uploaded on 03/29/2012 for the course PHY 302l taught by Professor Morrison during the Spring '08 term at University of Texas.

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HW11-solutions-1 - gilbert (amg3448) HW11 tsoi (57210) 1...

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