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Unformatted text preview: Niu (qn269) Homework #9 antoniewicz (58855) 1 This printout should have 16 questions. Multiplechoice questions may continue on the next column or page find all choices before answering. 001 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 7 . 3 m . 1 . 9cm 7 . 3 m . 97mm S 1 S 2 viewing screen What is the wave length if the distance from the central bright region to the fifth dark fringe is 1 . 9 cm . Correct answer: 561 . 033 nm. Explanation: Basic Concepts: For bright fringes, we have d sin = m , and for dark fringes, we have d sin = parenleftbigg m + 1 2 parenrightbigg , where m = 0 , 1 , 2 , 3 , . From geometry, we have y = L tan . Let : y = 1 . 9 cm = 0 . 019 m , L = 7 . 3 m , and d = 0 . 97 mm = 0 . 00097 m . r 2 r 1 y L d S 1 S 2 = ta n 1 parenleftBig y L parenrightBig viewing screen d sin r 2 r 1 P O negationslash S 2 Q S 1 90 Q r 2 r 1 d S 1 S 2 = ta n 1 parenleftBig y L parenrightBig d s i n r 2 r 1 negationslash S 2 Q S 1 9 Q Solution: The angle from the slits mid point to the y position on the screen is = arctan bracketleftBig y L bracketrightBig = arctan bracketleftbigg (0 . 019 m) (7 . 3 m) bracketrightbigg = 0 . 00260273 rad . The wavelength of the light for the fifth dark fringe, m = 4, is = d sin parenleftbigg m + 1 2 parenrightbigg = (0 . 00097 m) sin(0 . 00260273 rad) (4 . 5) = 5 . 61033 10 7 m = 561 . 033 nm . 002 10.0 points A pair of narrow parallel slits separated by a distance of 0.208 mm are illuminated by the green component from a mercury vapor lamp ( = 546 . 6 nm). What is the angle from the central maxi mum to the second dark fringe on either side of the central maximum? Correct answer: 0 . 225851 . Explanation: Niu (qn269) Homework #9 antoniewicz (58855) 2 Basic Concept: d (sin ) = parenleftbigg m + 1 2 parenrightbigg , m = 0 , 1 , 2 , Given : d = 0 . 208 mm 1 m 1000 mm = 2 . 08 10 4 m = 546 . 6 nm 1 m 10 9 nm = 5 . 466 10 7 m m = 1 , second dark fringe Solution: sin = parenleftbigg m + 1 2 parenrightbigg d = sin 1 parenleftbigg m + 1 2 parenrightbigg d = sin 1 bracketleftbigg 1 . 5(5 . 466 10 7 m) . 000208 m bracketrightbigg = . 225851 . 003 (part 1 of 2) 10.0 points Light of wavelength 747 nm illuminates a sin gle slit....
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 Spring '09
 Antoniewicz
 Work, Light

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