p37_031 - 31. (a) The angular positions of the bright...

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31. (a) The angular positions θ of the bright interference fringes are given by d sin θ = ,where d is the slit separation, λ is the wavelength, and m is an integer. The Frst di±raction minimum occurs at the angle θ 1 given by a sin θ 1 = λ ,where a is the slit width. The di±raction peak extends from θ 1 to + θ 1 , so we should count the number of values of m for which θ 1 <θ< + θ 1 , or, equivalently, the number of values of m for which sin θ 1 < sin θ< + sin θ 1 . This means 1 /a < m/d < 1 /a or d/a < m < + d/a .N ow d/a =(0 . 150 × 10 3 m) / (30 . 0 × 10 6 m) = 5 . 00, so the values of m are m = 4, 3, 2,
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This note was uploaded on 11/12/2011 for the course PHYS 2001 taught by Professor Sprunger during the Fall '08 term at LSU.

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