p36_064 - y ( y 2 + d 2 / 4) 2 y D 2 = 1 2 10 D 2 + 1 8 d D...

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64. Let the m = 10 bright fringe on the screen be a distance y from the central maximum. Then from Fig. 36-8(a) r 1 r 2 = p ( y + d/ 2) 2 + D 2 p ( y d/ 2) 2 + D 2 =10 λ, from which we may solve for y . To the order of ( d/D ) 2 we ±nd y = y 0 + y ( y 2 + d 2 / 4) 2 D 2 , where y 0 =10 Dλ/d . Thus, we ±nd the percent error as follows:
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Unformatted text preview: y ( y 2 + d 2 / 4) 2 y D 2 = 1 2 10 D 2 + 1 8 d D 2 = 1 2 5 . 89 m 2000 m 2 + 1 8 2 . 0 mm 40 mm 2 which yields 0 . 03%....
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