ch36-p081 - 81. (a) The central diffraction envelope spans...

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81. (a) The central diffraction envelope spans the range – θ 1 < < + 1 where 1 1 sin ( / ) a θλ = which could be further simplified if the small-angle approximation were justified (which it is not , since a is so small). The maxima in the double-slit pattern are at m m d = sin , 1 λ so that our range specification becomes 11 1 sin sin sin , m ad a −− λλλ ⎛⎞ ⎛ ⎞ −< < + ⎜⎟ ⎜ ⎟ ⎝⎠ ⎝ ⎠ which we change (since sine is a monotonically increasing function in the fourth and first quadrants, where all these angles lie) to . m a λ λλ << + Rewriting this as -d/a < m < + d / a we arrive at the result –7 < m < +7 which implies (since m must be an integer) –6 < m < +6 which amounts to 13 distinct values for
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This note was uploaded on 06/03/2011 for the course PHY 2049 taught by Professor Any during the Spring '08 term at University of Florida.

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