p37_074 - 74. The central diffraction envelope spans the...

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Unformatted text preview: 74. The central diffraction envelope spans the range −θ1 < θ < +θ1 where θ1 = sin−1 λ . a The maxima in the double-slit pattern are at θm = sin−1 mλ , d so that our range specification becomes − sin−1 λ a < sin−1 mλ λ < + sin−1 , d a which we change (since sine is a monotonically increasing function in the fourth and first quadrants, where all these angles lie) to mλ λ λ < <+ . − a d a Rewriting this as −d/a < m < +d/a we arrive at the result mmax < d/a ≤ mmax + 1 . Due to the symmetry of the pattern, the multiplicity of the m values is 2mmax + 1 = 17 so that mmax = 8, and the result becomes d 8< ≤9 a where these numbers are as accurate as the experiment allows (that is, “9” means “9.000” if our measurements are that good). ...
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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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