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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 doubleslit 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.
 Fall '08
 SPRUNGER
 Physics

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