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Unformatted text preview: 67. The central diﬀraction envelope spans the range −θ1 < θ < +θ1 where
θ1 = sin−1 λ
.
a The maxima in the doubleslit pattern are located 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 ﬁnd −6 < m < +6, or, since m is an integer, −5 ≤ m ≤ +5.
Thus, we ﬁnd eleven values of m that satisfy this requirement. ...
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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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