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107. (a)
The central diffraction envelope spans the range –
θ
1
<
< +
1
where
1
1
sin
,
a
λ
−
=
which could be further simplified
if
the smallangle approximation were justified (which
it is
not
, since
a
is so small).
The maxima in the doubleslit pattern are at
m
m
d
=
−
sin
,
1
λ
so that our range specification becomes
11
1
sin
sin
sin
,
m
ad
a
λλ
−−
−
⎛⎞
⎛ ⎞
−<
<
+
⎜⎟
⎜ ⎟
⎝⎠
⎝ ⎠
which we change (since sine is a monotonically increasing function in the fourth and first
quadrants, where all these angles lie) to
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 Spring '08
 Any
 Physics, Diffraction

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