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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 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
−−
−
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.
 Spring '08
 Any
 Physics, Diffraction

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