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31. (a) The angular positions
θ
of the bright interference fringes are given by
d
sin
θ
=
mλ
,where
d
is the
slit separation,
λ
is the wavelength, and
m
is an integer. The Frst di±raction minimum occurs at
the angle
θ
1
given by
a
sin
θ
1
=
λ
,where
a
is the slit width. The di±raction peak extends from
−
θ
1
to +
θ
1
, so we should count the number of values of
m
for which
−
θ
1
<θ<
+
θ
1
, or, equivalently,
the number of values of
m
for which
−
sin
θ
1
<
sin
θ<
+ sin
θ
1
. This means
−
1
/a < m/d <
1
/a
or
−
d/a < m <
+
d/a
.N
ow
d/a
=(0
.
150
×
10
−
3
m)
/
(30
.
0
×
10
−
6
m) = 5
.
00, so the values of
m
are
m
=
−
4,
−
3,
−
2,
−
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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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