7. (a) We use Eq. 36-3 to calculate the separation between the first (
m
1
= 1) and fifth
2
(
5)
m
=
minima:
∆
∆
∆
∆
y
D
D
m
a
D
a
m
D
a
m
m
=
=
F
H
G
I
K
J
=
=
−
sin
.
θ
λ
λ
λ
2
1
b
g
Solving for the slit width, we obtain
a
D
m
m
y
=
−
=
×
−
=
−
λ
2
1
6
400
550
10
5
1
0 35
2 5
b
g
b
gc
hb
g
∆
mm
mm
mm
mm
.
.
.
(b) For
m
= 1,
sin
.
.
.
θ
=
=
×
=
×
−
−
m
a
λ
1 550
10
2 5
2 2
10
6
4
b gc
h
mm
mm
The angle is
θ
= sin
–1
(2.2
×
10
–4
) = 2.2
×
10
–4
rad.

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