HOMEWORK 3 SOLUTIONS
PROBLEM 22.40
: A diffraction grating produces a firstorder maximum at an angle of 20.0 degree(s). What is
the angle of the secondorder maximum?
(
)
0
1
2
0
2
2
0
m
43
684
.
0
sin
684
.
0
20
sin
2
sin
d
2
sin
d
20
sin
d
m
sin
=
=
θ
=
=
θ
⎟
⎠
⎞
⎜
⎝
⎛
λ
=
θ
λ
=
λ
=
θ
−
PROBLEM 22.42
: White light (400700 nm) is incident on a 600 (line)/(mm) diffraction grating. What is the
width of the firstorder rainbow on a screen 2.0 m behind the grating?
For the 400 nm extreme:
(
)
(
)
(
)
m
49
.
0
9
.
13
tan
m
0
.
2
9
.
13
tan
L
y
9
.
13
24
.
0
m
10
67
.
1
m
10
400
sin
m
10
67
.
1
mm
10
67
.
1
600
1
a
L
y
tan
a
m
sin
0
0
1
0
6
9
6
3
mm
lines
m
m
m
=
=
=
=
θ
=
×
×
=
θ
×
=
×
=
=
=
θ
λ
=
θ
−
−
−
−
For the 700 nm extreme:
(
)
(
)
(
)
m
93
.
0
8
.
24
tan
m
0
.
2
8
.
24
tan
L
y
8
.
24
42
.
0
m
10
67
.
1
m
10
700
sin
0
0
1
0
6
9
=
=
=
=
θ
=
×
×
=
θ
−
−
The width is the difference between these two:
m
44
.
0
m
49
.
0
m
93
.
0
y
=
−
=
Δ
PROBLEM 22.52
: The figure shows the light intensity on a screen behind a single slit. The wavelength of the
light is 600 nm and the slit width is 0.15 mm. What is the distance from the slit to the screen?
The formula
below is for the dark spots.
The first dark spots are 0.5 cm from either side of the central maximum.
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 Spring '08
 Cardenas
 Light, Wavelength, Sin, 0.5 cm, 2 2 4L, 4.51nm

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