Kapoor (mk9499) – oldhomework 31 – Turner – (60230)
1
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001
(part 1 of 2) 10.0 points
The index of refraction for violet light in silica
flint glass is 1
.
65, and that for red light is 1
.
61.
R
O
Y
G
B
V
Visible light
Deviation of
yellow light
Measure of
dispersion
Screen
What is the angle of deviation for the red
ray passing through a prism of apex angle
58
.
4
◦
if the angle of incidence is 44
.
2
◦
?
Correct answer: 46
.
3453
◦
.
Explanation:
Given :
n
= 1
.
61
and
θ
1
= 44
.
2
◦
.
Going from air to glass,
sin
θ
1
=
n
2
sin
θ
2
.
θ
1
θ
4
θ
3
θ
2
φ
α
β
Let the angles of incidence and reflection
for the red light be
θ
1
,
θ
r
2
,
θ
r
3
, and
θ
r
4
.
At the first surface
sin
θ
r
2
=
sin
θ
1
n
θ
r
2
= sin
−
1
parenleftbigg
sin
θ
1
n
parenrightbigg
= sin
−
1
parenleftbigg
sin 44
.
2
◦
1
.
61
parenrightbigg
= 25
.
6595
◦
.
Considering the top triangle,
α
+
β
+
φ
= 180
◦
(90
◦

θ
2
) + (90
◦

θ
3
) +
φ
= 180
◦
θ
2
+
θ
3
=
φ
θ
r
3
=
φ

θ
r
2
= 58
.
4
◦

25
.
6595
◦
= 32
.
7405
◦
.
Going from glass to air,
n
sin
θ
r
3
= sin
θ
r
4
θ
r
4
= sin
−
1
(
n
sin
θ
r
3
)
= sin
−
1
(1
.
61 sin 32
.
7405
◦
)
= 60
.
5453
◦
.
The angle of deviation for the red ray is
θ
rd
=
θ
r
4
+
θ
1

φ
= 60
.
5453
◦
+ 44
.
2
◦

58
.
4
◦
=
46
.
3453
◦
.
002
(part 2 of 2) 10.0 points
What is the angular dispersion of visible light
with the same angle of incidence?
Correct answer: 4
.
74481
◦
.
Explanation:
Given :
n
= 1
.
65
.
Let the angles of incidence and refraction for
the violet light be
θ
1
,
θ
v
2
,
θ
v
3
, and
θ
v
4
.
θ
v
2
= sin
−
1
parenleftbigg
sin
θ
1
n
parenrightbigg
= sin
−
1
parenleftbigg
sin 44
.
2
◦
1
.
65
parenrightbigg
= 24
.
9941
◦
.
The incident angle at the second surface for
violent light is
θ
v
3
=
φ

θ
v
2
= 58
.
4
◦

24
.
9941
◦
= 33
.
4059
◦
.
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Kapoor (mk9499) – oldhomework 31 – Turner – (60230)
2
The refraction angle at the second surface for
violent light is
θ
v
4
= sin
−
1
(
n
sin
θ
v
3
)
= sin
−
1
[(1
.
65) sin 33
.
4059
◦
]
= 65
.
2901
◦
.
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 Fall '08
 Turner
 Physics, Work, Angle of Incidence, Snell's Law, Total internal reflection, Geometrical optics

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