PHYS 4D
Solution to HW 5
February 5, 2011
Problem Giancoli 3243
(II) A light beam strikes a 2
.
0cmthick piece of plastic with a refractive index of 1
.
62
at a 45
◦
angle. The plastic is on top of a 3
.
0cm thick piece of glass for which
n
= 1
.
47. What is the distance
D
in
Fig. 3248?
Solution:
The beam forms the hypotenuse of two right trangles as it passes through the plastic and then the
glass. The upper angle of the triangle is the angle of refraction in that medium. Note that the sum of the opposite
sides is equal to the displacement
D
. First, we calculate the angles of refraction in each medium using Snell’s Law
(Eq. 325)
sin 45
◦
=
n
1
sin
θ
1
=
n
2
sin
θ
2
.
θ
1
=
sin
−
1
(
sin 45
◦
n
1
) = sin
−
1
(
sin 45
◦
1
.
62
) = 25
.
88
◦
,
θ
2
=
sin
−
1
(
sin 45
◦
n
2
) = sin
−
1
(
sin 45
◦
1
.
47
) = 28
.
75
◦
.
We then use the trigonometric identity for tangent to calculate the two opposite sides, and sum to get the displace
ment.
D
=
D
1
+
D
2
=
h
1
tan
θ
1
+
h
2
tan
θ
2
= 2
.
0
cm
tan 25
.
88
◦
+ 3
.
0
cm
tan 28
.
75
◦
= 2
.
6
cm.
Problem Giancoli 3245
(II) In searching the bottom of a pool at night, a watchman shines a narrow beam
of light from his ﬂashlight, 1
.
3 m above the water level, onto the surface of the water at a point 2
.
5 m from his foot
at the edge of the pool (Fig. 3250). Where does the spot of light hit the bottom of the pool, measured from the
bottom of the wall beneath his foot, if the pool is 2
.
1
m
deep?
Solution:
We find the angle of incidence from the distances
tan
θ
1
=
l
1
h
1
=
2
.
5
m
1
.
3
m
= 1
.
9231
, θ
1
= 62
.
53
◦
.
For the refraction from air into water, we have
n
air
sin
θ
1
=
n
water
sin
θ
2
,
sin
θ
2
=
1
.
00
1
.
33
sin 62
.
53
◦
⇒
θ
2
= 41
.
84
◦
We find the horizontal distance from the edge of the pool from
l
=
l
1
+
l
2
=
l
1
+
h
2
tan
θ
2
=
2
.
5
m
+ 2
.
1
m
tan 41
.
84
◦
= 4
.
4
m
Problem Giancoli 3254
(II) A parallel beam of light containing two wavelengths,
λ
1
= 465
nm
and
λ
2
=
652
nm
, enters the silicate ﬂint glass of an equilateral prism as shown in Fig. 3254. At what angle does each beam
leave the prism (give angle with normal to the face)? See Fig. 3228.
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 Winter '08
 staff
 Physics, Light, Geometrical optics, DI, Problem Giancoli

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