benavides (jjb2356) – homework 35 – Turner – (59130)
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001
(part 1 of 2) 10.0 points
The index of refraction of a transparent liquid
(similar to water but with a different index of
refraction) is 1
.
51. A flashlight held under the
transparent liquid shines out of the transpar
ent liquid in a swimming pool. This beam of
light exiting the surface of the transparent liq
uid makes an angle of
θ
a
= 28
◦
with respect
to the vertical.
θ
θ
air
water
flashlight
ray
w
a
At what angle (with respect to the vertical)
is the flashlight being held under transparent
liquid?
Correct answer: 18
.
114
◦
.
Explanation:
By Snell’s Law
n
a
sin
θ
a
=
n
w
sin
θ
w
,
where
n
a
and
n
w
are the indices of refraction
for each substance and
θ
a
and
θ
w
are the inci
dent angles to the boundary in each medium,
respectively.
Assume that the surface of the transparent
liquid is a level horizontal plane, thus each
angle with respect to the vertical represents
the incident angle in each medium.
The index of refraction of air is (nearly)
n
a
= 1
.
0 while the index of refraction of trans
parent liquid is given as
n
w
= 1
.
51. The inci
dent angle in the air is given to be
θ
a
= 28
◦
.
Hence
sin
θ
w
sin
θ
a
=
n
a
n
w
sin
θ
w
sin 28
◦
=
1
1
.
51
sin
θ
w
=
0
.
469472
1
.
51
θ
w
= arcsin(0
.
310908)
θ
w
=
18
.
114
◦
.
002
(part 2 of 2) 10.0 points
The flashlight is slowly turned away from the
vertical direction.
At what angle will the beam no longer be
visible above the surface of the pool?
Correct answer: 41
.
4718
◦
.
Explanation:
This is solved in the same fashion as Part 1.
When the light ceases to be visible outside
the transparent liquid, then
θ
a
≥
90
◦
.
The
sin 90
◦
= 1. Hence (from above),
sin
θ
w
=
n
a
n
w
θ
w
= arcsin
parenleftbigg
1
1
.
51
parenrightbigg
θ
w
=
41
.
4718
◦
.
003
10.0 points
A flashlight on the bottom of a 3.87 m deep
swimming pool sends a ray upward and at an
angle so that the ray strikes the surface of the
water 1.17 m from the point directly above
the flashlight.
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 Spring '08
 Turner
 Work, Snell's Law, Correct Answer, Total internal reflection

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