Problem Solving Examples
Department of Physics
72
Example 1
As shown in figure, a layer of water covers
a slab of material X in a beaker.
A ray of light traveling upward follows the
path indicated. Using the information on
the figure, find
a) the index of refraction of material X
b) the angle the light makes with the
normal in the air.
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Example 1
Department of Physics
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Example 1
Department of Physics
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Example 2
▪
▪
A ray of light incident on a surface of a 90° prism and emerges at the second surface
such that the angle of refraction is 90°.
Calculate the index of refraction of the prism if the incident angle is 𝜙1 is 40°.
𝜙1
𝜙2
𝜙3
𝜙4
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Example 2
Department of Physics
75
Example 2
Department of Physics
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Example 2
Department of Physics
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Example 2
Department of Physics
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Example 2
Department of Physics
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Example 2
Department of Physics
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Example 3
▪
Normal
What should be the angle of
incidence 𝜙 for glass (n=1.60)
for the angle of refraction to
be 𝜙/2?
sin
𝜙
=
2
1 − cos 𝜙
2
𝜙
glass
𝜙
2
sin2 𝜙 + cos 2 𝜙 = 1
Department of Physics
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Example 3
Department of Physics
76
Example 3
Department of Physics
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Example 3
Department of Physics
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SEATWORK
A beaker with a mirrored bottom is filled with a
liquid whose index of refraction is 1.63. A light
beam strikes the top surface of the liquid at an
angle of 42.5 from the normal.
a)
At what angle from the normal will the beam
strikes the mirrored bottom of the beaker?
b)
At what angle from the normal will the beam
exit from the liquid after traveling down
through the liquid, reflecting from the
mirrored bottom, and returning to the
surface.
Department of Physics
77
SEATWORK
A beaker with a mirrored bottom is filled with a
liquid whose index of refraction is 1.63. A light
beam strikes the top surface of the liquid at an
angle of 42.5 from the normal.
a)
At what angle from the normal will the beam
strikes the mirrored bottom of the beaker?
b)
At what angle from the normal will the beam
exit from the liquid after traveling down
through the liquid, reflecting from the
mirrored bottom, and returning to the
surface.
Department of Physics
77
SEATWORK
Department of Physics
77
SEATWORK
Department of Physics
77
SEATWORK
Department of Physics
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SEATWORK
Department of Physics
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Example 4
A parallel beam of unpolarized light in air is
incident at an angle 54.5° (with respect to
the normal) on a plane glass surface.
The reflected beam is completely linearly
polarized.
(a) What is the refractive index of the glass?
(b) What is the angle of refraction of the
transmitted beam?
Department of Physics
78
Example 4
A parallel beam of unpolarized light in air is
incident at an angle 54.5° (with respect to
the normal) on a plane glass surface.
The reflected beam is completely linearly
polarized.
(a) What is the refractive index of the glass?
(b) What is the angle of refraction of the
transmitted beam?
Department of Physics
78
Example 4
A parallel beam of unpolarized light in air is
incident at an angle 54.5° (with respect to
the normal) on a plane glass surface.
The reflected beam is completely linearly
polarized.
(a) What is the refractive index of the glass?
(b) What is the angle of refraction of the
transmitted beam?
Department of Physics
78
Example 5
A 1.00-cm-thick by 4.00-cm-long
glass plate is made up of two
prisms. The top prism has an
index of refraction of 1.486 and
the bottom prism has an n of
1.878.
A light ray is incident on the top
face as shown in the figure. The
reflected ray A is completely
linearly polarized.
Determine the exit angle of this
ray that pass through the prisms.
𝜃𝑝 𝜃𝑝
𝑛′ = 1.486
1.00 𝑐𝑚
𝑛′′ = 1.878
4.00 𝑐𝑚
Department of Physics
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Example 5
Determine the exit
angle of this ray that
pass
through
the
prisms.
Department of Physics
80
Example 5
Determine the exit
angle of this ray that
pass
through
the
prisms.
Department of Physics
80
Example 5
Determine the exit
angle of this ray that
pass
through
the
prisms.
Department of Physics
80
Example 5
Determine the exit
angle of this ray that
pass
through
the
prisms.
Department of Physics
80
Example 5
Determine the exit
angle of this ray that
pass
through
the
prisms.
Department of Physics
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Example 6
●
The light beam strikes
surface 2 at the critical
angle. Determine the
angle of incidence 𝜃1
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Example 6
●
The light beam strikes
surface 2 at the critical
angle. Determine the
angle of incidence 𝜃1
Department of Physics
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Example 6
●
The light beam strikes
surface 2 at the critical
angle. Determine the
angle of incidence 𝜃1
Department of Physics
81
Example 6
●
The light beam strikes
surface 2 at the critical
angle. Determine the
angle of incidence 𝜃1
Department of Physics
81
Example 6
●
The light beam strikes surface 2 at the critical angle.
Determine the angle of incidence 𝜃1
Department of Physics
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Example 7
Three polarizing filters are stacked, with the polarizing axis of the second and
third filters at angles of 60° and 90°, respectively, to that of the first.
(a) What is the light intensity (in terms of ) at points and
(b) If we remove the middle filter, what will be the light intensity at point C?
Department of Physics
79
Example 7
Three polarizing filters are stacked,
with the polarizing axis of the second
and third filters at angles of 60° and
90°, respectively, to that of the first.
(a) What is the light intensity (in terms
of ) at points and
(b) If we remove the middle filter, what
will be the light intensity at point C?
Department of Physics
79
Example 7
Three polarizing filters are stacked,
with the polarizing axis of the second
and third filters at angles of 60° and
90°, respectively, to that of the first.
(a) What is the light intensity (in terms
of ) at points and
(b) If we remove the middle filter, what
will be the light intensity at point C?
Department of Physics
79
SEATWORK II
Three polarizing filters are stacked, with the polarizing axis of the second
and third filters at angles of 23.6 degrees and 62.2 degrees, respectively,
to that of the first.
If unpolarized light is incident on the stack, the light has an intensity of
75.5 W/cm2 after it passes through the stack.
If the incident intensity is kept constant, what is the intensity of the light
after it has passed through the stack if the second polarizer is removed?
Department of Physics
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SEATWORK II
Department of Physics
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SEATWORK II
Department of Physics
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SEATWORK II
Department of Physics
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