LECTURE 13
REFRACTION
Instructor: Kazumi Tolich
Lecture 13
2
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Reading chapter 26.5
¤ Index
of refraction
¤ Snell’s law
¤ Total internal reflection
¤ Total polarization
Index of refraction
3
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The speed of light in a transparent medium is less
than the speed of light in vacuum.
A transparent medium is characterized by an index
of refraction, 𝑛, given by
𝑛=
¤
¤
𝑐
𝑣
𝑐 : speed of light in vacuum
𝑣 : speed of light in the medium
Snell’s law/Demo: 1
4
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Light travels from one point to another along the path
that takes least time.
The angle of transmitted ray, θ2, is called angle of
refraction.
The angles of incidence and refraction, and indices of
refraction of two media are related by Snell’s Law:
𝑛% sin 𝜃% = 𝑛* sin 𝜃*
Lifeguard analog
Quiz: 1
5
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Parallel light rays cross interfaces from air into two different media, 1
and 2, as shown in the figures below. In which of the media is the light
traveling faster?
A.
B.
C.
medium 1
medium 2
both the same
air
Medium 1
air
Medium 2
Quiz: 13-1 answer
6
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Medium 1
The greater the difference in the speed of light between the two
media, the greater the bending of the light rays.
Follow-up: How does the speed of light in air compared to the speeds
of light in medium 1 or medium 2?
air
Medium 1
air
Medium 2
Quiz: 2
¨
You are trying to catch fish by using a spear. You observe a
large fish a couple of meters in front of you and a meter below
the water surface. Assuming that the fish is stationary, in order
to hit the fish with your spear you must aim
A.
B.
C.
directly at the point where you see the fish.
slightly above the point where you see the fish.
slightly below the point where you see the fish.
Quiz: 13-2 answer
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You must aim slightly below the point where you see the fish.
For you to see the fish, the light must travel from the fish to your eyes.
The ray is refracted at the water-air boundary.
The angle of incidence is smaller than the angle of refraction since light travels faster in air
than in water.
Follow-up: To shoot a fish with a laser gun instead, should you aim directly at the image, slightly
above, or slightly below?
Example 1
9
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A 2.00 m long vertical pole
extends from the bottom of a
swimming pool to a point 50.0 cm
above the water. Sunlight is
incident at 55.0º above the
horizon. What is the length of the
shadow of the pole on the level
bottom of the pool? The indices of
refraction of air and water are
1.00 and 1.33, respectively.
Total internal reflection/Demo: 2
10
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When the incident light is in a medium with a higher index of
refraction, the angle of refraction is greater than the incident
angle.
Total internal reflection occurs when the incident angle is greater
than the critical angle, 𝜃+ , and no refracted ray exists.
sin 𝜃+ =
𝑛*
𝑛%
Quiz: 3
11
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In an optical fiber, what can be said about the index of refraction of
the core, 𝑛+,-. , versus the index of refraction of the cladding,
𝑛+/011234 ?
Quiz: 13-3 answer
12
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𝑛+/011234 < 𝑛+,-.
In order for there to be total internal reflection light must travel in a higher index of
refraction and incident on a boundary with medium of a lower index of refraction.
Total internal reflection in fiber optic light pipes makes it possible to transport light
and light-encoded signals over long distances without significant loss.
Quiz: 4
13
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Can the person standing on the edge of the pool be prevented from
seeing the light by total internal reflection at the water-air surface?
A.
B.
Yes
No
Quiz: 13-4 answer
14
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No
The rays that make smaller incident angles than the critical angle still
make out of water and span the whole space above water.
Example: 2
15
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A light bulb is set in the bottom
of a 3.0 m deep swimming
pool. What is the diameter of
the pool’s surface where the
light can escape?
h = 3.0 m
Total polarization
16
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When light is incident at Brewster’s angle, 𝜃6 , the
reflected and refracted beams are at right angles
to one another, and the reflected light is totally
polarized parallel to the reflecting surface.
tan 𝜃6 =
𝑛*
𝑛%
Quiz: 5
17
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What kind of Polaroid sunglasses would be useful in reducing the
glare at sea? The stripes represent the directions of the transmission
axes.
Quiz: 13-5 answer/Demo: 3
18
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A
Since the glare is horizontally polarized, Polaroid sunglasses with vertical
transmission axis will absorb the horizontally polarized light.
Glasses C are useful for viewing 3D movies.
Example: 3 (Walker Ch. 26-59)
19
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While studying physics at the library
late one night, you noticed the image
of the desk lamp reflected from the
varnished tabletop. When you put on
your Polaroid sunglasses to look cool
(why not, right??), the reflected image
disappears. If this occurs when the
angle between the incident and
reflected rays is 110°, what is the
index of refraction of the varnish?