Index of Refraction
n = c/v
Angle of transmission, for various
angles of incidence, and various media
From |
To |
incident angle = 15 |
30 |
45 |
60 |
75 |
89 |
Air
| Water
| 11
| 22
| 32
| 41
| 47
| 49
|
Air
| Glass
| 10
| 19
| 28
| 35
| 40
| 42
|
Air
| Diamond
| 6
| 12
| 16
| 20
| 23
| 24
|
Glass
| Water
| 17
| 34
| 53
| 78
| -
| -
|
Glass | Air
| 23
| 49
| -
| -
| -
| -
|
|
Total internal reflection
In the above table some entries are blank. The reason is that
a beam that is trying to enter a faster medium (smaller n) at a
larger angle of incident would have to be bent away from the
normal more than 90o. This is not possible. Therefore
nothing is transmitted, and everything is reflected. This
is called total internal reflection. It only occurs
at sufficiently large incident angles at the inside (internally)
of a dense medium (larger n) bordered by a less dense medium
(smaller n). Of course the law of reflection holds. The angle
of incidence where total internal reflection first happens
is called the critical angle.
|
Fiber Optics
An application of total internal reflection is fiber optics, the
use of thin flexible glass or plastic fibers as light
pipes.
Light is sent down the fiber, which has a larger index of refraction
than its surroundings. If the light in the fiber hits the surface
at an angle of incidence greater than the critical angle, it is
totally internally reflected, and there are no losses due to light
escaping.
If the fiber is used to transmit a light signal consisting of
a rapid series of pulses, it is important not only that all the light
from a given pulse reach the other end of the fiber, but that it all
arrive there at one time. Otherwise the pulse becomes
spread out and might blur with the next pulse. Graded
fibers with varying index of refraction can be made so that
the time for rayis going straight down the center is the same as for
rays bouncing from side to side. Such fibers are replacing metal wire
for telephone lines andn for data transmission.
In general, the higher the frequency of a wave used for communication,
the more information can be transmitted per second. Since the
frequency of visible light is much higher than radio frequencies,
these fibers can carry many signals (or conversations) at the same
time. Further, they do not radiate signals, so they cannot be bugged
without directly connecting to them.
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Dispersion
Index of Refraction:
- c : speed of light in vacuum
- v : speed of light in material
Snell's law rephrased
- Light going from small n to large n is bent toward
the normal.
- Light going from large n to small n is bent away
from the normal.
Index of Refraction in Various Media:
Mediumn
| n
|
Vacuum
| 1
|
Air
| 1.0003
|
Water
| 1.33
|
Glass
| 1.5
|
Diamond
| 2.4
|
|
Mirages and atmospheric distortions
A mirage is produced by the bending
of light rays in the atmosphere when there are large temperature
differences between the gound and the air.
A dark asphalt road will get very hot in the summer sun. When this
happens, the air next to it may become much hotter than the higher
air. This, in turn, can cause light to be bent so much that
it appears reflected -- a mirage.
In a rough way one can
think of the effect as a gradual total internal reflection at the
boundary between hot and cool air. When you look at the road
ahead, you see a reflection in it of whatever lies ahead.
The reflections of the sky are mostly associated with the appearance
of water on the road.
We can see the sun after it has set below the geometrical horizon.
The atmosphere is denser toward the bottom, less dense toward the
top. The gradual change in density produces a gradual change in
the index of refraction, which bends the light coming from the sun
( figure ). Here is an example of
a sunset (Nova Scotia, Canada) .
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