# Total Internal Reflection (TIR)

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```					                          Total Internal Reflection (TIR)

Have you ever looked at the back of a fish tank and thought it looked like a mirror?
You were fooled by a phenomenon called Total Internal Reflection (TIR).

There are two conditions that must be met for TIR
to occur:
1. n1 > n2
2. 1>c

We already know that when light speeds up it will bend away from the normal. When
n1 > n2 the light will speed up as it refracts, which also means that the angle of refraction
will be greater than the angle of incidence. At some point the angle of refraction will be
90o and the light will not be able to leave the medium. The angle of incidence that produces
this situation is called the Critical Angle (c).
Let’s look at the fish tank problem. The light is in the water (n1 = 1.33) trying to get
out into the air (n2 = 1.0). The critical angle for water in air can be determined by setting
the angle of refraction to 90o.
n1  1.33     n2  1.0     1  c        2  90o       n1 sin 1  n2 sin 2
 1.0 
(1.33)sin c  (1.0)sin 90o           c  sin1         48.7
o

 1.33 

So any light that strikes the inside surface of the glass with an angle of incidence
greater than 49o will be reflected back into the tank. The back of the tank looks like a
mirror because you are viewing it from a large angle!
TIR is a very cool phenomenon that has a wide variety of applications:

Fibre-optics:   light ‘bounces’ down a very thin glass fibre, allowing us to see into very
strange places and communicate across vast distances.

Diamonds: light ‘bounces’ around inside the diamond and then comes back out, creating the
effect of ‘sparkle’.
Since diamonds have the
highest index of refraction, they
have the lowest critical angle.

```
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