Total Internal Reflection

When light travels from a slower medium (high 'n') to a faster medium (low 'n') the ray bends away from the normal.

This drawing not necessary.

So: < r is greater than < i.

As < i gets larger, so will < r.

If < i gets large enough, then < r will become 90o. This < i is called the critical angle.

And, if < i gets larger still, larger than the the critical angle, then something very interesting will happen.
If < i gets large enough, than < r (the angle of refraction) will eventually be greater than 90o,
which means the ray of light will not leave the original material but will reflect back staying within itself.
Never escaping !

Total Internal Reflection

This phenomenon is called total internal reflection. It explains the phenomenon observed when no light passes from one medium to another as light reaches a boundary. It happens when light tries to pass from a slower medium to a faster medium at an angle greater than the critical angle. As a result, no light is transmitted, all is reflected because the refracted ray stays in the original medium. All the light rays ends up following the law of reflection.

In the photo at left, there are
4 rays of light shining toward
the surface of the water.
The first (and largest) shines
straight up. The next 2 are
refracting into the air while
the last one is totally reflecting
and staying in the aquarium.

Total Internal Reflection Applet

Refraction Applet

When using the Refraction Applet:
Choose n i (Upper drop down box) to be much higher than n r (Lower drop down box).
Watch what happens when you increase the angle of incidence.

In each of the pictures above, light is refracting as it reaches the boundary of water to air. As the angle of incidence increases, the angle of refraction increases also until it gets so large that it total internally reflects. The angle of incidence at which it first begins to total internally reflect is called the critical angle. ( <critical )

  Diamonds have a very small critical angle.
This means most light entering the stone under-goes
total internal reflection and comes back out the top
of the stone making it seem luminous.

Calculating the critical angle:

We will always be calculating the critical angle for cases where the light is trying to pass from the incident medium into air. In this case it can be calculated using the following formula:

Sin <critical   =   1 / ni