Refraction in a Rectangular Block

What happens when a parallel beam of light enters a rectangular glass block? Assuming the light exits the block along the side opposite to the side it entered, what path does the light follow when it emerges from the block?

  1. The exact path it was following when it entered the block.
  2. A path parallel to the original path, but displaced from it.
  3. A path perpendicular to the original path.
  4. None of the above.

The path is parallel to the original path. In general it is displaced from the original path. The only case when it is not displaced is when the light strikes the block perpendicular to the surface.

Total Internal Reflection

At some angle, known as the critical angle, light travelling from a medium with higher n to a medium with lower n will be refracted at 90o; in other words, refracted along the interface. If the light hits the interface at any angle larger than this critical angle, it will not pass through to the second medium at all. Instead, all of it will be reflected back into the first medium, a process known as total internal reflection.

The critical angle is given by: θc = n2/n1.

A fiber optic cable is an excellent application of total internal reflection. An optical fiber is simply a long strand of glass, usually surrounded by a cladding layer, another type of glass with a larger index of refraction. The cladding prevents cross-talk, signals leaking from one fiber to another when a large number of fibers are bundled into a cable.

Signals sent along a fiber take the form of pulses of laser light. As long as the fiber does not take any sharp turns the light will stay inside the fiber, bouncing back and forth as it makes its way along.

Total internal reflection also explains why diamonds are so sparkly. Diamond has a very large index of refraction (around 2.4) so light entering the diamond has a hard time getting out. Diamonds are cut in such a way that most of the light entering the bottom and the sides goes out through the top. In addition, the light bounces around so much inside the diamond that white light spreads out nicely into its different colors.