Total internal reflection

When light waves move from a denser medium, such as glass, to a less dense medium, such as air, the speed at which the light is moving increases. This change of speed causes refraction.

If the waves are hitting the boundary between glass and air at an angle beyond a specific value, all of the light waves will be reflected back from the glass rather than passing through to the air. This angle is known as the critical angle, and its value varies depending on the type of medium being used.

The critical angle for most types of glass is around 42^o. If the light waves hit the glass at any angle higher than 42^o, all of the light waves are reflected back into the glass. This effect where all of the light waves are reflected back into the glass is known as total internal reflection.

You can investigate total internal reflection using a semi-circular glass block as shown in the diagram above. A light box is used to direct a ray of light through the centre of the block from the curved side.

The incident ray will hit the glass block at an angle above 42^o. As the angle used is above the critical angle, all of the light is reflected back into the block at the same angle and no refraction occurs.

The critical angle will depend on the media that is on either side of the boundary. If the less dense material is air, then the critical angle of glass is usually 42^o, and 49^o for water.

There is a relationship between the refractive index of the medium being used and the critical angle above which total internal reflection will occur.

This relationship is shown by the equation:

where sin (c) is the critical angle and n is the refractive index of the medium.

Using our previously calculated value for the refractive index of 1.27 for the Perspex block, we can now calculate the critical angle as follows:

To convert this into the critical angle, you need to remove the sin function.

To do this on your calculator press the shift key and then the sin button to get sin^-1.

Uses of total internal reflection

Previously we have seen how mirrors can be useful in periscopes to allow people to view areas that could otherwise not be seen. When looking at the image created by a mirrored plane, it is possible that little fainter images will be scattered around the central image. These occur because of the partial internal reflections that occur on the non-silvered glass surface on the mirror. These fainter images can interfere with the main image causing some slight fuzziness or blurring.

This blurring can be a problem especially when a high-quality image is needed. It can be solved by using a system of glass prisms, positioned in such a way as to alter the direction of the light as shown in the diagram below:

As the diagram shows, the incident ray enters the prism below A and hits the back edge of the prism between A and B at an angle of 45^o. The ray of light is reflected back at an equal angle of 45^o and hits the edge of the prism between B and C where it again is reflected out at an angle of 45^o.

The light continues to travel until it strikes the surface between A and C at an angle of 45^o. As the critical angle for glass is 42^o, the light ray hitting the glass prism at an angle of 45^o will be totally internally reflected.

A second prism can be placed so that the ray emerging from the first prism, travels directly into the second prism and the process of total internal reflection continues. If this system of prisms was continued along a long fibre, total internal reflection would continue through the whole fibre allowing a person at one end of the fibre to view the object at the other end of the fibre, as all of the light from the object is completely reflected into their eyes. The final image that is produced would be much clearer than that produced from a periscope using only two mirrors.

Reflectors

Reflectors can also use prisms. An example of this is a bicycle reflector. The reflector will have rows of prisms that will internally reflect light back towards the direction it came in.

Optical fibres

Optical fibres are very thin rods of glass that have an outer coating of plastic. They are used to carry information in the form of infrared signal such as computer data, telephone calls and internet signals in place of copper wires and cables. Optical fibres are a recent development and are popular as they effectively transport data over very long distances without weakening or loss of the signal. The light that enters at one end of the fibre repeatedly undergoes total internal reflection so none of the light is lost.