The conditions for total internal reflection

When light travels into a different medium, the speed of the light changes and the light is refracted (see The features of waves).

When light travels from a denser medium, eg glass, to a less dense medium, eg air, the speed of the light increases and the light refracts away from the normal. The angle of refraction is greater than the angle of incidence.

The diagram below shows the light refracting from glass into air.

Diagram of light refracting from glass into air showing that as the angle of incidence increases, the angle of refraction also increases.

As the angle of incidence is increased, the angle of refraction also increases. At a certain angle of incidence, the light will refract 90 degrees and travel along the boundary between the two media. This angle of incidence is called the critical angle. The critical angle varies for different materials, but it is useful to know that it is around 42 degrees for glass. You will be reminded of this fact in the exam. The diagram below shows light hitting the glass-air boundary at an angle that is equal to the critical angle.

Diagram of light refracting from glass into air. The light hits the glass-air boundary at an angle that is equal to the critical angle and travels along the boundary between the glass and the air.

If the angle of incidence is increased further, so that it is greater than the critical angle, the light will be totally internally reflected.

Diagram of light refracting from glass into air. The angle of incidence is greater than the critical angle, so the light is totally internally reflected.

The conditions required for total internal reflection (TIR) to occur are:

  • the light must be travelling from a more dense medium into a less dense medium (ie glass to air)
  • the angle of incidence must be greater than the critical angle