Explain the phenomenon of total internal reflection.

Total internal reflection is the complete reflection of light back into its original medium when it hits a boundary at a certain angle.

Total internal reflection (TIR) is a fascinating optical phenomenon that occurs when a propagating wave strikes a medium boundary at an angle larger than a particular critical angle with respect to the normal to the surface. If the refractive index is lower on the other side of the boundary and the incident angle is greater than the critical angle, the wave cannot pass through and is entirely reflected. This principle is used in optical fibres and prisms for example.

The critical angle is the angle of incidence above which the total internal reflection occurs. This angle is dependent on the refractive indices of the two media involved. It can be calculated using Snell's law by setting the refraction angle to 90 degrees. The formula is: Critical angle = arcsin (n2/n1), where n1 is the refractive index of the medium the light is coming from and n2 is the refractive index of the medium the light is entering.

When light travels from a medium with a higher refractive index to one with a lower refractive index, it speeds up. If the light hits the boundary at a shallow angle (less than the critical angle), it will refract and continue into the second medium. However, if the light hits the boundary at a steep angle (greater than the critical angle), it will not pass into the second medium. Instead, it will be totally internally reflected back into the first medium.

This phenomenon is utilised in many practical applications. For instance, in fibre optic cables, light signals are sent down thin strands of glass or plastic. The light is kept within the fibre by total internal reflection, allowing it to travel long distances without escaping. Similarly, in binoculars and periscopes, prisms are used to change the direction of light by total internal reflection, enabling the viewer to see around obstacles or over long distances.

In summary, total internal reflection is a fascinating and useful phenomenon that occurs when light travelling from a denser to a less dense medium hits the boundary at an angle greater than the critical angle.