Optical fibres utilise optical refraction to transmit light along the core of a transparent fibre.

Optical refraction results in the change in the direction of travel of light and occurs when light meets a junction between two materials that are optically different in terms of their optical density. In the diagram below material n1 is optically denser than material n2, with the result that the direction of travel of the light moves away from the normal (the right angle to the boundary between the materials).

The relationship between the angles to the normal are described by Snell’s Law ( see diagram below).
If we consider light travelling in an optically denser material (than the material the other side of the optical boundary between two materials) we see that there is a critical angle, c, where light does not travel through the boundary (line 2 in diagram below). There is total internal reflection of the light for any angle greater than c;

this is how optical fibres work – the light travels in an optically denser material, surrounded by a less optically dense material, with the light being totally internally reflected along the path of the fibre.
The core of the optical fibre has a high refractive index, which is then surrounded by lower refractive index cladding.

The core and cladding are the both surrounded by a buffer material for optical an physical isolation from the surrounding environment.
Optical fibres have a number of practical uses in the telephone, tv and data transmission industries, where bundles of optical fibres are used for the reliable transmission of data by light pulses. Other uses include data transmission from small medical cameras used in medical procedures and for illumination (e.g. Christmas tree and room lamps).