TOTAL INTERNAL REFLECTION
Fibre optic cables are now well known in the context of telecommunications and high-speed data transfer, when digital signals are sent not as electric current along copper wires, but as pulses of laser light. Optical fibres are glass or plastic, roughly the diameter of a human hair. Such fragile filaments need to be encased in flexible, shock-absorbing coatings, and the cables often need to bend. You’d expect light to be absorbed by the protective coating at each bend, causing it to become weaker and weaker. But if the fibre is also given an inner cladding of the right transparency, the light beam can be oriented so that an unusual consequence of the law of refraction – total internal reflection – enables virtually all of the beam to bend with the fibre.
This is only possible if the light meets the fibre’s edges at angles of incidence greater than a certain “critical angle”, ϴc – the angle corresponding to a 90° angle of refraction, where the light is refracted along the edge of the cladding, parallel to the fibre.
Since sin 90° = 1, the law of refraction shows that the sine of the critical angle is n2/n1. This must be less than (the maximum sine value), which means that n1 > n2, so the cladding (medium 2) must have a lower index of refraction than the fibre (medium 1). Given these refractive indices, the critical angle can be easily calculated from the law of refraction. For larger angles of incidence, the light is not refracted, but internally reflected along the fibre.