Refractive index:

The most important optical measurement for any transparent material is its refractive index (n). The refractive index is the ratio of the speed of light (c) in a vacuum to the speed of light in the medium:

The speed of light in a material is always slower than in a vacuum, so the refractive index is always greater than one in the optical part of the spectrum. Although light travels in straight lines through optical materials, something different happens at the surface. Light is bent as it passes through a surface where the refractive index changes. The amount of bending depends on the refractive indexes of the two materials and the angle at which the light strikes the surface between them.

The angle of incidence and refraction are measured not from the plane of the surfaces but from a line perpendicular to the surfaces. The relationship is known as "Snells Law", which is written; ni sin I = nr sin R, where ni and nr are the refractive indexes of the initial medium and the medium into which the light is refracted. I and R are the angles of incidence and refraction.

Snell's law indicates that refraction can't take place when the angle of incidence is too large. If the angle of incidence exceeds a critical angle, where the sine of the angle of refraction would equal one, light cannot get out of the medium. Instead the light undergoes total internal reflection and bounces back into the medium.

Figure  illustrates the law that the angle of incidence equals the angle of reflection. It is this phenomenon of total internal reflection that keeps light confined within a fibre optic.