Total Internal Reflection

Total internal reflection (TIR) — all of the light is reflected back into the denser medium at a boundary, with none refracting out.

Two conditions must both hold:

1. The light is travelling from a denser medium into a less dense one — glass to air, water to air, never the other way.
2. The angle of incidence is greater than the critical angle.

Critical angle (c) — the angle of incidence in the denser medium at which the refracted ray emerges along the boundary, at 90° to the normal. Below it, light refracts out (with some weak reflection); above it, all the light reflects.

The critical angle is related to the refractive index by:

sin c = 1 / n

A larger refractive index gives a smaller critical angle, so light is trapped more easily. Glass with n = 1.5 has a critical angle of about 42°, and water with n = 1.33 about 49°.

Optical fibres — a thin core of glass surrounded by cladding of lower refractive index. Light entering at a shallow angle strikes the core–cladding boundary above the critical angle every time, so it is totally internally reflected along the fibre, following it round bends with almost no loss.

Uses: communications, carrying telephone and internet data as pulses of infrared, with far greater capacity and much less signal loss than copper cable; and endoscopes, where one bundle of fibres carries light in to illuminate the inside of the body and another carries the image back out, allowing a surgeon to see inside without major surgery.

Prisms — a right-angled glass prism turns light through 90° or 180° by total internal reflection, because 45° exceeds the critical angle of glass. Used in periscopes and in binoculars, where prisms fold a long light path into a short body. A prism gives a brighter, sharper image than a mirror, because a mirror loses some light at its silvered backing and can produce faint double images.

Example: light inside a fibre with n = 1.5 meets the wall at 80° to the normal. Since 80° is well above the 42° critical angle, none escapes. Bend the fibre too sharply and the angle can fall below 42°, at which point light leaks out and the signal is lost — which is why fibre runs have a minimum bend radius.