Total Internal Reflection

Definition

When light trying to leave a dense material hits the boundary at too shallow an angle and bounces back completely — 100% reflected, nothing escapes.

θc=sin⁡−1 ⁣(n2n1)\theta_c = \sin^{-1}\!\left(\frac{n_2}{n_1}\right)

Technical definition

Complete reflection occurring when light travels from a higher-index to a lower-index medium at an incidence angle exceeding the critical angle θ_c = sin⁻¹(n₂/n₁). Beyond this angle no refracted ray exists.

Example

Fiber-optic cables trap laser pulses with total internal reflection: light zigzags down kilometers of glass fiber without leaking, carrying internet data at light speed. Diamonds sparkle for the same reason — their high index gives a tiny critical angle, so light bounces around inside before escaping.

Common confusion

Total internal reflection only works going from dense to rare — glass to air, water to air — never the reverse. Light entering water from air always partly refracts; it can never be totally reflected. Students who forget the direction requirement predict TIR in the wrong situations, like light entering a pool from above.