totalreflexion

Total internal reflection is an optical phenomenon in which a light ray traveling in a denser medium strikes the boundary with a less dense medium at an angle of incidence greater than the critical angle, resulting in all of the light being reflected back into the original medium. This effect occurs only when light moves from a medium with a higher refractive index n1 to a lower refractive index n2 (n1 > n2).

The critical angle, theta_c, is defined by the relation sin(theta_c) = n2 / n1. If the incident angle theta_i is less than theta_c, refraction occurs and some light passes into the second medium. When theta_i equals theta_c, the refracted ray travels along the boundary. For theta_i greater than theta_c, the refracted wave cannot propagate in the second medium; instead, an evanescent field penetrates a short distance into the second medium and all transmitted energy is reflected back into the first medium.

Conditions for total internal reflection include a smooth interface, sufficient index contrast, and low absorption. In practice, surface imperfections and material losses can reduce reflection efficiency, but the effect remains robust in common materials used for optics.

Applications of total internal reflection are widespread. Optical fibers rely on TIR to confine light within the core over long distances, enabling high-bandwidth communication. Endoscopes, periscopes, and light guides use TIR in prisms or curved interfaces to redirect light. TIR also plays a role in sensors and various imaging techniques where light confinement and controlled reflection are required.

A typical example is glass (n ≈ 1.5) to air (n ≈ 1.0), which yields a critical angle of about 41–42 degrees; incident angles above this value produce total internal reflection.