Total internal reflection (TIR)
The 100% reflection of light at an interface from a denser to a less dense medium when the angle of incidence exceeds the critical angle θ_c = arcsin(n₂/n₁). The basis of optical fibres, binoculars, and retroreflectors.
Definition
Total internal reflection occurs when a wave in a denser medium (refractive index n₁) strikes the interface with a less dense medium (n₂ < n₁) at an angle greater than the critical angle θ_c = arcsin(n₂/n₁). Above θ_c, Snell's law sin θ₂ = (n₁/n₂) sin θ₁ would demand sin θ₂ > 1 — mathematically impossible for a real refracted ray — so no light escapes into the second medium and 100% is reflected back into the denser medium. The reflection is perfect (in an ideal lossless system), far cleaner than any metallic mirror, because there is no absorption or transmission channel available.
Applications are everywhere optical. Optical fibres guide light along their core by total internal reflection at the core–cladding interface; the cone of input angles that successfully launch a guided mode is determined by the numerical aperture NA = √(n_core² − n_cladding²). Binocular and camera prism assemblies use TIR at 45° glass–air surfaces to redirect image-forming light paths without the intensity loss a silvered mirror would introduce. Bicycle reflectors and road-sign retroreflectors use corner-cube TIR to bounce light back to its source. Even though all the intensity reflects, an evanescent wave penetrates a fraction of a wavelength into the second medium — the basis of frustrated-total-internal-reflection couplers and TIR fluorescence microscopy.