• summary_type: concept
• word_count: 150

Total internal reflection requires two conditions: light traveling from denser to rarer medium, and angle of incidence exceeding the critical angle θ_c = s$in^{-1}$(n_rarer/n_denser). Key applications include optical fibres (light confined by repeated TIR at core-cladding interface, with numerical aperture NA = $\sqrt{n_{1}^{2} - n_{2}^{2}}$), totally reflecting prisms (45°-45°-90° prisms used in binoculars and periscopes replacing mirrors), the sparkle of diamond (θ_c ≈ 24.4° due to high n = 2.42), and mirages (continuous TIR in atmosphere due to temperature-induced refractive index gradient). For the glass-water interface, θ_c ≈ 62.5°, showing TIR is possible between any pair of media with different refractive indices as long as light goes from denser to rarer.