💎 Total Internal Reflection
When light travels from a denser medium into a less dense one, it bends away from the normal (Snell's law: n₁ sin θ₁ = n₂ sin θ₂). Above the critical angle θ_c = arcsin(n₂/n₁) the refracted ray disappears entirely — all light is reflected. This is the principle behind fibre optics, diamond brilliance, and mirages. Drag the incident ray or use the angle slider.
Medium 1 (dense, bottom)
Medium 2 (less dense, top)
Angle
Info
Physics
Snell's law n₁ sin θ₁ = n₂ sin θ₂ governs refraction at any interface. For light moving from dense (n₁) to less dense (n₂ < n₁) medium, θ₂ > θ₁. The critical angle θ_c = arcsin(n₂/n₁) is reached when θ₂ = 90°. Beyond this, sin θ₂ > 1 has no real solution — the wave becomes evanescent and all energy is reflected.
The Fresnel equations give the exact reflected fraction. At normal incidence (~0°), about 4% reflects off a glass-air interface. Near the critical angle, reflectance rises steeply to 100%.
Applications
Fibre optics (internet cables, medical endoscopes) trap light inside a glass core by TIR. Diamonds are cut so light entering the table hits every facet above the critical angle (24.4°) before exiting — maximizing brilliance. Mirages occur when heated road air acts as a less-dense layer, reflecting the sky downwards.