Total Internal Reflection

When light travels from a material with a higher refractive index to one with a lower refractive index (for example from glass to air), it bends away from the normal. As the angle of incidence increases, the refracted ray bends further until it travels along the boundary. The angle of incidence at which the angle of refraction is 90° is called the critical angle, C.If the angle of incidence is greater than the critical angle, no light is refracted. All of it is reflected back inside the material. This is total internal reflection (TIR).Two conditions are needed for TIR:
1. The light must be travelling from a higher to a lower refractive index.
2. The angle of incidence must be greater than the critical angle.Putting θ₂ = 90° into Snell's law gives n₁ sin C = n₂. For a boundary with air (n₂ = 1.00):sin C = 1 / nFor any two materials, sin C = n₂ / n₁, where n₁ is the larger index.Worked example: glass with n = 1.50: sin C = 1 / 1.50 = 0.667, so C = 41.8°. A ray inside this glass meeting the surface at 45° is totally internally reflected, because 45° is greater than 41.8°. A ray meeting it at 30° is mostly refracted out, with a weak partial reflection.The higher the refractive index, the smaller the critical angle. Diamond (n = 2.42) has C = 24.4°, so light entering a cut diamond is reflected many times inside it, which makes it sparkle.