Total internal reflection
When light passes from an optically denser medium (greater n₁) to a rarer one (n₂ < n₁), the angle of refraction is greater than the angle of incidence: sin β = (n₁/n₂)·sin α. As α increases we reach the limiting angle α₀ at which β = 90°, with sin α₀ = n₂/n₁. If the angle of incidence exceeds α₀, the ray does not enter the second medium but is totally reflected from the boundary: this is total internal reflection. For glass–air α₀ ≈ 42°, water–air ≈ 49°, diamond–air ≈ 24°; this is why diamond sparkles. Going from air into water or glass there is no total reflection since n₁ < n₂. The phenomenon is used in prismatic mirrors (binoculars, periscopes), in road reflectors and in optical fibre cables: the core of a fibre (higher n) is surrounded by a cladding (lower n), and light is totally reflected again and again at the core–cladding boundary and travels with almost no loss. Optical fibres are used in internet communication and in medicine (endoscope, by a doctor).
Safe observation: fill a transparent glass with water and look from the side and a little below eye level at the water surface: it looks like a silvery mirror. This is total internal reflection. Dip a spoon into the glass and watch the effect of refraction as well. Never shine laser pointers toward anyone’s eyes.