Snell Refraction Angle

Snell's law: n₁·sin θ₁ = n₂·sin θ₂

When light crosses the boundary between two media that have different refractive indices, it bends. Snell's law tells you by how much: n₁·sin θ₁ = n₂·sin θ₂, with the angles measured from the normal to the surface. A few common values to keep in mind are air ≈ 1.0003, water ≈ 1.33, crown glass ≈ 1.5 and diamond ≈ 2.42. Going the other way, from a denser medium into a thinner one (n₁ > n₂), you hit a critical angle θc = arcsin(n₂/n₁). Past that angle nothing refracts and all the light bounces back, which is total internal reflection (TIR). So light leaving air (n=1) for glass (n=1.5) at 30° comes out at θ₂ = arcsin(sin 30°/1.5) ≈ 19.47°, and the water-to-air critical angle sits around 48.6°.

Applications

Optical fibers rely on it, since TIR keeps the light trapped inside the core, and that's what every telecom backbone is built on. The same physics shows up in prisms (chromatic dispersion in spectroscopes and binoculars), in atmospheric mirages where the index changes near hot ground, and in gemstone cutting. A diamond sparkles because its high index combines with pavilion angles cut specifically to maximize TIR. You also see it in eyeglass lens design, in the anti-reflective coatings on camera lenses, and in underwater visibility, where the 1.33 factor makes a pool look shallower than it really is.

FAQ

What happens above the critical angle? There's no refracted ray at all; everything reflects (TIR). That's exactly why an optical fiber can carry light over thousands of kilometers with very little loss.

Why is the refractive index always ≥ 1? It comes from n = c/v, where v is the phase speed of light in the medium and c is its speed in vacuum. In any conventional medium light can't outrun c, so the ratio stays at or above 1.

Does Snell's law work for sound or water waves? It does. The law falls out of Fermat's principle of least time, and that holds for any wave. What changes is just the indices, which are set by how fast the wave moves in each medium.