Refractive index

The refractive index of a medium is defined as n = c/v_p, where v_p is the phase velocity of light of a given wavelength in the medium. By Snell's law (sin θ₁ / sin θ₂ = n₂/n₁), it also determines the angle at which light bends at an interface.

Common values: vacuum 1, air ~1.0003, water ~1.333, crown glass ~1.52, diamond ~2.42. The index always depends on wavelength — it is slightly larger for violet than for red — and that variation is what makes a prism split white light and a raindrop produce a rainbow. The empirical Cauchy formula n(λ) ≈ A + B/λ² captures the dependence for transparent materials across the visible band.

Snell's law, governing how light bends according to the ratio of indices, was formulated by Willebrord Snellius around 1621 and published by Descartes in 1637. Cauchy gave his empirical n(λ) fit in 1836.