Optical dispersion

Optical dispersion is the wavelength-dependence of the refractive index, n(λ). Because Snell's law sin θ_refracted = (n₁/n₂) sin θ_incident has n in it, different wavelengths refract at slightly different angles at any interface — the effect that splits white light into a rainbow when it passes through a glass prism. Newton's 1666 prism experiment established the effect as fundamental; nineteenth-century spectroscopy turned it into quantitative wavelength measurement.

In most optical glasses across the visible range, n decreases monotonically with wavelength — red refracts less than blue, the phenomenon called normal dispersion. The Sellmeier equation n²(λ) = 1 + Σᵢ B_i λ² / (λ² − C_i) gives an excellent fit across transparency windows, with the C_i parameters tied to absorption resonances in the UV and IR. Near those resonances, n(λ) behaves non-monotonically — anomalous dispersion, with dn/dλ > 0 (blue refracts less than red), first observed in strongly absorbing dyes in the 1860s. In imaging systems, dispersion produces chromatic aberration: a simple converging lens has different focal lengths for different colours, producing coloured fringes around high-contrast edges. Achromatic doublets, invented in the 1730s, combine a crown-glass converging lens with a flint-glass diverging lens of different dispersion to cancel the chromatic spread at two specified wavelengths.