refractiveindex

The refractive index, denoted n, is a property of a medium that describes how light propagates through it. It is defined as the ratio of the speed of light in vacuum to the phase velocity of light in the medium: n = c/v. It is a dimensionless quantity and is typically greater than or equal to 1 for ordinary materials.

When light crosses an interface between two media with refractive indices n1 and n2, its path is bent according to Snell's law: n1 sin θ1 = n2 sin θ2. If the medium is non-absorbing, n is real; in absorbing media the refractive index is complex, usually written as ñ = n + iκ, where κ is the extinction coefficient that accounts for attenuation of the wave.

The refractive index often depends on wavelength, a phenomenon known as dispersion. Shorter wavelengths generally experience larger n in many materials, leading to color separation. The dependence is commonly described by empirical formulas such as the Sellmeier equation.

In anisotropic materials like crystals, the refractive index can vary with direction and polarization, giving rise to birefringence where ordinary and extraordinary rays travel at different speeds.

The refractive index can be measured by refractometry, using prisms or critical-angle methods. It also relates to optical path length: the phase accumulated in traveling a distance L is proportional to nL. The index of air is very close to 1 (about 1.00029 at standard conditions).

Common values include water ≈ 1.333, glass ≈ 1.5, and diamond ≈ 2.42. Knowledge of n is essential in designing lenses, coatings, and fiber-optic systems, and it governs reflection and transmission at interfaces via Fresnel equations.