In optics, the refractive index (also known as refraction index or index of refraction) of a material is a dimensionless number that describes how fast light travels through the material. It is defined as

where c is the speed of light in vacuum and v is the phase velocity of light in the medium. For example, the refractive index of water is 1.333, meaning that light travels 1.333 times as fast in vacuum as in water. Increasing refractive index corresponds to decreasing speed of light in the material.

Illustration of the incidence and refraction angles
Refraction of a light ray

The refractive index determines how much the path of light is bent, or refracted, when entering a material. This is described by Snell's law of refraction, n1 sinθ1 = n2 sinθ2, where θ1 and θ2 are the angles of incidence and refraction, respectively, of a ray crossing the interface between two media with refractive indices n1 and n2. The refractive indices also determine the amount of light that is reflected when reaching the interface, as well as the critical angle for total internal reflection, their intensity (Fresnel's equations) and Brewster's angle.[1]

The refractive index can be seen as the factor by which the speed and the wavelength of the radiation are reduced with respect to their vacuum values: the speed of light in a medium is v = c/n, and similarly the wavelength in that medium is λ = λ0/n, where λ0 is the wavelength of that light in vacuum. This implies that vacuum has a refractive index of 1, and that the frequency (f = v/λ) of the wave is not affected by the refractive index. As a result, the perceived color of the refracted light to a human eye which depends on the frequency is not affected by the refraction or the refractive index of the medium.

The refractive index varies with wavelength, this causes white light to split into constituent colors when refracted. This is called dispersion. It can be observed in prisms and rainbows, and as chromatic aberration in lenses. Light propagation in absorbing materials can be described using a complex-valued refractive index.[2] The imaginary part then handles the attenuation, while the real part accounts for refraction. For most materials the refractive index changes with wavelength by several percent across the visible spectrum. Nevertheless, refractive indices for materials are commonly reported using a single value for n, typically measured at 633 nm.

The concept of refractive index applies within the full electromagnetic spectrum, from X-rays to radio waves. It can also be applied to wave phenomena such as sound. In this case the speed of sound is used instead of that of light, and a reference medium other than vacuum must be chosen.[3]