Refractive index

In optics, the refractive index (or refraction index) of an optical medium is the ratio of the apparent speed of light in the air or vacuum to the speed in the medium. 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 sin θ₁ = n₂ sin θ₂, where θ₁ and θ₂ are the angle of incidence and angle of 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 equations) and Brewster's angle.

The refractive index, ${\displaystyle n}$, 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 assumes that the frequency (f = v/λ) of the wave is not affected by the refractive index.

The refractive index may vary with wavelength. This causes white light to split into constituent colors when refracted. This is called dispersion. This effect 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. 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. Consequently, refractive indices for materials reported using a single value for n must specify the wavelength used in the measurement.

The concept of refractive index applies across 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. Refraction also occurs in oceans when light passes into the halocline where salinity has impacted the density of the water column.

For lenses (such as eye glasses), a lens made from a high refractive index glass will be thinner, and hence lighter, than a – usually cheaper – conventional lens with a lower refractive index.

Plastics materials tend to have lower refractive indices than glasses, but have significantly less density than glasses. Therefore since many years the lightest eyeglasses are fabricated from plastics.

The relative refractive index of an optical medium 2 with respect to another reference medium 1 (n₂₁) is given by the ratio of speed of light in medium 1 to that in medium 2. This can be expressed as follows: $${\displaystyle n_{21}={\frac {v_{1}}{v_{2}}}.}$$ If the reference medium 1 is vacuum, then the refractive index of medium 2 is considered with respect to vacuum. It is simply represented as n₂ and is called the absolute refractive index of medium 2.

The absolute refractive index n of an optical medium is defined as the ratio of the speed of light in vacuum, c = 299792458 m/s, and the phase velocity v of light in the medium, $${\displaystyle n={\frac {\mathrm {c} }{v}}.}$$ Since c is constant, n is inversely proportional to v: $${\displaystyle n\propto {\frac {1}{v}}.}$$ The phase velocity is the speed at which the crests or the phase of the wave moves, which may be different from the group velocity, the speed at which the pulse of light or the envelope of the wave moves. Historically air at a standardized pressure and temperature has been common as a reference medium.