Refractive index

In optics, the refractive index (or refraction index) of an optical medium is a dimensionless number that gives the indication of the light bending ability of that 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, , where ''θ''₁ and ''θ''₂ are the angle of incidence and angle of refraction, respectively, of a ray crossing the interface between two media with refractive indices ''n''₁ and ''n''₂. 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.

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 , and similarly the wavelength in that medium is , where ''λ''₀ is the wavelength of that light in vacuum. This implies that vacuum has a refractive index of 1, and assumes that the frequency () 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. 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 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.

For lenses (such as eye glasses), a lens made from a high refractive index material will be thinner, and hence lighter, than a conventional lens with a lower refractive index. Such lenses are generally more expensive to manufacture than conventional ones.

Definition

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:
:$n_=\frac.$
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, , and the phase velocity ''v'' of light in the medium,
:$n=\frac.$
Since ''c'' is constant, ''n'' is inversely proportional to ''v'' :
:$n\propto\frac.$
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.

History

Thomas Young was presumably the person who first used, and invented, the name "index of refraction", in 1807.
At the same time he changed this value of refractive power into a single number, instead of the traditional ratio of two numbers. The ratio had the disadvantage of different appearances. Newton, who called it the "proportion of the sines of incidence and refraction", wrote it as a ratio of two numbers, like "529 to 396" (or "nearly 4 to 3"; for water). Hauksbee, who called it the "ratio of refraction", wrote it as a ratio with a fixed numerator, like "10000 to 7451.9" (for urine). Hutton wrote it as a ratio with a fixed denominator, like 1.3358 to 1 (water).

Young did not use a symbol for the index of refraction, in 1807. In the later years, others started using different symbols:
''n, m'', and µ. Exponent des Brechungsverhältnisses is index of refraction The symbol ''n'' gradually prevailed.

Typical values

Refractive index also varies with wavelength of the light as given by Cauchy's equation:

The most general form of Cauchy's equation is
$n(\lambda) = A + \frac + \frac + \cdots,$
where ''n'' is the refractive index, λ is the wavelength, ''A'', ''B'', ''C'', etc., are coefficients that can be determined for a material by fitting the equation to measured refractive indices at known wavelengths. The coefficients are usually quoted for λ as the vacuum wavelength in micrometres.

Usually, it is sufficient to use a two-term form of the equation:
$n(\lambda) = A + \frac,$
where the coefficients ''A'' and ''B'' are determined specifically for this form of the equation.

For visible light most transparent media have refractive indices between 1 and 2. A few examples are given in the adjacent table. These values are measured at the yellow doublet D-line of sodium, with a wavelength of 589 nanometers, as is conventionally done. Gases at atmospheric pressure have refractive indices close to 1 because of their low density. Almost all solids and liquids have refractive indices above 1.3, with aerogel as the clear exception. Aerogel is a very low density solid that can be produced with refractive index in the range from 1.002 to 1.265. Moissanite lies at the other end of the range with a refractive index as high as 2.65. Most plastics have refractive indices in the range from 1.3 to 1.7, but some high-refractive-index polymers can have values as high as 1.76.

For