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In optics the refractive index (or index of refraction) n of a substance (optical medium) is a dimensionless number that describes how light, or any other radiation, propagates through that medium. Its most elementary occurrence (and historically the first one) is in Snell's law of refraction, n1sinθ1= n2sinθ2, where θ1 and θ2 are the angles of incidence of a ray crossing the interface between two media with refractive indices n1 and n2.
Refraction, critical angle and reflection of light at the interface between two media. Brewster's angle, the critical angle for total internal reflection, and the reflectivity of a surface also depend on the refractive index, as described by the Fresnel equations. More fundamentally, n is defined as the factor by which the wavelength and the velocity of the radiation are reduced with respect to their vacuum values: The speed of light in a medium is v = c/n, where c is the speed in vacuum. Similarly, for a given vacuum wavelength λ0, the wavelength in the medium is λ=λ0/n. This implies that vacuum has a refractive index of 1. Historically other reference media (e.g., air at a standardized pressure and temperature) have been common. Refractive index of materials varies with the wavelength. This is called dispersion; it causes the splitting of white light in prisms and rainbows, and chromatic aberration in lenses. In opaque media, the refractive index is a complex number: while the real part describes refraction, the imaginary part accounts for absorption. The concept of refractive index is widely used within the full electromagnetic spectrum, from x-rays to radio waves. It can also be used with wave phenomena other than light (e.g., 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. Contents [hide] * 1 Typical values * 1.1 Refractive index below 1 * 1.2 Negative refractive index * 2 Microscopic explanation * 3 Dispersion * 4 Complex index of refraction and absorption * 5 Relations to other quantities * 5.1 Phase speed * 5.2 Refraction * 5.3 Reflectivity * 5.4 Lenses * 5.5 Dielectric constant * 5.6 Density * 5.7 Group index * 5.8 Momentum (Abraham–Minkowski controversy) * 5.9 Other relations * 5.10 Refractivity * 6 Nonscalar, nonlinear, or nonhomogeneous refraction * 6.1 Birefringence * 6.2 Nonlinearity * 6.3 Inhomogeneity * 7 Refractive index measurement * 7.1 Homogeneous media * 7.2 Refractive index variations * 8 Applications * 9 See also * 10 References * 11 External links
Selected refractive indices at λ=589 nm. For references, see the extended List of refractive indices.
Gases at 0 °C and 1 atm
Liquids at 20 °C
Crown glass (typical)
Flint glass (typical)
See also: List of refractive indices
For visible light most transparent media have refractive indices between 1 and 2. A few examples are given in the table to the right. These values are measured at the yellow doublet sodium D-line, 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. Most plastics have refractive indices in the range from 1.3 to 1.7, but some high-refractive-index polymers can have a value as high as 1.76. For infrared light refractive indices can be considerably higher. Germanium is transparent in this region and has a refractive index of about 4,...
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