Hydrogen |
1.000visible 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.[15] 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.[16] 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.[17]
For infrared light refractive indices can be considerably higher. Germanium is transparent in the wavelength region from 2 to 14 µm and has a refractive index of about 4.[18] A type of new materials termed "topological insulators", was recently found which have high refractive index of up to 6 in the near to mid infrared frequency range. Moreover, topological insulators are transparent when they have nanoscale thickness. These properties are potentially important for applications in infrared optics.[19]
Refractive index below unity
According to the theory of relativity, no information can travel faster than the speed of light in vacuum, but this does not mean that the refractive index cannot be less than 1. The refractive index measures the phase velocity of light, which does not carry information.[20] The phase velocity is the speed at which the crests of the wave move and can be faster than the speed of light in vacuum, and thereby give a refractive index below 1. This can occur close to resonance frequencies, for absorbing media, in plasmas, and for X-rays. In the X-ray regime the refractive indices are lower than but very close to 1 (exceptions close to some resonance frequencies).[21]
As an example, water has a refractive index of 0.99999974 = 1 − 2.6×10−7 for X-ray radiation at a photon energy of 30 keV (0.04 nm wavelength).[21]
An example of a plasma with an index of refraction less than unity is Earth's ionosphere. Since the refractive index of the ionosphere (a plasma), is less than unity, electromagnetic waves propagating through the plasma are bent "away from the normal" (see Geometric optics) allowing the radio wave to be refracted back toward earth, thus enabling long-distance radio communications. See also infrared light refractive indices can be considerably higher. Germanium is transparent in the wavelength region from 2 to 14 µm and has a refractive index of about 4.[18] A type of new materials termed "topological insulators", was recently found which have high refractive index of up to 6 in the near to mid infrared frequency range. Moreover, topological insulators are transparent when they have nanoscale thickness. These properties are potentially important for applications in infrared optics.[19]
According to the theory of relativity, no information can travel faster than the speed of light in vacuum, but this does not mean that the refractive index cannot be less than 1. The refractive index measures the phase velocity of light, which does not carry information.[20] The phase velocity is the speed at which the crests of the wave move and can be faster than the speed of light in vacuum, and thereby give a refractive index below 1. This can occur close to resonance frequencies, for absorbing media, in plasmas, and for X-rays. In the X-ray regime the refractive indices are lower than but very close to 1 (exceptions close to some resonance frequencies).[21]
As an example, water has a refractive index of 0.99999974 = 1 − 2.6×10−7 for X-ray radiation at a photon energy of 30 keV (0.04 nm wavelength).[21]
An example of a plasma with an index of refraction less than unity is Earth's ionosphere. Since the refractive index of the ionosphere (a plasma), is less than unity, electromagnetic waves propagating through the plasma are bent "away from the normal" An example of a plasma with an index of refraction less than unity is Earth's ionosphere. Since the refractive index of the ionosphere (a plasma), is less than unity, electromagnetic waves propagating through the plasma are bent "away from the normal" (see Geometric optics) allowing the radio wave to be refracted back toward earth, thus enabling long-distance radio communications. See also Radio Propagation and Skywave.[22]
Recent research has also demonstrated the existence of materials with a negative refractive index, which can occur if permittivity and permeability have simultaneous negative values.[23] This can be achieved with periodically constructed metamaterials. The resulting negative refraction (i.e., a reversal of Snell's law) offers the possibility of the superlens and other new phenomena to be actively developed by means of metamaterials.[24][25]
Three conceptions- Veselago's negative-index medium, Pendry's superlense and Efimov's non-reflecting crystal[26] are foundations of the theory of metamaterials with interesting properties of reflection.
Microscopic explanation
In optical mineralogy, electric field creates a disturbance in the charges of each atom (primarily the electrons) proportional to the electric susceptibility of the medium. (Similarly, the magnetic field creates a disturbance proportional to the magnetic susceptibility.) As the electromagnetic fields oscillate in the wave, the charges in the material will be "shaken" back and forth at the same frequency. [1]:67 The charges thus radiate their own electromagnetic wave that is at the same frequency, but usually with a phase delay, as the charges may move out of phase with the force driving them (see sinusoidally driven harmonic oscillator). The light wave traveling in the medium is the macroscopic superposition (sum) of all such contributions in the material: the original wave plus the waves radiated by all the moving charges. This wave is typically a wave with the same frequency but shorter wavelength than the original, leading to a slowing of the wave's phase velocity. Most of the radiation from oscillating material charges will modify the incoming wave, changing its velocity. However, some net energy will be radiated in other directions or even at other frequencies (see scattering).
Depending on the relative phase of the original driving wave and the waves radiated by the charge motion, there are several possibilities:
- If the electrons emit a light wave which is 90° out of phase with the light wave shaking them, it will cause the total light wave to travel slower. This is the normal refraction of transparent materials like glass or water, and corresponds to a refractive index which is real and greater than 1.[27]
- If the electrons emit a light wave which is 270° out of phase with the light wave shaking them, it will cause the wave to travel faster. This is called "anomalous refraction", and is observed close to absorption lines (typically in infrared spectra), with X-rays in ordinary materials, and with radio waves in Earth's ionosphere. It corresponds to a permittivity less than 1, which causes the refractive index to be also less than unity and the phase velocity of light greater than the speed of light in vacuum c (note that the signal velocity is still less than c, as discussed above). If the response is sufficiently strong and out-of-phase, the result is a negative value of permittivity and imaginary index of refraction, as observed in metals or plasma.[27]
- If the electrons emit a light wave which is 180° out of phase with the light wave shaking them
Depending on the relative phase of the original driving wave and the waves radiated by the charge motion, there are several possibilities:
For most materials at visible-light frequencies, the phase is somewhere between 90° and 180°, corresponding to a combination of both refraction and absorption.
Dispersion
Light of different colors has slightly different refractive indices in water and therefore shows up at different positions in the rainbow.
In a prism, dispersion causes different colors to refract at different angles, splitting white light into a rainbow of colors.
frequency) of light. [28] This is called dispersion and causes prisms and rainbows to divide white light into its constituent spectral colors. [29] As the refractive index varies with wavelength, so will the refraction angle as light goes from one material to another. Dispersion also causes the focal length of lenses to be wavelength dependent. This is a type of chromatic aberration, which often needs to be corrected for in imaging systems. In regions of the spectrum where the material does not absorb light, the refractive index tends to decrease with increasing wavelength, and thus increase with frequency. This is called "normal dispersion", in contrast to "anomalous dispersion", where the refractive index increases with wavelength. [28] For visible light normal dispersion means that the refractive index is higher for blue light than for red.
For optics in the visual range, the amount of dispersion of a lens material is often quantified by the Abbe number:[29]

For a more accurate description of the wavelength dependence of the refractive index, the Sellmeier equation can be used.[30] It is an empirical formula that works well in describing dispersion. Sellmeier coefficient For optics in the visual range, the amount of dispersion of a lens material is often quantified by the Abbe number:[29]
For a more accurate description of the wavelength dependence of the refractive index, the Sellmeier equation can be used.[30] It is an empirical formula that works well in describing dispersion. Sellmeier coefficients are often quoted instead of the refractive index in tables.
Because of dispersion, it is usually important to specify the vacuum wavelength of light for which a refractive index is measured. Typically, measurements are done at various well-defined spectral emission lines; for example, nD usually denotes the refractive index at the Fraunhofer "D" line, the centre of the yellow sodium double emission at 589.29 nm wavelength.[15]
Complex refractive index
When light passes through a medium, some part of it will always be attenuated. This can be conveniently taken into account by defining a complex refractive index,
Because of dispersion, it is usually important to specify the vacuum wavelength of light for which a refractive index is measured. Typically, measurements are done at various well-defined spectral emission lines; for example, nD usually denotes the refractive index at the Fraunhofer "D" line, the centre of the yellow sodium double emission at 589.29 nm wavelength.[15]
When light passes through a medium, some part of it will always be attenuated. This can be conveniently taken into account by defining a complex refractive index,
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