Dispersion (optics)

In optics, dispersion is a phenomenon that causes the separation of a wave into spectral components with different frequencies, due to a dependence of the wave's speed on its frequency. It is most often described in light waves, though it may happen to any kind of wave that interacts with a medium or can be confined to a waveguide, such as sound waves. There are generally two sources of dispersion: material dispersion, which comes from a frequency-dependent response of a material to waves; and waveguide dispersion, which comes because the transverse mode solutions for waves confined laterally within a finite waveguide generally depend upon the frequency (i.e. on the relative size of the wave, the wavelength, and that of the waveguide).

Material dispersion in optics

In optics, the phase velocity of a wave v in a given uniform medium is given by:

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:v = rac{c}{n}

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where c is the speed of light in a vacuum and n is the refractive index of the medium.

Related Topics:
Speed of light - Refractive index

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In general, the refractive index is some function of the frequency ν of the light, thus n = n(ν), or alternately, with respect to the wave's wavelength n = n(λ). The wavelength dependency of a material's refractive index is usually quantified by an empirical formula, the Sellmeier equation.

Related Topics:
Wavelength - Sellmeier equation

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The most commonly seen consequence of dispersion in optics is the separation of white light into a color spectrum by a prism. From Snell's law it can be seen that the angle of refraction of light in a prism depends on the refractive index of the prism material. Since that refractive index varies with wavelength, it follows that the angle that the light is refracted will also vary with wavelength, causing an angular separation of the colors known as angular dispersion.

Related Topics:
Color spectrum - Prism - Snell's law - Refraction

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For visible light, most transparent materials (e.g. glasses) have:

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:1

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or alternatively:

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:rac{dn}{dlambda} < 0,

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that is, refractive index n decreases with increasing wavelength λ.

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At the interface of such a material with air or vacuum (index of ~1), Snell's law predicts that light incident at an angle θ to the normal will be refracted at an angle rcsin(sin( heta)/n). Thus, blue light, with a higher refractive index, will be bent more strongly than red light, resulting in the well-known rainbow pattern.

Related Topics:
Normal - Rainbow

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