Editing Dispersion (optics) (section)

== Material dispersion in optics ==
[[File:Mplwp dispersion curves.svg|upright=1.35|thumb|The variation of refractive index vs. vacuum wavelength for various glasses. The wavelengths of visible light are shaded in grey.]]
[[File:Spidergraph Dispersion.GIF|upright=1.45|thumb|Influences of selected glass component additions on the mean dispersion of a specific base glass (''n''<sub>F</sub> valid for ''λ''&nbsp;=&nbsp;486&nbsp;nm (blue), ''n''<sub>C</sub> valid for ''λ''&nbsp;=&nbsp;656&nbsp;nm (red))<ref>[http://glassproperties.com/dispersion/ Calculation of the Mean Dispersion of Glasses].</ref>]]

Material dispersion can be a desirable or undesirable effect in optical applications. The dispersion of light by glass prisms is used to construct [[spectrometer]]s and [[spectroradiometer]]s. However, in lenses, dispersion causes [[chromatic aberration]], an undesired effect that may degrade images in microscopes, telescopes, and photographic objectives.

The ''[[phase velocity]]'' ''v'' of a wave in a given uniform medium is given by
: <math>v = \frac{c}{n},</math>
where ''c'' is the [[speed of light]] in vacuum, and ''n'' is the [[refractive index]] of the medium.

In general, the refractive index is some function of the frequency ''f'' of the light, thus ''n''&nbsp;=&nbsp;''n''(''f''), or alternatively, with respect to the wave's wavelength ''n''&nbsp;=&nbsp;''n''(''λ''). The wavelength dependence of a material's refractive index is usually quantified by its [[Abbe number]] or its coefficients in an empirical formula such as the [[Cauchy's equation|Cauchy]] or [[Sellmeier equation]]s.

Because of the [[Kramers–Kronig relations]], the wavelength dependence of the real part of the refractive index is related to the material [[absorption (electromagnetic radiation)|absorption]], described by the imaginary part of the refractive index (also called the [[refractive index#Dispersion and absorption|extinction coefficient]]). In particular, for non-magnetic materials ([[permeability (electromagnetism)|''μ'']]&nbsp;=&nbsp;[[magnetic constant|''μ''<sub>0</sub>]]), the [[linear response function|susceptibility]] ''χ'' that appears in the Kramers–Kronig relations is the [[electric susceptibility]] ''χ''<sub>e</sub>&nbsp;=&nbsp;''n''<sup>2</sup>&nbsp;−&nbsp;1.

The most commonly seen consequence of dispersion in optics is the separation of [[electromagnetic spectrum#Visible radiation (light)|white light]] into a [[optical spectrum|color spectrum]] by a [[triangular prism (optics)|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 by will also vary with wavelength, causing an angular separation of the colors known as ''angular dispersion''.

For visible light, refraction indices ''n'' of most transparent materials (e.g., air, glasses) decrease with increasing wavelength ''λ'':
: <math>1 < n(\lambda_\text{red}) < n(\lambda_\text{yellow}) < n(\lambda_\text{blue}),</math>
or generally,
: <math>\frac{dn}{d \lambda} < 0.</math>

In this case, the medium is said to have ''normal dispersion''. Whereas if the index increases with increasing wavelength (which is typically the case in the ultraviolet<ref>Born, M. and Wolf, E. (1980) "[[Principles of Optics]]", 6th&nbsp;ed., p.&nbsp;93. Pergamon Press.</ref>), the medium is said to have ''anomalous dispersion''.

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 [[surface normal|normal]] will be refracted at an angle arcsin({{sfrac|sin ''θ''|''n''}}). Thus, blue light, with a higher refractive index, will be bent more strongly than red light, resulting in the well-known [[rainbow]] pattern.