A plot of the refractive index vs. wavelength using the Sellmeier equation for BK7 glass.

In optics, the Sellmeier equation is an empirical relationship between refractive index n and wavelength λ for a particular transparent medium. The usual form of the equation for glasses is: Image File history File links Sellmeier-equation. ... Optical redirects here. ... In science, an empirical relationship is one based on observation rather than theory: that is, there is no theoretical reason to believe that a relationship should be as claimed; only data that indicates it is. ... The refractive index (or index of refraction) of a material is the factor by which the phase velocity of electromagnetic radiation is slowed in that material, relative to its velocity in a vacuum. ... The wavelength is the distance between repeating units of a wave pattern. ... This article needs to be cleaned up to conform to a higher standard of quality. ...

(definition used by Schott Glass)

where B_1,2,3 and C_1,2,3 are experimentally determined Sellmeier coefficients. These coefficients are usually quoted for λ measured in micrometres. Note that this λ is the vacuum wavelength; not that in the material itself, which is λ/n(λ). In mathematics, a coefficient is a multiplicative factor of a certain object such as a variable (for example, the coefficients of a polynomial), a basis vector, a basis function and so on. ... A micrometre (American spelling: micrometer), symbol µm, is an SI unit of length. ...

The equation is used to determine the dispersion of light in a refracting medium. A different form of the equation is sometimes used for certain types of materials, e.g. crystals. Dispersion of a light beam in a prism. ... Prism splitting light Light is electromagnetic radiation with a wavelength that is visible to the eye (visible light) or, in a technical or scientific context, electromagnetic radiation of any wavelength. ... The straw seems to be broken, due to refraction of light as it emerges into the air. ... Quartz crystal In chemistry and mineralogy, a crystal is a solid in which the constituent atoms, molecules, or ions are packed in a regularly ordered, repeating pattern extending in all three spatial dimensions. ...

The equation was deduced in 1871 by W. Sellmeier, and was a development of the work of Augustin Cauchy on Cauchy's equation for modelling dispersion. 1871 (MDCCCLXXI) was a common year starting on Sunday (see link for calendar). ... Augustin Louis Cauchy Augustin Louis Cauchy (August 21, 1789 – May 23, 1857) was a French mathematician. ... A plot of refactive index vs. ...

As an example, the coefficients for a common borosilicate crown glass known as BK7 are shown below: Borosilicate glass is a particular type of glass, better known under the brand names Pyrex and Kimax. ... Glass can be made transparent and flat, or into other shapes and colours as shown in this ball from the Verrerie of Brehat in Brittany. ...

The Sellmeier coefficients for many common optical glasses can be found in the Schott Glass catalogue, or in the Ohara catalogue. Schott Glass AG is a manufacturer of high-quality industrial glass products, such as fiber-optics and components used in flat panel displays. ...

For common optical glasses, the refractive index calculated with the 3 terms Sellmeier equation only deviates from the actual refractive index by less than 5.10^-6 for wavelengths ranging fron 365nm to 2.3µm [1], which is of the order of the homogeneity of a glass sample [2]. Additional terms are sometimes added to make the calculation even more precise. In its most general form, the Sellmeier equation is given as:

with each term of the sum representing an absorption resonance of strength B_i at a wavelength √C_i. For example, the coefficients for BK7 above correspond to two absorption resonances in the ultraviolet, and one in the mid-infrared region. Close to each absorption peak, the equation gives unphysical values of n=±∞, and in these wavelength regions a more precise model of dispersion such as Helmholtz's must be used. Absorption, in optics, is the process by which the energy of a photon is taken up by another entity, for example, by an atom whose valence electrons make a transition between two electronic energy levels. ... Ultraviolet (UV) light is electromagnetic radiation with a wavelength shorter than that of visible light, but longer than soft X-rays. ... Image of a small dog taken in mid-infrared (thermal) light (false color) Infrared (IR) radiation is electromagnetic radiation of a wavelength longer than that of visible light, but shorter than that of radio waves. ...

At long wavelengths far from the absorption peaks, the value of n tends to:

where ε_r is the relative dielectric constant of the medium. The dielectric constant εr (represented as or K in some cases) is defined as the ratio: where εs is the static permittivity of the material in question, and ε0 is the vacuum permittivity. ...

The Sellmeier equation can also be given in another form:

here the coefficient A is an approximation of the short-wavelength (e.g., ultraviolet) absorption contributions to the refractive index at longer wavelengths.

Coefficients