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The Sellmeier equation is an empirical relationship between refractive index and wavelength for a particular transparent medium. The equation is used to determine the dispersion of light in the medium. It was first proposed in 1871 by Wilhelm Sellmeier, and was a development of the work of Augustin Cauchy on Cauchy's equation for modelling dispersion. ==The equation== The usual form of the equation for glasses is : where ''n'' is the refractive index, ''λ'' is the wavelength, and ''B''1,2,3 and ''C''1,2,3 are experimentally determined ''Sellmeier coefficients''.〔(Refractive index and dispersion ). Schott technical information document TIE-29 (2007).〕 These coefficients are usually quoted for λ in micrometres. Note that this λ is the vacuum wavelength, not that in the material itself, which is λ/''n''(λ). A different form of the equation is sometimes used for certain types of materials, e.g. crystals. As an example, the coefficients for a common borosilicate crown glass known as ''BK7'' are shown below: The Sellmeier coefficients for many common optical materials can be found in the online database of (RefractiveIndex.info ). For common optical glasses, the refractive index calculated with the three-term Sellmeier equation deviates from the actual refractive index by less than 5×10−6 over the wavelengths' range〔http://oharacorp.com/o2.html〕 of 365 nm to 2.3 µm, which is of the order of the homogeneity of a glass sample.〔http://oharacorp.com/o7.html〕 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 . 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 non-physical values of ''n''2 = ±∞, and in these wavelength regions a more precise model of dispersion such as Helmholtz's must be used. If all terms are specified for a material, at long wavelengths far from the absorption peaks the value of ''n'' tends to : where εr is the relative dielectric constant of the medium. 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. Other variants of the Sellmeier equation exist that can account for a material's refractive index change due to temperature, pressure, and other parameters. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Sellmeier equation」の詳細全文を読む スポンサード リンク
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