Sellmeier

The Sellmeier equation is an empirical relation that describes the refractive index of a material as a function of wavelength. It is commonly used in optics to predict the dispersion of light in a substance. The equation relates the refractive index, n, to the wavelength of light, λ, and a set of material-specific constants.

The general form of the Sellmeier equation is given by:

n²(λ) = 1 + Σ [Aᵢ λ² / (λ² - Bᵢ)]

where Aᵢ and Bᵢ are the Sellmeier coefficients, which are determined experimentally for each material. The summation is typically over several terms, with the number of terms depending on the material and the range of wavelengths considered. The constants Aᵢ represent the strengths of the absorption bands, and Bᵢ represent the resonant wavelengths of these bands.

The Sellmeier equation is particularly useful for transparent materials over a wide range of wavelengths. It accurately describes dispersion in glasses, crystals, and other optical materials. For shorter wavelengths, where absorption becomes significant, the equation may not be as accurate. In such cases, more complex dispersion models are often employed. The Sellmeier equation is a cornerstone in optical design, enabling precise calculations for lens fabrication, prism design, and the behavior of light in various optical systems.