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# Sellmeier equation

In optics, the Sellmeier equation is an empirical relationship between refractive index n and wavelength λ for a particular transparent medium. The usually form of the equation for glasses is:

$n^2(\lambda) = 1 + \frac{B_1 \lambda^2 }{ \lambda^2 - C_1} + \frac{B_2 \lambda^2 }{ \lambda^2 - C_2} + \frac{B_3 \lambda^2 }{ \lambda^2 - C_3}$

where B1,2,3 and C1,2,3 are experimentally determined Sellmeier coefficients. These coefficients are usually quoted for λ measured in micrometres.

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.

As an example, the coefficients for a common borosilicate crown glass known as BK7 are shown below:

CoefficientValue
B11.15150
B21.18584x10-1
B31.26301
C11.05984x10-2
C2-1.18225x10-2
C31.29618x102

Using these in the above equation produces the following plot for refractive index versus wavelength: .

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