Sellmeier equation
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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:
- <math>
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} <math>
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:
| Coefficient | Value |
|---|---|
| B1 | 1.03961212 |
| B2 | 2.31792344x10-1 |
| B3 | 1.01046945 |
| C1 | 6.00069867x10-3 |
| C2 | 2.00179144x10-2 |
| C3 | 1.03560653x102 |
Using these in the above equation produces the following plot for refractive index versus wavelength:
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Sellmeier-equation.png
image:Sellmeier-equation.png
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