Dispersion Formulas

Each optical material (glasses, plastics, gases) have a different refraction index for each wavelength.

Instead of keeping long tables, it’s possible to describe the behaviour of optical materials by formulas.

here are the main formulas used :

1: Sellmeier (preferred)
$n^2-1=C_1 + \frac{C_2 \lambda^2}{\lambda^2-C_3^2} + \frac{C_4 \lambda^2}{\lambda^2-C_5^2} + \frac{C_6 \lambda^2}{\lambda^2-C_7^2} + \frac{C_8 \lambda^2}{\lambda^2-C_9^2} + \frac{C_{10} \lambda^2}{\lambda^2-C_{11}^2} + \frac{C_{12} \lambda^2}{\lambda^2-C_{13}^2} + \frac{C_{14} \lambda^2}{\lambda^2-C_{15}^2} + \frac{C_{16} \lambda^2}{\lambda^2-C_{17}^2}$

2: Sellmeier-2
$n^2-1=C_1 + \frac{C_2 \lambda^2}{\lambda^2-C_3} + \frac{C_4 \lambda^2}{\lambda^2-C_5} + \frac{C_6 \lambda^2}{\lambda^2-C_7} + \frac{C_8 \lambda^2}{\lambda^2-C_9} + \frac{C_{10} \lambda^2}{\lambda^2-C_{11}} + \frac{C_{12} \lambda^2}{\lambda^2-C_{13}} + \frac{C_{14} \lambda^2}{\lambda^2-C_{15}} + \frac{C_{16} \lambda^2}{\lambda^2-C_{17}}$

3: Polynomial
$n^2 = C_1 + C_2 \lambda^{C_3} + C_4 \lambda^{C_5} + C_6 \lambda^{C_7} + C_8 \lambda^{C_9} + C_{10} \lambda^{C_{11}} + C_{12} \lambda^{C_{13}} + C_{14} \lambda^{C_{15}} + C_{16} \lambda^{C_{17}}$

4: RefractiveIndex.info
$n^2 = C_1 + \frac{C_2 \lambda^{C_3}}{\lambda^2-{C_4}^{C_5}} + \frac{C_6 \lambda^{C_7}}{\lambda^2-{C_8}^{C_9}} + C_{10} \lambda^{C_{11}} + C_{12} \lambda^{C_{13}} + C_{14} \lambda^{C_{15}} + C_{16} \lambda^{C_{17}}$

5: Cauchy
$n = C_1 + C_2 \lambda^{C_3} + C_4 \lambda^{C_5} + C_6 \lambda^{C_7} + C_8 \lambda^{C_9} + C_{10} \lambda^{C_{11}}$

6: Gases
$n-1 = C_1 + \frac{C_2}{C_3-\lambda^{-2}} + \frac{C_4}{C_5-\lambda^{-2}} + \frac{C_6}{C_7-\lambda^{-2}} + \frac{C_8}{C_9-\lambda^{-2}} + \frac{C_{10}}{C_{11}-\lambda^{-2}}$