S-TIM8 by Ohara

$$n(\lambda) = \sqrt{1 + \frac{1.37263\,\lambda^2}{\lambda^2 - 0.010322} + \frac{0.112636\,\lambda^2}{\lambda^2 - 0.0550195} + \frac{1.39786\,\lambda^2}{\lambda^2 - 147.736}}$$

$$\frac{dn}{dT} = \frac{n_0^2 - 1}{2\,n_0}\left[-7.53 \times 10^{-7} + 2(1.17 \times 10^{-8})\,\Delta T + 3(-3.62 \times 10^{-11})\,\Delta T^2 + \frac{5.72 \times 10^{-7} + 2(6.09 \times 10^{-10})\,\Delta T}{\lambda - 0.291}\right] \Delta T = T - T_0, \quad T_0 = 25\,°\text{C}$$