S-TIM39 by Ohara

$$n(\lambda) = \sqrt{1 + \frac{1.47008\,\lambda^2}{\lambda^2 - 0.01029} + \frac{0.224753\,\lambda^2}{\lambda^2 - 0.0541277} + \frac{2.44969\,\lambda^2}{\lambda^2 - 237.435}}$$

$$\frac{dn}{dT} = \frac{n_0^2 - 1}{2\,n_0}\left[-2.24 \times 10^{-6} + 2(1.21 \times 10^{-8})\,\Delta T + 3(-4.81 \times 10^{-11})\,\Delta T^2 + \frac{6.82 \times 10^{-7} + 2(7.42 \times 10^{-10})\,\Delta T}{\lambda - 0.299}\right] \Delta T = T - T_0, \quad T_0 = 25\,°\text{C}$$