S-TIH57 by Ohara

$$n(\lambda) = \sqrt{1 + \frac{2.21103\,\lambda^2}{\lambda^2 - 0.014233} + \frac{0.450347\,\lambda^2}{\lambda^2 - 0.0638573} + \frac{2.47747\,\lambda^2}{\lambda^2 - 161.938}}$$

$$\frac{dn}{dT} = \frac{n_0^2 - 1}{2\,n_0}\left[-2.66 \times 10^{-6} + 2(1.11 \times 10^{-8})\,\Delta T + 3(-1.56 \times 10^{-11})\,\Delta T^2 + \frac{1.12 \times 10^{-6} + 2(1.58 \times 10^{-9})\,\Delta T}{\lambda - 0.293}\right] \Delta T = T - T_0, \quad T_0 = 25\,°\text{C}$$