S-TIH53 by Ohara

$$n(\lambda) = \sqrt{1 + \frac{1.87905\,\lambda^2}{\lambda^2 - 0.0144122} + \frac{0.36972\,\lambda^2}{\lambda^2 - 0.0638818} + \frac{2.33731\,\lambda^2}{\lambda^2 - 182.668}}$$

$$\frac{dn}{dT} = \frac{n_0^2 - 1}{2\,n_0}\left[-4.85 \times 10^{-6} + 2(8.97 \times 10^{-9})\,\Delta T + 3(-3.32 \times 10^{-11})\,\Delta T^2 + \frac{1.13 \times 10^{-6} + 2(1.6 \times 10^{-9})\,\Delta T}{\lambda - 0.29}\right] \Delta T = T - T_0, \quad T_0 = 25\,°\text{C}$$