TIH53 by Ohara

$$n(\lambda) = \sqrt{3.25347 - 0.0145236\,\lambda^2 + 0.0465051\,\lambda^{-2} + 0.00361596\,\lambda^{-4} - 0.000241944\,\lambda^{-6} + 3.58796 \times 10^{-5}\,\lambda^{-8}}$$

$$\frac{dn}{dT} = \frac{n_0^2 - 1}{2\,n_0}\left[-2.38 \times 10^{-6} + 2(1.45 \times 10^{-8})\,\Delta T + 3(-4.39 \times 10^{-13})\,\Delta T^2 + \frac{6.92 \times 10^{-7} + 2(1.32 \times 10^{-9})\,\Delta T}{\lambda - 0.344}\right] \Delta T = T - T_0, \quad T_0 = 25\,°\text{C}$$