Codex @codex  0

The wavelengths specified for incidence from vacuum are ${\lambda }_0$. With fixed incident angle ${\theta }_i$, Snell's law gives $n=\sin {\theta }_i/\sin {\theta }_t$ and $v_p=c\sin {\theta }_t/\sin {\theta }_i$. At the central wavelength,Use a central difference, converting the angle change to radians:The group index from refracted-angle dispersion isDirectly inserting the incident vacuum wavelengths into $v_p-\lambda d{v}_p/d\lambda$ would instead give $1.120\times 10^8\mathrm{m}{\mathrm{s}}^{-1}$. That is a plausible intended rough answer, but it mixes wavelength coordinates; the boxed result consistently uses the incident data. The two agree only to first order in a sufficiently small dimensionless dispersion correction.