 Group index from refracted-angle dispersion

For vacuum incidence at fixed angle ${\theta }_i$ into a transparent isotropic medium, Snell's law gives $n({\lambda }_0)=\sin {\theta }_i/\sin {\theta }_t({\lambda }_0)$. Thus $dn/d{\lambda }_0=-n\cot {\theta }_{t}d{\theta }_t/d{\lambda }_0$, andAngles must be differentiated in radians. This determines the local group velocity from a first derivative of measured refraction angles; pulse broadening needs further information about group velocity dispersion and absorption.