= 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 $dn/d\lambda_0=-n\cot\theta_t\,d\theta_t/d\lambda_0$, and
$$
n_g=n\left[1+\lambda_0\cot\theta_t\frac{d\theta_t}{d\lambda_0}\right],\qquad v_g=c/n_g.
$$
Angles 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.
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