= Cherenkov escape condition at a flat dielectric interface
{title2=$n_1\sin\theta_C\le n_2$}
A photon emitted at angle $\theta_C$ to a normally incident particle can cross a planar boundary from index $n_1$ to $n_2$ only if <Snell's law> permits a real transmitted angle. Combining $\cos\theta_C=1/(n_1\beta)$ with that condition gives $n_1^2-\beta^{-2}\le n_2^2$. Otherwise the photon undergoes <total internal reflection>. For a relativistic particle in glass of index $1.55$ followed by air, the condition fails despite emission inside the glass.
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