= Stationary deviation of a primary rainbow ray
{title2=$\cos\alpha=(n/2)\cos\beta$}
For the one-internal-reflection branch, <Snell's law> and $\delta=\pi+2\alpha-4\beta$ give $\delta'=2-4\cos\alpha/(n\cos\beta)$. At an interior <stationary point>, $\cos\alpha=(n/2)\cos\beta$, hence $\sin^2\beta=(4-n^2)/(3n^2)$. Another <differentiation> gives $\delta''=3\tan\beta>0$ there. The interior minimum exists for $1<n<2$. The internal <specular reflection> can be partial; <total internal reflection> is not required.
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