One-reflection path through an equilateral prism (source code)

= One-reflection path through an equilateral prism
{title2=$\delta=180^\circ-2\alpha+2\theta$}

For the lower-face-first ray path through an equilateral <optical prism>, take external entry angle $\theta$, internal refraction angle $r$, base incidence $\alpha-r$ and one <total internal reflection> at the horizontal base. At the other sloped face the internal incidence equals $r$, so <Snell's law> gives exit angle $\theta$ again. Its counterclockwise, oriented direction change is the displayed expression with $\alpha=60^\circ$. It is independent of <refractive index> for this route, but whether the base reflection is total is not. Under <normal dispersion>, a setting at the green critical threshold sends shorter wavelengths along the total-reflection route while longer wavelengths can leak through the base.