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

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.