Prism (optics)

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.

For a homogeneous optical prism in air, with apex angle $\varphi$ and refractive index $n>1$, minimum deviation occurs at the symmetric ray path. Then both internal angles are $\varphi /2$ and both external angles are $({\gamma }_{\min }+\varphi )/2$, so Snell's law givesMeasuring the deviation therefore determines the refractive index at the chosen wavelength.