Minimum deviation of a prism (${\Delta }_{\min }=2\arcsin (n\sin (A/2))-A$)

For a homogeneous optical prism in the same medium on both sides, the minimum transmitted-ray deviation occurs for a symmetric path: the two internal refraction angles equal half its apex angle $A$. The expression requires $n\sin (A/2)\le 1$; equality is a grazing limiting path.