 Solution

Square the stationary condition and eliminate the angle of incidence using Snell's law:Rearranging yields $3n^2{\sin }^2\beta =4-n^2$. Taking the positive root for a physical incident light ray,An interior minimum exists for $1<n<2$, which includes water at visible wavelengths. For illustration, $n=4/3$ gives $\beta =40.20^{\circ }$, $\alpha =59.39^{\circ }$ and ${\delta }_{\min }=137.97^{\circ }$. The corresponding angle from the antisolar direction is $180^{\circ }-{\delta }_{\min }=42.03^{\circ }$. At $n=2$ the stationary solution reaches the endpoint, and for $n>2$ the displayed square root is not real; the water result is not a formula for every possible refractive index.