Fermat’s principle makes $\int ds/c$ stationary. Writing the ray as $x=x(y)$ gives a <Lagrangian> independent of $y$, and its first <integral> is $\sin\theta/c=K$. At the origin $K=(1/\sqrt2)/(1/\sqrt3)=\sqrt{3/2}$. At $x=1$, $c=1/\sqrt2$, so $\sin\theta=\sqrt3/2$ and the forward angle is $\theta=\pi/3$.

Solution

Past exam of the mathematics course of the University of Cambridge / 2026 / ib / Paper 1 / 4B / Solution

 Solution (source code)