\(\sin i \times n_{1}=\sin r \times n_{2}\)

\(\sin i \times 1=\sin \frac{i}{2} \times \sqrt{2 n}\)

\(\frac{\sin i}{\sin \frac{i}{2}}=\sqrt{2 n}\)

\(\frac{\sin \frac{i}{2} \cos \frac{i}{2}}{\sin \frac{i}{2}} \sqrt{2 n}\)

\(\cos \frac{i}{2}=\sqrt{\frac{n}{2}}\)

\(\frac{i}{2}=\cos ^{-1}\left(\sqrt{\frac{n}{2}}\right)\)

\(i=2 \cos ^{-1}\left(\sqrt{\frac{n}{2}}\right)\)