(i) The angle of minimum deviation
\(x = \frac{sin{\left(\frac{A+S_m}{2}\right)}}{sin\left(\frac A2\right)}\)
\(\sqrt2=\frac{sin\left(\frac{60 + S_m}{2}\right)}{sin\left(\frac{60}2\right)}\)
\(\sqrt2 \,sin\,30^\circ = sin\left(\frac{60^\circ+S_m}{2}\right)\)
\(\sqrt2 \times\frac12= sin\left(\frac{60^\circ+S_m}{2}\right)\)
\(\frac1{\sqrt2}= sin\left(\frac{60^\circ+S_m}{2}\right)\)
\(sin^{-1}\left(\frac1{\sqrt2}\right)= \frac{60^\circ+S_m}{2}\)
\(45^\circ= \frac{60^\circ+S_m}{2}\)
\(90^\circ= {60^\circ+S_m}\)
\(S_m = 30^\circ\)
(ii) Angle of incidence
\(i = \frac{A+S_m}{2}\)
\(i = \frac{60^\circ+30^\circ}{2}\)
\(i = 45^\circ\)
