\(r_1  =90^{\circ}-c\)           \(.......(1)\)

\(\sin c=\frac{1}{\mu}  \Rightarrow \cos c=\frac{\sqrt{\mu^2-1}}{\mu}\)

\(\Rightarrow\) Apply Snell's law, on incidence surface

\(1 \cdot \sin 30^{\circ}=\mu \sin \left(r_1\right) \Rightarrow 1 \times \frac{1}{2}=\mu \times \sin \left(90^{\circ}-c\right)\)

\(\frac{1}{2}=\mu \times \frac{\sqrt{\mu^2-1}}{\mu}\)

On squaring \(\frac{1}{4}=\mu^2-1\)

\(\Rightarrow \mu^2=\frac{5}{4} \Rightarrow \mu=\frac{\sqrt{5}}{2}\)