In prism, $r_1+c=A$
$\begin{gathered}
r_1=90^{\circ}-c \ldots(1)\\
\sin c=\frac{1}{\mu} \Rightarrow \cos c=\frac{\sqrt{\mu^2-1}}{\mu}
\end{gathered}$
$\Rightarrow$ Apply Snell's law, on incidence surface
$\begin{aligned}
1 \cdot \sin 30^{\circ}=\mu \sin \left(r_1\right) \Rightarrow 1 \times \frac{1}{2} & =\mu \times \sin \left(90^{\circ}-c\right) \\
\frac{1}{2} & =\mu \times \frac{\sqrt{\mu^2-1}}{\mu}
\end{aligned}$
On squaring $\frac{1}{4}=\mu^2-1$
$\Rightarrow \mu^2=\frac{5}{4} \Rightarrow \mu=\frac{\sqrt{5}}{2}$