In prism, $r_1+c=A$

$$\begin{aligned} \quad \& r_1=90^{\circ}-c \quad \text{.... (1)}\\ \& \sin c=\frac{1}{\mu} \Rightarrow \cos c=\frac{\sqrt{\mu^2-1}}{\mu} \end{aligned}$$

$\Rightarrow$ 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 $\frac{1}{4}=\mu^2-1$

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