The refractive index of prism is μ= 3 and the ratio of the angle of...

For $\delta_{\min }$$\begin{aligned} & \mathrm{i}=\mathrm{e} \\ & \mathrm{r}_1=\mathrm{r}_2=\frac{\mathrm{A}}{2} \\ & \frac{\delta_{\min }}{\mathrm{A}}=1 \\ & \frac{2 \mathrm{i}-\mathrm{A}}{\mathrm{A}}=1 \\ & \\ & 2 \mathrm{i}=2 \mathrm{~A} \\ & \mathrm{i}=\mathrm{A} \end{aligned}$$$<br />Snell's law$$\begin{aligned} & 1 \times \sin i=\mu \sin r \\ & \sin i=\mu \sin \left(\frac{A}{2}\right) \\ & \sin A=\mu \sin \left(\frac{A}{2}\right) \\ & 2 \sin \frac{A}{2} \cos \frac{A}{2}=\sqrt{3} \sin \left(\frac{A}{2}\right) \\ & \cos \left(\frac{A}{2}\right)=\frac{\sqrt{3}}{2} \\ & \therefore \frac{A}{2}=30^{\circ} \\ & \therefore A=60^{\circ} \end{aligned}$$