Glass prism having a refractive index \(\mu\), placed in a air, for that angle of minimum deviation of prism is same as angle of prism. Then what is value of angle of prism?

(D) \(2 \cos ^{-1}\left(\frac{\mu}{2}\right)\)
\(\mu=\frac{\sin \left(\frac{\mathrm{A}+\mathrm{D}_{m}}{2}\right)}{\sin \frac{\mathrm{A}}{2}}\)
\(\therefore \quad \mu=\frac{\sin \left(\frac{\mathrm{A}+\mathrm{A}}{2}\right)}{\sin \frac{\mathrm{A}}{2}}\)
\(\therefore \mu=\frac{\sin \mathrm{A}}{\sin \frac{\mathrm{A}}{2}}\)
\(\therefore \quad \mu=\frac{2 \sin \frac{\mathrm{~A}}{2} \cos \frac{\mathrm{~A}}{2}}{\sin \frac{\mathrm{~A}}{2}}\)
\(\therefore \quad \frac{\mu}{2}=\cos \frac{\mathrm{A}}{2}\)
\(\therefore \frac{\mathrm{A}}{2}=\cos ^{-1}\left(\frac{\mu}{2}\right)\)
\(\therefore \quad \mathrm{A}=2 \cos ^{-1}\left(\frac{\mu}{2}\right)\)