Question

A prism of refractive index $\mu$ and angle of prism $A$ is placed in the position of minimum angle of deviation. If minimum angle of deviation is also $A$, then in terms of refractive index

• A. $2 \cos ^{-1}\left(\frac{\mu}{2}\right)$
• B. $ \sin ^{-1}\left(\frac{\mu}{2}\right)$
• C. $\sin ^{-1}\left(\sqrt{\frac{\mu-1}{2}}\right)$
• D. $\cos ^{-1}\left(\frac{\mu}{2}\right)$

Answer 1

Answer: (A)

$\mu=\frac{\sin \left(\frac{A+\delta_{\min }}{2}\right)}{\sin \left(\frac{A}{2}\right)}$
$\mu=\frac{\sin \left(\frac{A+A}{2}\right)}{\sin \left(\frac{A}{2}\right)}$
$\mu=\frac{\sin A}{\sin \frac{A}{2}}=2 \cos \frac{A}{2}$
$A=2 \cos ^{-1}\left(\frac{\mu}{2}\right)$