A prism of refractive index


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 $\mathrm{A}$, then in terms of refractive index

  1. $2 \cos ^{-1}\left(\frac{\mu}{2}\right)$

  2. $\sin ^{-1}\left(\frac{\mu}{2}\right)$

  3. $\sin ^{-1}\left(\sqrt{\frac{\mu-1}{2}}\right)$

  4. $\cos ^{-1}\left(\frac{\mu}{2}\right)$

Correct Option: 1


$\mu=\frac{\sin \left(\frac{\mathrm{A}+\delta_{\min }}{2}\right)}{\sin \left(\frac{\mathrm{A}}{2}\right)}$

$\mu=\frac{\sin \left(\frac{\mathrm{A}+\mathrm{A}}{2}\right)}{\sin \left(\frac{\mathrm{A}}{2}\right)}$

$\mu=\frac{\sin \mathrm{A}}{\sin \frac{\mathrm{A}}{2}}=2 \cos \frac{\mathrm{A}}{2}$

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

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