Q125 / 180 · AIIMS 2014 · Physics

The length of deviation for a glass prism is equal to its refracting angle. The refractive index of glass is 1.5. Then the angle of prism is

  • Correct answer
    A
    $2 \cos ^{-1}(3 / 4)$
  • B
    $\sin ^{-1}(3 / 4)$
  • C
    $2 \sin ^{-1}(3 / 2)$
  • D
    $\cos ^{-1}(3 / 2)$

Solution

Here, $\delta_m=A, \mu=1.5$ $\therefore \mu=\frac{\sin \frac{\left(A+\delta_m\right)}{2}}{\sin \frac{A}{2}}=\frac{\sin \frac{(A+A)}{2}}{\sin \frac{A}{2}}$ $=\frac{2 \sin \left(\frac{A}{2}\right) \cos \left(\frac{A}{2}\right)}{\sin \left(\frac{A}{2}\right)}$ $\frac{3}{2}=2 \cos \frac{A}{2} \quad\left(\because \mu=1.5=\frac{3}{2}\right)$ $\cos \frac{A}{2}=\frac{3}{4}$ $\frac{A}{2}=\cos ^{-1}\left(\frac{3}{4}\right)$ or $A=2 \cos ^{-1}\left(\frac{3}{4}\right)$

Hence, the correct answer is option: 'A'.

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