Q. The least angle 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
A) $2\cos^{- 1}\left( \frac{3}{4} \right)$
B) $\sin^{- 1}\left( \frac{3}{4} \right)$
C) $2\sin^{- 1}\left( \frac{3}{2} \right)$
D) $\cot^{- 1}\left( \frac{3}{2} \right)$
Explanation
(a) $\mu = \frac{sin(\frac{A + \delta_{m}}{2})}{\sin\frac{A}{2}} = \frac{\sin(A + A)/2}{sin(A/2)}$
$= 2\cos\frac{A}{2}$
$or\ \ \ A = 2\cos^{- 1}\left( \frac{\mu}{2} \right)$
$= 2\cos^{- 1}\left( \frac{1.5}{2} \right) = 2\cos^{- 1}\left( \frac{3}{4} \right)$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.