Question

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. $\cos^{-1}\left( \frac{3}{2} \right) $

Answer 1

Answer: (A)

$\mu=\frac{\sin \frac{\left(A+\delta_{m}\right)}{2}}{\sin \frac{A}{2}}$
$=\frac{\sin (A+A) / 2}{\sin (A / 2)}$
$=2 \cos A / 2$
or $A=2 \cos ^{-1}\left(\frac{\mu}{2}\right)$
$=2 \cos ^{-1}\left(\frac{1.5}{2}\right)$
$=2 \cos ^{-1}\left(\frac{3}{4}\right)$