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 $A=2{\cos }^{-1}\left(\frac{\mu }{2}\right)$
$=2{\cos }^{-1}\left(\frac{1.5}{2}\right)$
$=2{\cos }^{-1}\left(\frac{3}{4}\right)$