Question

A ray of light propagates from glass (refractive index $= 3/2$) to water (refractive index $= 4/3$). The value of the critical angle is

• A. $\sin ^{1}\left( \frac{1}{2} \right) $
• B. $\sin^{-1}\left( \sqrt{\frac{8}{9}} \right) $
• C. $\sin^{-1}\left( \frac{8}{9} \right) $
• D. $\sin^{-1}\left( \frac{5}{7} \right) $

Answer 1

Answer: (C)

Refractive index of glass with respect to water
${ }_{w} \mu_{g}=\frac{{ }_{a} \mu_{g}}{{ }_{a} \mu_{w}}=\frac{3 / 2}{4 / 3}$
$=\frac{9}{8}{ }_{w} \mu_{g}=\frac{1}{\sin C}$
$\frac{9}{8}=\frac{1}{\sin C} \sin C =\frac{8}{9} C$
$=\sin ^{-1}\left(\frac{8}{9}\right)$