Q. A ray of light propagates from glass (refractive index$= \frac{3}{2})\ $to water (refractive index $= \frac{4}{3}).$The value of the critical angle is
A) $\sin^{- 1}\left( \frac{1}{2} \right)$
B) $\sin^{- 1}\left( \sqrt{\frac{9}{8}} \right)$
C) $\sin^{- 1}\left( \frac{8}{9} \right)$
D) $\sin^{- 1}\left( \frac{5}{7} \right)$
Explanation
(c) $\mu\ ᷿$and $\mu_{g}$ are refractive indices for rarer (water) and denser (glass) media, then
$\frac{\sin C}{\sin{90{^\circ}}} = \frac{\mu_{w}\ ᷿}{\mu_{g}}$
$\Rightarrow \sin{C = \frac{4/3}{3/2}} = \frac{8}{9}$
$\Rightarrow C = \ \sin^{- 1}\left( \frac{8}{9} \right)$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.