Q. If light travels a distance $x$ in $t_{1}\ sec$ in air and $10\ x$ distance in $t_{2}$ in a medium, the critical angle of the medium will be
A) $\tan^{- 1}\left( \frac{t_{1}}{t_{2}} \right)$
B) $\sin^{- 1}\left( \frac{t_{1}}{t_{2}} \right)$
C) $\sin^{- 1}\left( \frac{10t_{1}}{t_{2}} \right)$
D) $\tan^{- 1}\left( \frac{{10t}_{1}}{t_{2}} \right)$
Explanation
(c) From the formula $\sin C = \frac{1}{\ _{1}\mu_{2}} \Rightarrow \sin C = \ _{2}\mu_{1}$
$= \frac{\mu_{1}}{\mu_{2}} = \frac{v_{2}}{v_{1}} \Rightarrow \sin C = \frac{10x/t_{2}}{x/t_{1}}$
$\Rightarrow \sin C = \frac{10t_{1}}{t_{2}} \Rightarrow C = \sin^{- 1}\left( \frac{10t_{1}}{t_{2}} \right)$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.