Q. Two media having speeds of light $2 \times 10⁸\ ms\ \bar{}¹$ and $2.4 \times 10^{8}{ms}^{- 1},$ are separated by a plane surface. What is the angle for a ray going from medium I to medium II?
A) $\sin^{- 1}\left( \frac{5}{6} \right)$
B) $\sin^{- 1}\left( \frac{5}{12} \right)$
C) $\sin^{- 1}\left( \frac{1}{\sqrt{2}} \right)$
D) $\sin^{- 1}\left( \frac{1}{2} \right)$
Explanation
(a) The critical angle $\left( \theta_{C} \right)$ is given by
$\theta_{C} = \ \sin^{- 1}\left( \frac{n_{2}}{n_{1}} \right)$
Where $n_{2}$ is refractive index of less denser medium and $n_{1}$ is refractive index of the denser medium.
Also, $\frac{n_{2}}{n_{1}} = \frac{v_{2}}{v_{1}}$
$\therefore\ \theta_{C} = \ \sin^{- 1}\left( \frac{v_{2}}{v_{1}} \right)$
Given, $v_{2}\ = 2 \times 10^{8}\ {ms}^{- 1}\ $
$v_{1} = 2.4 \times 10^{8}\ \ ms^{- 1}$
$\theta_{C} = \ \sin^{- 1}\left( \frac{2 \times 10^{8}\ }{2.4 \times 10^{8}\ } \right)$
$\theta_{C} = \ \sin^{- 1}\left( \frac{5}{6} \right)$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.