Q. The speed of light in media $M_{1}$ and $M_{2}$ is $1.5 \times 10^{8}$ m/s and $2.0 \times 10^{8}\ m/s$ respectively. A ray of light enters from medium $M_{1}$ to $M_{2}$ at an incidence angle $i$. If the ray suffers total internal reflection, the value of $i$ is
A) Equal to $\sin^{- 1}\left( \frac{2}{3} \right)$
B) Equal to or less than $\sin^{- 1}\left( \frac{3}{5} \right)$
C) Equal to or greater than $\sin^{- 1}\left( \frac{3}{4} \right)$
D) Less than $\sin^{- 1}\left( \frac{2}{3} \right)$
Explanation
(c) $\mu_{1} = 2,\ \mu_{2} = \frac{3}{2}$
$2\sin i \geq \frac{3}{2}\sin{90{^\circ}} \Rightarrow \sin i \geq \frac{3}{4} \Rightarrow i \geq \sin^{- 1}\left( \frac{3}{4} \right)$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.