Question

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 enter 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 or less than ${\sin }^{-1}\left(\frac{3}{5}\right)$
• B. Equal to or greater than ${\sin }^{-1}\left(\frac{3}{4}\right)$
• C. Less than ${\sin }^{-1}\left(\frac{2}{3}\right)$
• D. Equal to ${\sin }^{-1}\left(\frac{2}{3}\right)$

Answer 1

The correct option is B Equal to or greater than ${\sin }^{-1}\left(\frac{3}{4}\right)$

In total internal reflection, the angle of incidence (1) must be greater than critical angle $C$

$\begin{array}{c}2\mu =2and{\mu }_2=\frac{3}{2}\\ 2\sin i\ge \frac{3}{2}\sin {90}^0\\ \sin i\ge \frac{3}{4}\\ i\ge {\sin }^{-1}\left(\frac{3}{4}\right)\\ Hence,\\ optionBiscorrectanswer.\end{array}$