Question

The speed of light in media $M_1$ and $M_2$ are $1.5\times {10}^8$ 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 $si{n}^{-1}\left(\frac{2}{3}\right)$
• B. Equal to or less than $si{n}^{-1}\left(\frac{3}{5}\right)$
• C. Equal to or greater than $si{n}^{-1}\left(\frac{3}{4}\right)$
• D. Less than $si{n}^{-1}\left(\frac{2}{3}\right)$

Answer 1

Answer: (C)

Equal to or greater than $si{n}^{-1}\left(\frac{3}{4}\right)$

For the given question, $\sin c=\frac{c_1}{c_2}=\frac{1.5}{2}=\frac{3}{4}$
Therefore, $c={\sin }^{-1}\frac{3}{4}$
So to suffer total internal reflection $i>{\sin }^{-1}\frac{3}{4}$