Question

The speed of light in media $M_1$ and $M_2$ is $1.5\times {10}^8\text{m/s}$ and $2.0\times {10}^8\text{m/s}$ 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 or less than ${\sin }^{-1}\left(\frac{3}{5}\right)$
• B. less than ${\sin }^{-1}\left(\frac{2}{3}\right)$
• C. equal to ${\sin }^{-1}\left(\frac{2}{3}\right)$
• D. equal to or greater than ${\sin }^{-1}\left(\frac{3}{4}\right)$

Answer 1

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

The refractive index of medium $1$ w.r.t medium $2$ will be,

$\mu =\frac{v_2}{v_1}$ ​ ​

Thus, $\mu =\frac{2\times {10}^8}{1.5\times {10}^8}=\frac{4}{3}$

Now, for the ray to suffer total internal reflection,

$\sin i\ge \sin c=\frac{1}{\mu }$

$\Rightarrow \sin i\ge \frac{3}{4}$

$\therefore i\ge {\sin }^{-1}\left(\frac{3}{4}\right)$

Hence, $\left(C\right)$ is the correct answer.