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

Answer 1

The correct option is C Equal to or greater than $si{n}^{-1}\left(3/4\right)$

The refractive index of medium 1 wrt medium 2 will be,
$\mu =\frac{v_2}{v_1}$

Thus, $\mu =\frac{2}{1.5}=\frac{4}{3}$

Now, for the ray to suffer total internal reflection,

$sini>sinc=$ $\frac{1}{\mu }$

Thus, $i>$ ${sin}^{-1}\frac{3}{4}$