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 $\theta$. If the ray suffers total internal reflection, Then the value of the angle of incidence $\theta$ is

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

Answer 1

Answer: (C)

Refractive index for medium $M_1$ is
${\mu }_1=\frac{c}{v_1}=\frac{3\times 10^8}{1.5\times 10^8}=\frac{3}{2}$
For total internal reflection
$\sin i\ge \sin C$
where $i=$ angle of incidence
$C=$ critical angle
But $\sin C=\frac{{\mu }_2}{{\mu }_1}$
$\sin i\ge \frac{{\mu }_2}{{\mu }_1}\ge \frac{3/2}{2}$
$\Rightarrow i\ge {\sin }^{-1}\left(\frac{3}{4}\right)$