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
$\sin i \geq \sin C$
where $i=$ angle of incidence
$C =$ critical angle
But $\sin C=\frac{\mu_{2}}{\mu_{1}}$
$\sin i \geq \frac{\mu_{2}}{\mu_{1}} \geq \frac{3 / 2}{2} $
$\Rightarrow i \geq \sin ^{-1}\left(\frac{3}{4}\right)$