Question

Two transparent media $\text{A}$ & $\text{B}$ having refractive indices ${\mu }_A=1.5$ and ${\mu }_B=1.2$ respectively in an optical fibre are seperated by a plane boundary. The speed of light in medium $\text{A}$ is $2\times {10}^3\text{m/s}$ and in medium $B$ is $2.5\times {10}^3\text{m/s}$. The critical angle for which a ray of light going from $\text{A}$ to $\text{B}$ is totally internally reflected is :-

• A.
  ${\sin }^{-1}\left(\frac{1}{2}\right)$
• B.
  ${\sin }^{-1}\left(\frac{2}{5}\right)$
• C.
  ${\sin }^{-1}\left(\frac{4}{5}\right)$
• D.
  ${\sin }^{-1}\left(\frac{1}{3}\right)$

Answer 1

The correct option is C

${\sin }^{-1}\left(\frac{4}{5}\right)$


Applying Snell's law to the interface between the given two media we get,

${\mu }_A\sin {\theta }_c={\mu }_B\sin r$....(i)

At critical angle, $\angle r={90}^{\circ }$

From $\left(i\right)$ we get,

$1.5\times \sin {\theta }_c=1.2\times \sin {90}^{\circ }$

$\sin {\theta }_c=\frac{4}{5}\Rightarrow {\theta }_c={\sin }^{-1}\left(\frac{4}{5}\right)$

Hence, option (c) is the correct answer.