Question

A light ray is travelling from Region $1$ to $4$ as shown in the figure. The refractive index of the regions are also mentioned there. The angle of incidence $\theta$ for which the beam just missess entering region $4$ is :

• A. ${\sin }^{-1}\left(\frac{3}{4}\right)$
• B. ${\sin }^{-1}\left(\frac{1}{8}\right)$
• C. ${\sin }^{-1}\left(\frac{1}{4}\right)$
• D. ${\sin }^{-1}\left(\frac{1}{3}\right)$

Answer 1

The correct option is B ${\sin }^{-1}\left(\frac{1}{8}\right)$

As per the question, the ray will graze at the boundary of Region $4$. To satisfy this condition incident ray will fall at critical angle on the interface between medium $3$ and $4$.

Therefore, from Snell's law we have:
$n_0\sin \theta =\frac{n_0}{8}\sin {90}^{\circ }$
$\Rightarrow \theta ={\sin }^{-1}\left(\frac{1}{8}\right)$