Question

Consider the ray diagram for the refraction given below. The maximum value of angle $\theta$ for which the light suffers total internal reflection at the vertical surface, is

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

Answer 1

Answer: (B)

The critical angle for this case is
$\theta''=\sin ^{-1} \frac{1}{1 \cdot 25}=\sin ^{-1} \frac{4}{5}$
or $ \sin \theta''=\frac{4}{5}$
Since, $\theta''=\frac{\pi}{2}-\theta'$,
we have $\sin \theta'=\cos \theta''=3 / 5$.
From Snell's law,
$\frac{\sin \theta}{\sin \theta'}=1.25$
or $\sin \theta=1.25 \times \sin \theta'$
$=1.25 \times \frac{3}{5}=\frac{3}{4} $
$\Rightarrow \theta=\sin ^{-1}(3 / 4)$