Question

A ray of light is incident on surface $AB$ of an equilateral prism of refractive index $\sqrt{2}$ . What should be the maximum angle of incidence $i$ so that the ray could not emerge in air from surface $AC$

• A. $30^\circ $
• B. $45^\circ $
• C. $\left(sin\right)^{- 1}\left(0 . 366\right)$
• D. $\left(sin\right)^{- 1}\left(0 . 677\right)$

Answer 1

Answer: (C)

For total internal reflection on surface $AC$
$r_{2}>\theta _{C}$
$\Rightarrow 60^\circ -r_{1}>\theta _{C}$
$\Rightarrow sinr_{1} < sin\left(60 ^\circ - \left(sin\right)^{- 1} \frac{1}{\sqrt{2}}\right)$
$\Rightarrow \frac{sin i}{\sqrt{2}} < sin15^\circ $
$\Rightarrow i < \left(sin\right)^{- 1}\left(0 . 366\right)$