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 $AC$
$r_2>{\theta }_C$
$\Rightarrow 60^{\circ }-r_1>{\theta }_C$
$\Rightarrow sin{r}_1<sin\left(60^{\circ }-{\left(sin\right)}^{-1}\frac{1}{\sqrt{2}}\right)$
$\Rightarrow \frac{sini}{\sqrt{2}}<sin15^{\circ }$
$\Rightarrow i<{\left(sin\right)}^{-1}\left(0.366\right)$