Question

A light ray is incident normally on the face AB of a right-angled prism ABC $(\mu =1.50)$ as shown in figure. What is the largest angle $\varphi$ for which the light ray is totally reflected at the surface AC ?

Answer 1

Let ${\theta }_c$ be the critical angle for the glass,

$\frac{sin{\theta }_c}{sin{90}^{\circ }}=\frac{1}{x}$

$\Rightarrow sin{\theta }_c=\frac{1}{1.5}=\frac{2}{3}$

$\Rightarrow {\theta }_c=si{n}^{-1}\frac{2}{3}$

For total internal reflection ${90}^{\circ }=\varphi >{\theta }_c$

$\Rightarrow \theta <{90}^{\circ }={\theta }_c$

$\Rightarrow \theta <co{s}^{-1}\left(\frac{2}{3}\right)$

So, the largest angle for which light is totally reflected at the surface is $co{s}^{-1}\left(\frac{2}{3}\right)$.