Question

A light ray incidents normally on the face of AB of a right angled prism ABC. Prism is made of a material having refractive index of $\mu$ = 1.5 as shown in the figure. What is the largest angle $\theta$ for which light is totally reflected at the surface AC?

• A. sin${}^{-1}\left(\frac{2}{3}\right)$
• B. cos${}^{-1}\left(\frac{2}{3}\right)$
• C. sin${}^{-1}\left(\frac{3}{4}\right)$
• D. cos${}^{-1}\left(\frac{3}{4}\right)$

Answer 1

Answer: (B)

cos${}^{-1}\left(\frac{2}{3}\right)$

Total internal reflection first takes place at D
$\therefore \angle$ PDN = c
$\angle$ ADP = $({90}^{\circ }-c)$
From the figure we see $\theta +c={90}^{\circ }$
c = ${90}^{\circ }-\theta$
$sinc=sin({90}^{\circ }-\theta )$ = cos $\theta$
$\therefore \mu =\frac{1}{\sin c}$ or $\frac{3}{2}=\frac{1}{\sin c}$
$sinc=\frac{2}{3}$ or cos $\theta =\frac{2}{3}$
$\theta ={\cos }^{-1}\left(\frac{2}{3}\right)$