Question

At what angle should a ray of light be incident on the face of a prism of refracting angle ${60}^{\circ }$ so that it just suffers total internal reflection at the other face. The refractive index of the prism is 1.524.

• A. ${30}^{\circ }$
• B. ${40}^{\circ }$
• C. ${50}^{\circ }$
• D. ${60}^{\circ }$

Answer 1

Answer: (A)

${30}^{\circ }$

$\sin c=\frac{1}{\mu }=\frac{1}{1.524}=0.65orc={40}^{\circ }{30}^{{}^{\prime }}$
$r={19}^{\circ }{30}^{{}^{\prime }}=\left[{180}^{\circ }{-120}^{\circ }{-40}^{\circ }{30}^{{}^{\prime }}\right]$
$\mu =\frac{\sin i}{\sin r}or\sin i=1.524sin{19}^{\circ }{30}^{{}^{\prime }}$
$=1.524\left(.3340\right)=0.5ori={30}^{\circ }$