Question

At what angle, a ray of light should be incident on the first face $AB$ of a regular glass prism $ABC$ so that the emergent ray grazes the adjacent face $AC$?
(Refractive Index of glass $=1.6$)

Answer 1

From figure, we can say that:

$\sin r_2=\frac{1}{n}$

$⟹\sin r_2=\frac{1}{1.6}=0.625$

$⟹r_2={38.68}^{\circ }$

Now,

$r_1+r_2=A={60}^{\circ }$

$⟹r_1={60}^{\circ }-{38.68}^{\circ }$

$⟹r_1={21.32}^{\circ }$

Now,

$n=\frac{\sin i}{\sin r_1}$

$⟹\sin i=1.6\times \sin r_1$

$⟹\sin i=0.5817$

$⟹i={35.57}^{\circ }$