Question

If $i={90}^{\circ },$ find minimum value of angle of prism $A$ in degrees for which emergence is not possible:

• A.
  ${15}^{\circ }$
• B.
  ${30}^{\circ }$
• C.
  ${45}^{\circ }$
• D.
  ${60}^{\circ }$

Answer 1

The correct option is D

${60}^{\circ }$

Using Snell's law at face $AB$
${\mu }_1\sin i={\mu }_2\sin r$

Given, ${\mu }_1=1$ and ${\mu }_2=2$

$\therefore 1\times \sin {90}^{\circ }=2\sin r$

$\Rightarrow \sin r=\frac{1}{2}$

$\Rightarrow r={30}^{\circ }$

$r^{\prime }>{\theta }_c$ , for no emergence

$r+r^{\prime }=A$

$\therefore r^{\prime }=A-r$

$\Rightarrow A-r>{\theta }_c$

$\Rightarrow A>r+{\theta }_c.....\left(1\right)$

Using Snell' law at face $AC$

$\Rightarrow 2\times \sin {\theta }_c=1\times \sin {90}^{\circ }$

$\Rightarrow {\theta }_c={30}^{\circ }$

So, from equation $\left(1\right)$,

$A>{30}^{\circ }+{30}^{\circ }$

$\therefore A>{60}^{\circ }$

Hence, Option (d) is the correct answer.