Question

At what angle will a ray of light be incident on one face of an equilateral prism, so that the emergent ray may graze the second surface of the prism $(\mu=2) ?$

• A. $30^{\circ}$
• B. $90^{\circ}$
• C. $45^{\circ}$
• D. $60^{\circ}$

Answer 1

Answer: (B)

Let $C$ by critical angle $\mu=2=\frac{\sin i}{\sin r}$
$i_{\theta}=90^{\circ}$
$60^{\circ}=r+C$ from geometry
$\frac{1}{\mu}=\frac{1}{2}=\frac{\sin C}{\sin i_{e}}$
[At emergent interface]
$C=\sin ^{-1} \frac{1}{2}=30^{\circ} $
$r=30^{\circ}$
$\frac{\sin i}{\sin r}=2 $
$\sin i=1 $
$i=\frac{\pi}{2}$