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]
$C={\sin }^{-1}\frac{1}{2}=30^{\circ }$
$r=30^{\circ }$
$\frac{\sin i}{\sin r}=2$
$\sin i=1$
$i=\frac{\pi }{2}$