Question

A beam of monochromatic light reflects and refracts at point $A$, as shown in the diagram. Find the angle of refraction at point $A$.

• A. $60^{\circ }$
• B. $45^{\circ }$
• C. $30^{\circ }$
• D. None of these

Answer 1

Answer: (C)

By Snells law
$\frac{\sin i}{\sin r}=\frac{n_2}{n_1}$
$[\because i=(90-30)]$
$\frac{\sin 60^{\circ }}{\sin r}=\frac{\sqrt{3}}{\frac{1}{\sqrt{3}}}$
$\frac{\sqrt{3}}{2\sin r}=\frac{\sqrt{3}}{1}$
$\sin r=\frac{1}{2}$
$\sin r=\sin 30^{\circ }$
$r=30^{\circ }$
So, the angle of refraction at point $A$ is $30^{\circ }$.