Question

Consider the refraction of light ray as shown in the figure below. Incident ray is rotating with constant angular velocity 2 rad/sec. What is the angular velocity of refracted ray, when the angle of incidence becomes ${30}^{\circ }$? (Given $\frac{n_1}{n_2}=\sqrt{3}$)

• A. 2 rad/s
• B. $\sqrt{3}$ rad/s
• C. $\frac{1}{2}$ rad/s
• D. 6 rad/s

Answer 1

The correct option is D 6 rad/s

$n_{1}sin{\theta }_1=n_{2}sin\theta$ ...(i)
$\left(n_{1}cos{\theta }_1\right){\omega }_1=\left(n_{2}cos{\theta }_2\right){\omega }_2$ ...(ii)
Solving (i) and (ii)
${\omega }_2=6$ rad/s