Question

In the given figure $ABC$ is a right-angled isosceles prism kept in air. A ray of light is incident on it normally as shown in figure. Refractive index of the prism is varying with time t as $\mu =1+0.4t$ , here $t$ is in seconds. What is the angular velocity of the emergent ray at time $t=1sec$ ?

• A. 1.2 rad/sec
• B. 1 rad/sec
• C. 2 rad/sec
• D. 1.5 rad/sec

Answer 1

Answer: (C)

In the given
$\mu sin45=1sin\theta \Rightarrow \theta ={\left(sin\right)}^{-1}\left(\frac{\mu }{\sqrt{2}}\right)$

$\frac{d\theta }{dt}=\frac{1}{\sqrt{1-\frac{{\left(\mu \right)}^2}{2}}}\times \frac{1}{\sqrt{2}}\left(\frac{du}{dt}\right)=2$ radisec