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
μ
=
1
+

0.
4t
here t is in seconds. The angular velocity of the emergent ray at time t = 1 sec is:

Answer 1

Answer:

The angular velocity of the emergent ray at t = 1 s is 2 rad/s

Explanation:

By Snell's law at the inclined surface we know that

$\mu_1 sin\theta_1 = \mu_2 sin\theta_2$

so here we know that

$\mu_1 = 1 + 0.4 t$

As we know that prism is right angled isosceles prism so we will have

$\theta_1 = 45^o$

$(1 + 0.4 t) sin45 = 1 sin\theta$

now in order to find the rate of change in the angle we can differentiate the above equation with time

$0.4 sin45 = cos\theta (\frac{d\theta}{dt})$

now at t = 1 s we have

$(1 + 0.4) sin45 = 1 sin\theta$

$\theta = 81.86^o$

now we have

$0.4 sin45 = cos81.86 \omega$

$\omega = 2 rad/s$

#Learn

Topic : Refraction through Prism

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