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 m = 1 + 0.4 t here t is in seconds. The angular velocity of the emergent ray at time t = 1 sec is –

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

Answer 1

Answer: (C)

2 rad/sec

Answer 2

sin e = (1 + 0.4 t) × sin 45ŗ

cos e × $\frac { \mathrm { de } } { \mathrm { dt } }$ = $\frac { 1 } { \sqrt { 2 } }$ × 0.4

at t = 1 sec m = 1.4 \ sin e = $\frac { 1.4 } { \sqrt { 2 } }$

cos e = 0.141 \ = $\frac { 0.4 } { 0.141 }$ × $\frac { 1 } { \sqrt { 2 } }$ = 2 rad/sec.