JEE Main202225 Jul 2022Morning ShiftPhysicsRay OpticsActual
Time taken by light to travel in two different materials A and B of refractive indices μ A and μ B of same thickness is t 1 and t 2 respectively. If t 2 - t 1 = 5 × 10 - 10 s and the ratio of μ A to μ B is 1 : 2 . Then the thickness of material, in meter is: (Given v A and v B are velocities of light in A and B materials respectively).
Options
- A5 × 10 - 10 v A   m
- B5 × 10 - 10   m
- C1 . 5 × 10 10   m
- D5 × 10 - 10 v B   m
Correct answer
A. 5 × 10 - 10 v A   m
Step-by-step solution
The speed of light in a medium is inversely proportional to the refractive index of the material. Therefore, μ A μ B = v B v A = 1 2 Let the thickness is d ⇒ t 2 - t 1 = d v B - d v A = 5 × 10 - 10   s As v A = 2 v B ⇒ d = 5 × 10 - 10 × 2 v B ⇒ d = 5 × 10 - 10 × v A   m .