JEE Main 2022 · 25 July · morning · Single correct · +4 / −1
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 t₁ and t₂ respectively. If t₂-t₁=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.)
- (a) 5 × 10⁻¹⁰ v_A m
- (b) 5 × 10⁻¹⁰ m
- (c) 1.5 × 10⁻¹⁰ m
- (d) 5 × 10⁻¹⁰ v_B m
Answer and solution
Answer (a) 5 × 10⁻¹⁰ v_A m
Solution
Physics sir · 3 steps
Write each time as thickness over speed, then use the index ratio to link the two speeds.
- Link the speeds. Speed in a medium is v = c/μ, so speed varies inversely with refractive index. With μ_A : μ_B = 1 : 2, light is twice as fast in A: v_A = 2v_B.
- Write both times. For the same thickness d, t₁ = d/v_A and t₂ = d/v_B = 2d/v_A.
t₂ - t₁ = 2d/v_A - d/v_A = d/v_A = 5 × 10⁻¹⁰ s
- So. d = 5 × 10⁻¹⁰ v_A m, which is option (a).
The idea to keep. Time in a slab is t = (μ d)/c, so a bigger refractive index means a slower, longer trip. Turn index ratios into speed ratios first, and the algebra stays short.
Answer from the NTA final answer key. Solution by PrepWiser.