Question

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 μA to μB 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 1

The Correct Option is A

\(\frac{\mu_A}{\mu_B}\)=\(\frac{\frac{c}{V_A}}{\frac{c}{V_B}}\)=\(\frac{V_B}{V_A}\)=\(\frac{1}{2}\)
Let the thickness be d
\(\frac{d}{v_B}\)−\(\frac{d}{v_A}\)=5×10⁻¹⁰
d=5×10⁻¹⁰×\(\frac{v_Av_B}{v_A-v_B}\)
As v_A=2v_B
⇒d=5×10⁻¹⁰×2v_B
Or 
d=5×10⁻¹⁰×v_A