Time taken by light to travel in two different materials A and B of refractive indices μA and μB 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 vA and vB are velocities of light in A and B materials respectively.) (a) 5 × 10⁻¹⁰ vA m (b) 5 × 10⁻¹⁰ m (c) 1.5 × 10⁻¹⁰ m (d) 5 × 10⁻¹⁰ vB m

Answer: (a). Time in thickness d: t = d/v, and v ∝ 1/μ. μA: μB = 1:2 ⇒ vA = 2vB, so 1/vB = 2/vA. t₂ - t₁ = d(2/vA - 1/vA) = d/vA = 5 × 10⁻¹⁰. d = 5 × 10⁻¹⁰ vA m, so the answer is (a).

Time taken by light to travel in two different materials A and B of… | JEE Main 2022 (25 Jul, Shift 1)

Q48JEE Main 2022 · 25 JUL · SHIFT 1Medium

Refraction, Glass Slab & Apparent Depth

Time taken by light to travel in two different materials $A$ and $B$ of refractive indices $\mu_A$ and $\mu_B$ of same thickness is $t_1$ and $t_2$ respectively. If $t_2 - t_1 = 5 \times 10^{-10}$ s and the ratio of $\mu_A$ to $\mu_B$ is $1:2$ . Then, the thickness of material, in meter is: (Given $v_\text{A}$ and $v_\text{B}$ are velocities of light in $A$ and $B$ materials respectively.)

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Answer: (a)

Time in thickness $d$ : $t = \dfrac{d}{v}$ , and $v \propto \dfrac{1}{\mu}$ .
$\mu_A : \mu_B = 1:2 \Rightarrow v_A = 2v_B$ , so $\dfrac{1}{v_B} = \dfrac{2}{v_A}$ .
$t_2 - t_1 = d\left(\dfrac{2}{v_A} - \dfrac{1}{v_A}\right) = \dfrac{d}{v_A} = 5 \times 10^{-10}$ .
$d = 5 \times 10^{-10}\,v_A$ m, so the answer is (a).

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