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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.)
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.)
Updated On: Jul 8, 2024
5 × 10-10 vA m
5 × 10-10 m
1.5 × 10-10 m
5 × 10-10 vB m
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The Correct Option is A
Solution and Explanation
\(\frac{\mu_A}{\mu_B}\)=\(\frac{\frac{c}{V_A}}{\frac{c}{V_B}}\)=\(\frac{V_B}{V_A}\)=\(\frac{1}{2}\)
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 vA=2vB
⇒d=5×10−10×2vB
Or
d=5×10−10×vA
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