Ray Optics

JEE Main level, single correct, medium

100 of 295

Question 100 of 295

Time taken by light to travel in two different materials AA and BB of refractive indices μA{\mu }_{A} and μB{\mu }_{B} of same thickness is t1{t}_{1} and t2{t}_{2} respectively. If t2−t1=5×10−10s{t}_{2}-{t}_{1}=5\times {10}^{-10}s and the ratio of μA{\mu }_{A} to μB{\mu }_{B} is 1:21:2. Then the thickness of material, in meter is: (Given vA{v}_{A} and vB{v}_{B} are velocities of light in AA and BB materials respectively).

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Answer: (A) 5×10−10vAm5\times {10}^{-10}{v}_{A}m

The speed of light in a medium is inversely proportional to the refractive index of the material. Therefore,
μAμB=vBvA=12\dfrac{{\mu }_{A}}{{\mu }_{B}}=\dfrac{{v}_{B}}{{v}_{A}}=\dfrac{1}{2}
Let the thickness is dd
⇒t2−t1=dvB−dvA=5×10−10s\Rightarrow {t}_{2}-{t}_{1}=\dfrac{d}{{v}_{B}}-\dfrac{d}{{v}_{A}}=5\times {10}^{-10}s
As vA=2vB⇒d=5×10−10×2vB{v}_{A}=2{v}_{B}\Rightarrow d=5\times {10}^{-10}\times 2{v}_{B}
⇒d=5×10−10×vAm\Rightarrow d=5\times {10}^{-10}\times {v}_{A}m.

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