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 t 1 and t 2 respectively. If t 2 - t 1 = 5 × 10 - 10 s and the ratio of μ A to μ

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 t 1 and t 2 respectively. If t 2 - t 1 = 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).

TestHub · Accepted Answer

The speed of light in a medium is inversely proportional to the refractive index of the material. Therefore,
$\frac{μ_{A}}{μ_{B}} = \frac{v_{B}}{v_{A}} = \frac{1}{2}$
Let the thickness is $d$
$\Rightarrow t_{2} - t_{1} = \frac{d}{v_{B}} - \frac{d}{v_{A}} = 5 \times 10^{- 10} s$
As $v_{A} = 2 v_{B} \Rightarrow d = 5 \times 10^{- 10} \times 2 v_{B}$
$\Rightarrow d = 5 \times 10^{- 10} \times v_{A} m$ .

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