JEE MAIN - Physics (2022 - 25th July Morning Shift - No. 16)
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 $$v_{\mathrm{A}}$$ and $$v_{\mathrm{B}}$$ are velocities of light in $$A$$ and $$B$$ materials respectively.)
$$5 \times 10^{-10} \,v_{\mathrm{A}}\, \mathrm{m}$$
$$5 \times 10^{-10} \mathrm{~m}$$
$$1.5 \times 10^{-10} \mathrm{~m}$$
$$5 \times 10^{-10} \,v_{\mathrm{B}} \,\mathrm{m}$$
Explanation
$${t_2} - {t_1} = 5 \times {10^{ - 10}}$$
$$ \Rightarrow {d \over {{v_B}}} - {d \over {{v_A}}} = 5 \times {10^{ - 10}}$$
and, $${{{v_B}} \over {{v_A}}} = {{{\mu _A}} \over {{\mu _B}}} = {1 \over 2}$$
$$ \Rightarrow d\left( {1 - {{{v_B}} \over {{v_A}}}} \right) = 5 \times {10^{ - 10}} \times {v_B}$$
$$ \Rightarrow d\left( {1 - {1 \over 2}} \right) = 5 \times {10^{ - 10}} \times {v_B}$$
$$ \Rightarrow d = 10 \times {10^{ - 10}} \times {v_B}\,m$$
$$ \Rightarrow d = 5 \times {10^{ - 10}} \times {v_A}\,m$$
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