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.)
Solution
<p>${t_2} - {t_1} = 5 \times {10^{ - 10}}$</p>
<p>$\Rightarrow {d \over {{v_B}}} - {d \over {{v_A}}} = 5 \times {10^{ - 10}}$</p>
<p>and, ${{{v_B}} \over {{v_A}}} = {{{\mu _A}} \over {{\mu _B}}} = {1 \over 2}$</p>
<p>$$ \Rightarrow d\left( {1 - {{{v_B}} \over {{v_A}}}} \right) = 5 \times {10^{ - 10}} \times {v_B}$$</p>
<p>$$ \Rightarrow d\left( {1 - {1 \over 2}} \right) = 5 \times {10^{ - 10}} \times {v_B}$$</p>
<p>$\Rightarrow d = 10 \times {10^{ - 10}} \times {v_B}\,m$</p>
<p>$\Rightarrow d = 5 \times {10^{ - 10}} \times {v_A}\,m$</p>
About this question
Subject: Physics · Chapter: Optics · Topic: Refraction and Snell's Law
This question is part of PrepWiser's free JEE Main question bank. 197 more solved questions on Optics are available — start with the harder ones if your accuracy is >70%.