Question

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 $v_A$ and $v_B$ are velocities of light in $A$ and $B$ materials respectively).

• A. $5 \times 10^{-10} v _{ a } m$
• B. $5 \times 10^{-10} m$
• C. $1.5 \times 10^{-10} m$
• D. $5 \times 10^{-10} v _{ B } m$

Answer 1

Answer: (A)

$\frac{\mu_{ A }}{\mu_{ B }}=\frac{ c / V _{ A }}{ c / V _{ B }}=\frac{ V _{ B }}{ V _{ A }}=\frac{1}{2}$
Let the thickness is $d$
$\frac{ d }{ v _{ B }}-\frac{ d }{ v _{ A }}=5 \times 10^{-10} $
$d =\frac{5 \times 10^{-10} \times v _{ A } v _{ B }}{ v _{ A }- v _{ B }}$
As $v _{ A }=2 v _{ B } \Rightarrow d =5 \times 10^{-10} \times 2 v _{ B }$
Or $d =5 \times 10^{-10} \times v _{ A }$