Question

The ratio of thickness of plates of two transparent media $A$ & $B$ is $6:4$. If light takes equal time in passing through them, then refractive index of $B$ with respect to $A$ will be :

• A.
  $1.4$
• B.
  $1.5$
• C.
  $1.75$
• D.
  $1.33$

Answer 1

The correct option is B

$1.5$
According to the problem:

$X_A:X_B=6:4$


$\Rightarrow \frac{X_A}{X_B}=\frac{6}{4}....\left(1\right)$

Time taken to cross the thickness $X_A,$

$t_A=\frac{X_A}{V_A}=\frac{X_A}{\frac{c}{{\mu }_A}}=\frac{{\mu }_A{X}_A}{c}...\left(2\right)$

Where, $c$ is the velocity of light.

Similarly, time taken to cross the thickness $X_B$,

$t_B=\frac{X_B}{V_B}=\frac{X_B}{\frac{c}{{\mu }_B}}=\frac{{\mu }_B{X}_B}{c}...\left(3\right)$

Since, $t_A=t_B$

$\Rightarrow \frac{{\mu }_A{X}_A}{c}=\frac{{\mu }_B{X}_B}{c}$

$\Rightarrow \frac{{\mu }_B}{{\mu }_A}=\frac{X_A}{X_B}=\frac{6}{4}$

$\Rightarrow {\mu }_{BA}=1.5$

Hence, option (b) is the correct answer.

$\begin{array}{c}\text{Why this question?}\\ \text{To understand the refraction through}\\ \text{a parallel composite slab.}\end{array}$