Question

Two transparent slabs have the same thickness as shown in figure. One is made pf material $A$ of refractive index $1.5$. The other is made of two materials $B$ and $C$ with thickness in the ratio $1:2$. The refractive index of $C$ is $1.6$. If a monochromatic parallel beam passing through the slabs has the same number of wavelengths inside both, the refractive index of $B$ is

• A. $1.1$
• B. $1.2$
• C. $1.3$
• D. $1.4$

Answer 1

The correct option is C $1.3$

Given: $n_A=1.5$; $n_C=1.6$

Optical path length traveled by beam is same in both the slabs.

$\therefore$ $n_{A}t=n_B\times \frac{t}{3}+n_C\times \frac{2t}{3}$

$\therefore$ $\left(1.5\right)t=n_B\times \frac{t}{3}+\left(1.6\right)\times \frac{2t}{3}$

$⟹n_B=1.3$