Q. Two transparent slabs have the same thickness as shown. One is made of material $A$ of refractive index 1.5. The other is made of two material $B$ and $C$ with thickness in the ratio $1\ :2$. The refractive index $C$ is 1.6. If a monochromatic parallel beam passing through the slabs has the same number of waves inside both, the refractive index of $B$ is
A) 1.1
B) 1.2
C) 1.3
D) 1.4
Explanation
(c) For $A$
Total number of waves $= \frac{(1.5)t}{\lambda}\ \ \ \ \ \ldots(i)$
$\because\begin{pmatrix}
Total\ number \\
of\ waves
\end{pmatrix} = \left( \frac{optical\ path\ length}{wavelength} \right)$
For $B$ and $C$
Total number of waves $= \frac{n_{B}\left( \frac{t}{3} \right)}{\lambda} + \frac{(1.6)\left( \frac{2t}{3} \right)}{\lambda}\ \ldots(ii)$
Equating (i) and (ii) $n_{B} = 1.3$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.