Question

A transparent film of thickness $5\mu \text{m}$ and refractive index $1.4$ is placed in front of the lower slit as shown in the diagram. As a result, the interference pattern shifts through a distance $2\text{mm}$. Find the order of the bright/dark band forming at point $O$ after placing the film. The wavelength of the monochromatic light used is $5000\mathring{\text{A}}$.

• A. Fourth dark fringe
• B. Second bright fringe
• C. Fourth bright fringe
• D. Second dark fringe

Answer 1

The correct option is C Fourth bright fringe

The shift in interference pattern is, $S=\frac{\beta }{\lambda }(\mu -1)t$

$2\times {10}^{-3}=\frac{\beta }{5\times {10}^{-7}}\times (1.4-1)\times 5\times {10}^{-6}$

$\beta =0.5\text{mm}$

Now, the shift in pattern, $S=2\text{mm}=4\beta$

So, fourth bright fringe will be formed at point $O$.

Hence, $\left(C\right)$ is the correct answer.