Q 12-10-069JEE MainJEE Main 2024 (9 Apr, Shift 2)Easy
Monochromatic light of wavelength $500\ \text{nm}$ is used in Young's double slit experiment. An interference pattern is obtained on a screen. When one of the slits is covered with a very thin glass plate (refractive index $= 1.5$), the central maximum is shifted to a position previously occupied by the $4^{\text{th}}$ bright fringe. The thickness of the glass plate is ______ $\mu\text{m}$.
Numerical value type. Enter your answer.
Answer: 4
The plate adds an optical path $(\mu - 1)t$, which shifts the pattern by 4 fringes:
$$(\mu - 1)t = 4\lambda \;\Rightarrow\; t = \frac{4\times500\times10^{-9}}{0.5} = 4\times10^{-6}\ \text{m} = 4\ \mu\text{m}$$
Solution by Sreeraj P, M.Sc Physics