In Young's double slit experiment, two slits $S_1$ and $S_2$ are $d$ distance apart and the separation from slits to screen is $D$ (as shown in figure). Now if two transparent slabs of equal thickness $0.1\ \text{mm}$ but refractive index $1.51$ and $1.55$ are introduced in the path of beam $\lambda=4000\ \text{Å}$ from $S_1$ and $S_2$ respectively, the central bright fringe spot will shift by ______ number of fringes.
Numerical value type. Enter your answer.
Answer: 10
Each slab adds an optical path $(\mu-1)t$. The difference between the two paths is
$$\Delta=(\mu_2-\mu_1)t=(1.55-1.51)\times0.1\times10^{-3}=4\times10^{-6}\ \text{m}$$
Number of fringes shifted $=\dfrac{\Delta}{\lambda}=\dfrac{4\times10^{-6}}{4\times10^{-7}}=10$.
Solution by Sreeraj P, M.Sc Physics