Question

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 $0.1mm$ but refractive index $1.51$ and $1.55$ are introduced in the path of beam $(\lambda =4000\mathring{A})$ from $S_1$ and $S_2$ respectively, The central bright fringe spot will shift by ______number of fringes.

Answer 1

Answer: 10

Path difference at $P$ be $\Delta x$
$\Delta x=\left({\mu }_2-{\mu }_1\right)t$
$=(1.55-1.51)0.1mm$
$=0.04\times 10^{-4}$
$\Delta x=4\times 10^{-6}=4\mu m$
$y=\frac{\Delta xD}{d}=4\times 10^{-6}\frac{D}{d}$
$\{y$ is the distance of central maxima from geometric center $\}$
$\underset{(\beta )}{\text{ fringe width }}=\frac{\lambda D}{d}=4\times 10^{-6}m\frac{D}{d}=4\mu m\frac{D}{d}$
$\therefore$ Central bright fringe spot will shift by ' $x$ '
Number of shift $=\frac{y}{\beta }$
$=\frac{4\times 10^{-6}D/d}{4\times 10^{-7}D/d}=10$