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 $0.1 \,mm$ 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

The correct answer is 10.

Path difference at P be Δx
Δx=(μ2​−μ1​)t
=(1.55−1.51)0.1mm
=0.04×10−4
Δx=4×10−6=4μm
y=dΔxD​=4×10−6dD​
{y is the distance of central maxima from geometric center }
(β) fringe width ​=dλD​=4×10−6mdD​=4μmdD​
∴ Central bright fringe spot will shift by ' x '
Number of shift =βy​
=4×10−7D/d4×10−6D/d​=10