Question

In a Young’s double slit interference experiment, the slits are at a distance 2L from each
other and the screen is at a distance D from the slits. If a glass slab of refractive index 
and thickness d is placed in the path of one of the beams, the minimum value of d for
the central fringe to be dark is

Answer 1

Youngs double slit experiment

$\Delta x =S$₂$*P-S$ _1*P

from pathegorian relationship$\Delta x=d \sin \theta$

$\sin \theta$ =$\dfrac{Xn}{S}$

$\therefore$ $\Delta x =$ $\dfrac{Xnd}{S}$

from constructive interference $\Delta x =m \lambda$

$\therefore m \lambda =$ $\dfrac{Xn d}{S}$

x_n =$\dfrac{m \lambda}{d}$