What should be the minimum thickness of a mica sheet having refractive index n =3/2  which should be placed in front of one of the slits in Young’s double slits experiment so that intensity at the centre of the screen reduced to half of the maximum intensity?

$\frac{\lambda}{2}$

$\text{ For Intensity to be half of maximum at centre of screen the phase difference to be }\frac{\pi}{2}$

$\Rightarrow \text{Path difference} = \frac{\lambda}{2\pi} \times \text {phase difference }= \frac{\lambda}{4}$

$ \text{Path difference} = (\mu -1)t$ 

$ t = \frac{\lambda /4}{3/2 -1} = \frac{\lambda}{2}$