A double - slit apparatus is immersed in a liquid of refractive index `1.33` it has slit separation of 1mm and distance between the plane of slits and screen `1.33` m the slits are illuminated by a parallel beam of light whose wavelength in air is 800 nm.
(i) Calculate the fringe width.
(ii) One of the slits of apparatus is covered by a thin glass sheet of refractive index `1.53` Find the smallest thickness of the sheet to bring the adjacent minima on the axis.

Explanation

Given `mu_(m)=4/3, d=1mm D=4/3m` and `lambda=630nm`
Wavelength `lambda_(m)=lambda/(mu_(m))=800/(4//3)=600nm`
(i) Fringe width `beta=(Dlambda_(m))/d=((4/3)xx600xx10^(-9))/(10^(-3))=800xx10^(-6)m`
(ii) Let thickness of plate `t=mu_(p)=1.53`
Refractive index `._(m)mu_(p)=(mu_(p))/(mu_(m))=(1.53)/(4//3)`
Shift due to plate `=((._(m)mu_(p)-1)tD)/d rArr((._(m)mu_(p)-1)tD)/d=(Dlambda_(m))/(2d)`
Thickness of sheet , t `=lambda_(m)/(2(._(m)mu_(p)-1))=(600xx10^(-9))/(2((1.53)/(4//3)-1))`
`=2033xx10^(-9)m`