A double slit apparatus is immersed in a liquid of refractive index 1.33. It has slit and the screen 1 mm. The slits are illuminated by a parallel beam of light whose wavelength in air is `6300 Å`
a. calculate the fringe width.
b. One of the slits of the apparatus is covered by a thin glass sheet of refractive index 1.53. Find the smallest thickness of the sheet to bring athe adjacent minima on the axis.

Explanation

`mu_(m)=4/3, d=1 mm, D=4/3 m, lambda=630 nm`
`lambda_(m)=lambda/mu_(m)=630/(4//3)=1890/4 nm`
(a) `beta=(Dlambda_(m))/d=(4/3xx1890/4xx10^(-9))/10^(-3)=630xx10^(-6) m`
(b) Let thickness of plate t, `mu_(p)=1.53 _(m)mu_(p)=mu_(p)/mu_(m)=1.53/(4//3)`
Shift due to plate=`((._(m)mu_(p)-1)tD)/d`
`((._(m)mu_(p)-1)tD)/d =(Dlambda_(m))/(2d)`
`t=lambda_(m)/(2(._(m)mu_(p)-1))=((1890//4)xx10^(-9))/(2(1.53/(4//3)-1))`
`=1571xx10^(-9)m`