In Young's double slit experiment, the fringe width is β. If the entire arrangement is now placed in a liquid of refractive index μ, the fringe width becomes

we know that β=λD(2d)where 2 d is  distance between two slits. When the arrangement is placed inside a liquid of refractive index υ.let new fringe width becomes βRemembering that in liquid, the wavelength is reduced  by λ/μ, we have β′=(λ/μ)D2d=1μλD2d=βμ