A monochromatic beam of light is used for the formation of fringes on the screen by illuminating the two slits in the Young’s double slit interference experiment. When a thin film of mica is interposed in the path of one of the  interfering beams then

Fringe width does not change as wavelength  λ remains unchanged.Mica film increased the length of optical path of the ray.by an amount (μ-1) t.At the position of central bright fringe,optical path difference between interfering rays must be zero.So the position of central bright fridge and hence the whole fringe pattern shift towards the slit which is covered by mica film.