In a Young's double  slit experiment the source S and the two slits A and B are vertical with slit A above slit B. The fringes are observed on a vertical screen K. The optical path length from S to B is increased very slightly (by introducing a transparent material of higher refractive index) and the optical path length from S to A is not changed, as a result the fringe system on K moves

We know that the wavelength is smaller in a medium where the refractive index is higher than that of air or vacuum. Since the bottom slit (B) has the increased optical path, thus the two waves will not meet at the center now because of the introduced phase difference. Instead the fringes will tend to shift somewhat downwards because the bottom slit waves take longer time to reach the screen