The ratio of the intensity at the centre of a bright fringe to the intensity at a point one-quarter of the distance between two fringe from the centre is

I=4I0cos2ϕ2At central position I1=4I0               …(i)Since the phase difference between two successive fringes is 2x, the phase difference between two points separated by a distance equal to one quarter of the distance between the two, successive fringes is equal to δ=(2π)14=π2 radian ⇒I2=4I0cos2π22=2I0           ….(ii)Using (i) and (ii)   I1I2=4I02I0=2