In a Young's double slit interference experiment, the fringe pattern is observed on a screen placed at a distance D, the slits are separated by d and are illuminated by light of wavelength λ the distance from the central point where the intensity falls to half the maximum is

the intensity at any point on the screen due to two identical slits is given by I = 4 I1 cos2 (δ/2) where I1 intensity  due to either slit. At the center of a bright fringe δ=2nπ At center I = 4I1 ( 8 = 0)  this is maximum intensity Let at a distance x from the center, the intensity is half of maximum intensity, i.e.2 I1 Hence 2I1=4I1cos2⁡δ2or or cos2⁡δ2=12 or cos⁡δ2=12 or δ2=cos−1⁡12=π4  or  δ=π2  Phase difference π/2 corresponds to path difference  λ/4 xdD=λ4  or  x=λD4d