Why are fringes are formed in the Young double slit experiment?

In the Young double slit experiment, coherent light of wavelength λ from a single source illuminates a system of two slits separated from each other by a small distance a. Each slit causes the light entering it to diffract, and behaves like a light source. Light from each slit is then observed on a screen at a distance D far away from the set of slits.At certain points on the screen, the light waves from each slit arrive in phase (phase difference of 2nπ, with n an integer) with each other, due to the difference in the length the waves have travelled (path difference) being nλ. This causes constructive interference and produces a bright fringe. At other points, the waves from each slit arrive in anti-phase (phase difference of (2n+1)π), corresponding to a path length of (2n+1)λ/2, causing destructive interference and producing no resultant wave which looks like a dark fringe. As a result, an alternating pattern of light and dark fringes is formed. The spacing Δx between light fringes is found using Δx = Dλ/a.