White light consists inumerable wavelengths. If monochromatic light is replaced by white light in Young's double slit experiment, then each wavelength form their separate interference pattern. The resultant effect of all these patterns is obtained on the screen.
The waves of all colours reach at mid-point with same or zero phase difference. Therefore, central fringe is white. As fringe width i.e. wavelength increases in order of colours denoted by VIBGYOR, therefore on either side of it some coloured fringes are obtained in reverse order of VIBGYOR. After this the fringes of many colours overlap at each point of the screen and so the screen appears uniformly illuminated.