In Young's double slit experiment, if the monochromatic source of light is replaced by white light, then one sees:

The difference in path lengths, being zero at the center gives zero phase difference at the center for all wavelengths. Hence, the center fringe will be white. But at other points on the screen, phase difference will be given by $\mathrm{\varphi } = \mathrm{k}∆\mathrm{x} = \frac{2\mathrm{\pi }}{\mathrm{\lambda }}∆\mathrm{x}$.
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Where Δx is the difference in path lengths. Since λ is different for different colors, hence fringe width will be different for each color and hence all other fringes will be colored.