[Physics] Why is the central maximum white when white light passes through a diffraction grating

Question

I can't see how path difference and central maximum (where path difference is 0) work when there are more than 2 wave sources.

When a beam of white light passing through a diffraction grating, it is obvious that the central maximum is a white fringe, while other bright fringes are arranged in spectra (due to the composition of white light).

However, I can't understand how the central maximum can be like this. When there are more than 2 circular wave sources, there will be no points where the path difference is 0 for all the waves. Therefore, there should be no path where the antinodal lines from all coloured lights overlap to produce a white fringe.
Can someone please point out what is wrong with my reasoning above?

Answer 1

I am not sure if I am using the same geometry as you. This is my best guess.

Here are a couple images from https://sites.google.com/a/perthgrammar.co.uk/physics/courses/higher/particles-and-waves/35-interference-and-diffraction/353-diffraction-of-waves

This is using a laser with a single wavelength. The important thing is it has a maximum in the center.

Here is a similar image with many lasers with different colors. The higher order maxima do not occur at the same place, leading to rainbows. But they all have a central maximun at the same place. All those colors add to white.