Today my teacher was discussing the Poisson spot and gave a simple explanation for why there must be a bright spot on the axis of the disc when illuminated with parallel monochromatic light.
What he said was:
Say we instead have a circular aperture in an infinite plane, we know there must be a bright spot at the centre/axis (The Airy Disk pattern). Now, instead of making a circular hole in the plane, we remove the plane itself to get an opaque disk.
So, we have 2 systems one of an opaque disk and one of a circular aperture of the same dimensions in an infinite plane. If we superimpose both these systems, the light ceases to exist as there is no longer an opening. And since only bright can cancel bright, the center of our first system (opaque disk) must be brightly illuminated to cancel the airy disk pattern.
Now my issue is, how did a phase difference of $\pi$ come about between the two systems to induce a destructive interference? Is it just because of complementarity or is there something fundamental going on.
There is a path difference between them for sure, but how are we certain that it is $(n+\frac{1}{2}) \lambda$. Also, how are the intensities same.