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I read in [1] that for a camera obscura the total spot diameter is equal to the diameter of the spot produced concerning geometric optics only plus the diameter of the spot concerning only diffraction. I am interested to know if this is a general result and how can it be proven?

(I would naively assume that the diameter of the spot just took the maximum of these two diameters)

References

[1]Yung-Kuo, L. (editor) 2007. Problems and Solutions on Optics. New Jersey: World Scientific (p130)

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Yes, it is generally true.

Imagine that your source is composed of many many point sources. Each point source produces a diffraction spot. The complete image is the sum of all of those spots. The points at the edge of an object will "spill" some intensity into the interior of the geometric image, but the diffracted intensity will "spill" outside of the geometric image, resulting in a "diffraction fringe".

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