Corpuscular theory of light and Double slit experiment

Question

I am sure many scientists would initially have attempted to explain Young's double slit experiment's results using the concept of light as a stream of particles. Can somebody tell me what these attempts were and how they failed?

Answer 1

Young specifically designed the experiment to rule out corpuscular explanations, see How did Young perform his double slit experiment?, so the Newtonians' reactions were more of the nature of Brougham's "absurdity and one of the most incomprehensible suppositions that we remember to have met with in the history of human hypothesis" than alternative explanations. Not even Newton himself could offer a corpuscular explanation of interference, he had to come up with a speculative hybrid of corpuscles with "fits of easy reflection and easy transmission" and a pilot wave. But neither he nor his successors offered a quantitative theory based on it, which wave optics provided, see How did Newton explain his interference rings without wave optics? Here is the gist from Hypothesis Explaining the Properties of Light, 1675:

"And the vibrations or tremors incited in the air by percussion continue a little time to move from the place of percussion in concentric spheres to great distances. And in like manner, when a ray of light falls upon the surface of any pellucid body, and is there refracted or reflected, may not waves of vibrations, or tremors, be thereby excited in the refracting or reflecting medium at the point of incidence and continue to arise there, and to be propagated from thence... and are not these vibrations propagated from the point of incidence to great distances? And do they not overtake the rays of light, and by overtaking them successively, do they not put them into the fits of easy reflexion and easy transmission described above?"