Newton's unpublished theory for the trajectory of a light beam in a medium with varying index of refraction and spherical symmetry is reconstructed. He assumed that light consisted of particles (corpuscles), and derived Snell's refraction law from the assumption that the velocity of these corpuscles is proportional to the index of refraction of the medium, and the acceleration is proportional to its gradient. Surprisingly, Newton's theory leads to a relation for the refraction of light in such a medium that is identically the same as the modern theory based on the wave theory of light.

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