The optical rainbow is nowadays of much use, in the laboratory and in industry, in the field of optical characterization. However, the geometrical optics interpretation of the optical rainbow generates a caustic singularity which is a clue that something is wrong, and that a more fundamental theory (in practice, wave optics, or Maxwell's equations) is required to explain the optical rainbow and to accurately enough interpret experiments. There also exists a mechanical rainbow in classical mechanics, also leading to a singularity, implying that classical mechanics is wrong too. To smooth out this singularity, we have to turn to a wave mechanics. By lifting the Hamilton-Jacobi formulation of classical mechanics to a wave mechanics and looking to a time evolution equation, we may reach Schrodinger's equation. We therefore establish a beautiful connection between the rainbow in the sky, and the structure of atoms, in the sky and on earth.