Hamilton's optical–mechanical analogy between the trajectory of material particles in potential fields and the path of light rays in media with continuously variable refractive index played an important role in the development of Schrödinger's wave mechanics. We shall examine how the Hamilton's analogy between charged-particle beam optics and light beam optics is extended to the wavelength-dependent regime. Brief accounts of the quantum prescriptions of charged-particle beam optics along with the non-traditional prescriptions of light beam optics are also presented. These prescriptions have been instrumental in seeing the analogy in the wavelength-dependent regime.