The Law of Dispersion and Bohr's Theory of Spectra

Abstract

IT is well known that a consistent description of the phenomena of dispersion, reflection, and scattering of electromagnetic waves by material media can be given on the fundamental assumption that an atom, when exposed to radiation, becomes a source of secondary spherical wavelets, which are coherent with the incident waves. If we imagine that the incident radiation consists of a train of polarised harmonic waves of frequency v, the electric vector of which at the point in space where the atom is situated at rest can be represented by where E is the amplitude and v is a unit vector; the secondary wavelets can be described as originating from a varying electrical doublet, the strength of which is given by where P is the amplitude and w also a unit vector, while represents the phase difference between the secondary and primary waves. The quantities P, w, and depend on u, v, and on the peculiarities of the atom; moreover, the amplitude P will be proportional to the amplitude E of the incident waves.