Dispersion Electron Theory

A complete theory of dispersion based on electromagnetic theory was propounded by Lorentz. He assumed that the atomic dipoles in a medium execute forced oscillations under the influence of the electric field due to the incident electromagnetic radiation. If E is the electric field at any instant, the force on the electron = Ee. In addition, the electron also experiences
    
(i) An elastic restoring force proportional to displacement = .
    
(ii) A frictional damping force proportional to the velocity



Taking the mass of the electron as m, the total force



In the absence of the external electric field,

E = 0



This equation is similar to the equation



The general solution of this equation is

x = e^-bt [Ae^mt + Be^-mt]

The natural frequency of the system is



If damping is low,



Further, taking (β/m) = g₀ and substituting these values in equation (ii) we get

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