In the absence of a driving force, the dipole oscillator (electron cloud and positive core) vibrates at its resonance frequency. In the presence of an E-field whoseFreq the oscillator motion is in the direction of the driving force. When, Freq-, the displacement of the oscillator is in an opposing direction to the E-field, and therefore out of phase by π. The dipole moment is given as






and since


Finally, we arrive with the dispersion equation which shows that refractive index n is a function of the driving frequency


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