# Permittivity a function of frequency

1. Aug 4, 2008

### morrobay

How is permittivity a function of frequency ?
And how is permittivity a function of frequency in relation to the refractive index ?

2. Aug 4, 2008

### Hootenanny

Staff Emeritus
The permittivity of a given media depends on the electric susceptibility of the media, which can be considered a measure of how easily the media is polarised by the application of an external electric field. Now in general, when an electric field is applied to dielectric media, the media will not polarise instantaneously. In other words, polarisation occurs some time after the electric field was initially applied, this results in a so-called 'phase difference' between the frequency of the applied electric field and the polarisation of the dielectric media.

The refractive index is defined as the ratio of the speed of light in vacuum to the phase velocity of light in the dielectric media. The phase velocity of light is a function of the permittivity and permeability of the media.

I hope that helps.

3. Aug 4, 2008

### morrobay

Yes I have both Wikipedia papers on permittivity and one on permeabilty and a classics physics text : Haliday Resnick
I have definitions and equations. Permittivity seems to be quite a flexable term.
I would like an explanation on the specific mechanisms of permittivity as it relates to the refractive index. In particular on the 'phase difference' as it relates to an increasing refractive index with frequency.
I understand that the natural resonance frequency of electrons in the medium corresponds more closely to the higher frequencies in the visable part of the spectrum, resulting in preferential absorption and re emission . And when this re emitted light combines with the incident light the average velocity is lower which increases the refractive index at these wavelenghs.If this is related to the so called 'phase difference' then could you explain the specific mechanism in terms of permittivity.