Before we go on, we should understand a few things:

- is now
*complex!*The imaginary part is explicitly connected to the damping constant. - Consequently we can now see how the index of refraction

(9.115) *complex*. A complex index of refraction describes*absorption*(or amplification!) and arises from the*damping*term in the electrons' EOM (or non-linear, non-equilibrium effects in lasers, which we will*not*consider here). This makes energy conservation kind of sense. Energy absorbed by the electrons and*dissipated*via the ``frictional'' damping force is removed from the EM field as it propagates through the medium. This (complex dispersion of incident waves) is the basis for the ``optical'' description of scattering which is useful to nuclear physicists. - The term

has a form that you will see again and again and again in your studies. It should be meditated upon, studied, dreamed about, mentally masticated and enfolded into your beings until you*understand*it. It is a complex equation with*poles*in the imaginary/real plane. It describes (very generally speaking)*resonances*.It is useful to convert this into a form which has manifest real and imaginary parts, since we will have occasion to compute them in real problems one day. A bit of algebra gives us:

- If is ``small'' ( molecules/cc for a gas) is small (just like in the static case) and the medium is nearly transparent at most frequencies.
- if is ``large'' ( molecules/cc for a liquid or
solid) can be quite large in principle, and near a resonance can be
quite large and
*complex!*

These points and more require a new language for their convenient description. We will now pause a moment to develop one.