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## Main Question or Discussion Point

Say we have an electromagnetic wave propagating inside a dielectric material. Of course physically this material will radiate, due to the little electrons being excited by the wave (their wiggling is also the physical cause of the [tex]\epsilon \neq \epsilon_0[/tex]), and oscillating dipoles radiate. And of course in usual situations this can and should be ignored, but my question is something else: how come in simple treatments of dielectric materials, there is no radiation, none at all? For example, in my book of Griffiths, in chapter 9 we deduce (the properties of) the reflection and refraction of light on a dielectric surface, but it turns out the energy going in (in the initial light beam), is the same as the energy in the reflected beam + the transmitted beam. In other words, the dielectric isn't radiating any energy. This would not seem weird

*if we had made that assumption beforehand*, but it seems that we never made such an approximation. So even though usually negligible, shouldn't there be a certain amount of radiation due to the oscillating dipoles?**Apparently the equations of Maxwell for matter don't account for the radiation caused by the time-variation of [tex]\vec P \quad \textrm{ in } \quad \vec D = \epsilon_0 \vec E + \vec P,[/tex]**

is this correct?(ifis this correct?

*not*correct, how do you explain the first paragraph?)