  We present a pedagogic derivation of the electromagnetic field established in
a dielectric material by an impinging external field. We consider the problem
from the point of view of the physical mechanism involved at the microscopic
level. The internal field emerges when the material is thought of as an
assembly of atoms in vacuum, each of them being polarized by the external
incident field and by the re-radiated fields of all the other polarized atoms
of the material. In this way, each atom becomes itself a source of secondary
radiation that adds and interferes with all the other internal fields
(including the internal extension of the externally impinging field),
contributing to build up the total internal field within the dielectric
material as well as the externally scattered field. This picture naturally
leads to a connection between the microscopic properties of the material and
its index of refraction, that describes the dielectric response to the applied
electromagnetic field. Calculations also show that the incident radiation is
extinguished inside the dielectric by an equal but opposite field generated by
the total induced polarization currents, and is substituted by a macroscopic
electric field which propagates with the new speed c/n.
