  We derive the force of the electromagnetic radiation on material objects by a
direct application of the Lorentz law of classical electro-dynamics. The
derivation is straightforward in the case of solid metals and solid
dielectrics, where the mass density and the optical constants of the media are
assumed to remain unchanged under internal and external pressures, and where
material flow and deformation can be ignored. For metallic mirrors, we separate
the contribution to the radiation pressure of the electrical charge density
from that of the current density of the conduction electrons. In the case of
dielectric media, we examine the forces experienced by bound charges and
currents, and determine the contribution of each to the radiation pressure.
These analyses reveal the existence of a lateral radiation pressure inside the
dielectric media, one that is exerted at and around the edges of a
finite-diameter light beam. The lateral pressure turns out to be compressive
for s-polarized light and expansive for p-polarized light. Along the way, we
derive an expression for the momentum density of the light field inside
dielectric media, one that has equal contributions from the traditional
Minkowski and Abraham forms. This new expression for the momentum density,
which contains both electromagnetic and mechanical terms, is used to explain
the behavior of light pulses and individual photons upon entering and exiting a
dielectric slab. In all the cases considered, the net forces and torques
experienced by material bodies are consistent with the relevant conservation
laws. Our method of calculating the radiation pressure can be used in
conjunction with numerical simulations to yield the distribution of fields and
forces in diverse systems of practical interest.
