The connection between 
with 
is just
where c is the speed of light.
We may understand this with the guide of the figure below as follows.
First, to compute the energy flux [energy/area/time] R of an
electromagnetic wave traveling directly toward a surface, we
compute first the total volume of the wave which will pass through the
surface in a time t and multiply that by the energy density of the
wave u to find the total energy passing through the
surface, 
.
To get the flux, we then just divide by the area and the
time 
. The remaining factor of 4 in Eq.
(3) then comes from two corrections. First, only half of
the waves in the cavity are traveling towards the opening through
which we make our measurement (half are traveling away). That gives
one factor of 
. Second, not all of the waves in the
cavity travel directly toward the opening. Most come in at some
angle. In those cases, part of the motion of the wave is parallel to
the surface A reducing the rate at which energy crosses the surface.
Averaging this effect over all directions give the final factor of
in Eq. (3).
