Gene Fuller wrote:
Cecil Moore wrote:
Keith Dysart wrote:
When the instantaneous energy flows are examined it can be seen
that Prs is not equal to 50 W plus Pref.

That is irrelevant. The power (irradiance) model
doesn't apply to instantaneous energy and power.
Hecht says as much in "Optics".

Nobody has ever claimed that the energy/power
analysis applies to instantaneous values. The
energy/power values are all based on RMS voltages
and currents. There is no such thing as an
instantaneous RMS value.

Interesting.

What is interesting is that in the formula for power
dissipated in the source resistor, the 50 watts is
an average power. It is an invalid procedure to try
to add instantaneous power to an average power.

Do you also use only the RMS phase and RMS interference to come up with
your RMS answers?

I didn't say anything about "RMS phase and RMS interference".
The phase angle used in Hecht's irradiance equation is the
phase between the electric fields of the two waves. The
magnitude of the interference is an average magnitude based
on the RMS values of voltage and current.

I do exactly what Eugene Hecht did in "Optics". He said:

"Furthermore, since the power
arriving cannot be measured instantaneously, the detector
must integrate the energy flux over some finite time, 'T'.
If the quantity to be measured is the net energy per unit
area received, it depends on 'T' and is therefore of limited
utility. If however, the 'T' is now divided out, a highly
practical quantity results, one that corresponds to the
average energy per unit area per unit time, namely 'I'."
'I' is the irradiance (*AVERAGE* power density).

i.e. The irradiance/interference equation does not work
for instantaneous powers which are "of limited utility".
--
73, Cecil http://www.w5dxp.com