Cecil Moore wrote:
Gene Fuller wrote:

Does Hecht really say that more power goes into the glass than enters
the 1/4WL film? Can we somehow bottle this free energy and save the
world?


Gene, here's a complete fixed font irradiance diagram of
the air to thin-film interface including all components.
Reflectance = 0.01, Transmittance = 0.99

Forward irradiance component

Ifor=1W --|
|-- I1=0.99W
I3=0.01W--|

air | thin-film

Reflected irradiance component

|-- Iref=0.0101W
I4=0.01W--|
|-- I2=0.0001W

I1 + I2 + 2*SQRT(I1*I2) = 1.0101W = Ifor in the thin-film
This is "total constructive interference" per Hecht.

Not exactly as per Hecht. Note to the casual reader: please be
advised that unlike Cecil, Eugene Hecht does not claim that power is
equal to irradiance. Nor does he imply that scaler quantities can be
treated mathematically in the same way as vector quantities, and he
therefore does not substitute power for irradiance in any of his
textbook equations as Cecil has want to do.

These equations do in fact give correct results macroscopically.
However, it is inaccurate to infer from interference equations that a
given electromagnetic wave is 100% reflected from any partially
reflecting boundary. It is only after multiple partial reflections
from the inner boundaries of the intermediate medium that the total
energy from any given wave in conveyed from source to load.

73, ac6xg