Richard Clark wrote:

Cecil Moore wrote:
Wave cancellation in a transmission line redistributes the energy in
the opposite direction as constructive interference.

It is established there is "some" amount of energy in the "second"
medium (in other words, beyond the match point as I have
demonstrated); it then follows there is not a total reflection (same
demonstration), and certainly not as constructive (to what?)
interference.

What's wrong with this picture? Looking at it upside down?
With the source on the left, the second medium is to the right
(load side) of the first medium. Of course, there is energy to
the right of the match point - because of standing waves, more
energy than exists in the first medium to the left of the match point.
There's no reflected energy in the first medium to the left of the
match point. It appears to look something like my earlier example:

1w | 1/4WL |
laser-----air-----|---thin-film---|---glass---...
1st medium | 2nd medium | 3rd medium
n=1.0 n=1.2222 n=1.4938
Pfor=1w Pfor=1.0101w Pfor=1w
Pref=0w Pref=0.0101w Pref=0w

Reflected energy is eliminated at the air to thin-film interface
because of wave cancellation (total destructive interference).
According to Hecht and every other reference I've seen, the
reflected energy involved in the wave cancellation event at the
match point joins the forward wave in the 2nd medium. Of course,
that increases the amount of energy in the 2nd medium beyond what
exists in the 1st medium. The necessary (total constructive inter-
ference) energy is contained in those standing waves in the 2nd medium.

www.mellesgriot.com/products/optics/oc_2_1.htm

"Clearly, if the wavelength of the incident light and the thickness
of the film are such that a phase difference exists between reflections
of p, then reflected wavefronts interfere destructively, and overall
reflected intensity is a minimum. If the two reflections are of equal
amplitude, then this amplitude (and hence intensity) minimum will be
zero." [total destructive interference]

"In the absence of absorption or scatter, the principle of conservation
of energy indicates all 'lost' reflected intensity will appear as
enhanced intensity [constructive interference energy] in the transmitted
beam. The sum of the reflected and transmitted beam intensities is always
equal to the incident intensity. This important fact has been confirmed
experimentally." [my notes]

In the above example, the laser's transmitted beam intensity is 1w.
In the 2nd medium, the reflected beam intensity is 0.0101w. The incident
intensity upon the 3rd medium is 1.0101w. "This important fact has been
confirmed experimentally." The above example is equivalent to a
matched 1/4WL transmission line section having the following
lossless characteristics.

1w XMTR--50 ohm coax--+--1/4WL 61.2 ohm coax--+--75 ohm coax--75 ohm load
Pfor=1w Pfor=1.0101w Pfor=1w
Pref=0w Pref=0.0101w Pref=0w
--
73, Cecil http://www.qsl.net/w5dxp


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