Corrections:

The *magnitude* of the reflection coefficient for horizontally polarized
waves is very close to one. But the angle is 180 degrees. That is,
there's a phase reversal when the wave reflects. I was also incorrect in
saying that the difference in distances for a 30 degree elevation angle
for the half wave high antenna is exactly a wavelength. The distance
from the antenna to the reflection point is one wavelength, but the
difference in distances the rays travel to a distant point is exactly
1/2 wavelength. This can be seen by drawing a line perpendicular to the
direct and reflected rays as I suggested in my earlier posting, and
looking at the total distances traveled by both rays from their
intersection with it. Combined with the phase reversal, the 1/2
wavelength difference in distances results in complete reinforcement at
a distant point.

I apologize for the errors. Many thanks to John Farr for reminding me of
the phase reversal of the reflection.

Roy Lewallen, W7EL

Roy Lewallen wrote:
. . .
For example, if the antenna is a half
wavelength high, you'll find that at an elevation angle of 30 degrees,
the reflected ray travels exactly one wavelength farther than the direct
ray, so the two rays will exactly add in phase.

. . .

You do also have to
include a factor for the reflection coefficient of the reflected ray
from the ground. But for horizontally polarized waves at moderate to
low angles, it's very close to one.

. . .