Pete old pal, too much caffeine?
Firstly, rf energy does refract as it passes through the near field of a
tuned element/antenna... If it did not, no radio antenna could work - just
think, no MTV, what a shame...
A good place to look for this without a lot of calculus is in Les Moxon's,
G6XN, "HF Antennas For All Locations" published by the RSGB... Review the
discussion of Super Gain Antennas for a two element array consisting of a
driven half wave dipole element and a closely coupled parasitic dipole
director... The incoming wave front interacts with the director as it passes
over it, and is bent/refracted, focusing it on the driven element raising
the gain of the antenna in exactly the same manner as a telescopic lens...
John Kraus,W8JK, also has good discussions on this in his tome - Antenna
Engineering Handbook - ...

And you are correct that Arecibo dish is mainly a reflector - which,
interestingly, is simply a special case of refraction - but I was using it
to make the point about gathering power increasing as the diameter of the
antenna in wavelengths, increases - and it is one antenna most non technical
folks are familiar with......

Have a look at Feinman's discussion on the relationship between % of
reflected waves and % of refracted waves as light passes through glass with
two plane parallel surfaces where the distance between the two surfaces is
varied in fractions of a wavelength.. Fascinating... Reflection/refraction
are two sides of the same coin...

And I don't know what to think about your last statement... But let me
point out that the faster lens 'gathers more light' because it has a larger
diameter in wavelengths, compared to the slower lens (assuming same focal
length for both)

cheers ... denny

"Peter Duniho" Radio antennae such as that one use reflection, not
refraction, to focus
radio waves. In fact, I'm not aware of a single refractor radio antenna.

Larger optical lenses are "faster" (i.e. lower f- number) because they
gather more light. It has nothing to do with wavelengths.

Pete