The image "theory" is a simplification of a problem involving an antenna
over an infinite, perfect, ground plane.

Four radials behave nothing like an infinite, perfect ground plane, so
the premises upon which the image model is based do not apply. Trying to
extend it to such systems as four radials will inevitably lead to
seriously mistaken conclusions. The claim about stacked Yagis is just
one example.

Roy Lewallen, W7EL

David wrote:
Image theory is used to justify the idea that a ground plane reflects the
radio wave emitted by a vertical monopole antenna. The radio wave emitted by
the vertical induces currents in the metal ground plane. A charge on the
vertical induces an opposite charge in the ground plane. If charge on end of
vertical is +q, then it induces a charge of -q in the ground plane. The
effect is that the charge -q appears to be a distance below the ground, the
distance being equal to the distance between ground and charge +q above
ground. A distibution of charge is induced in the ground plane by the
radiating vertical.

With a dipole the electric field lines go from +q to -q. If a ground plane
is inserted at the zero or middle point, with charge below ground plane
removed, the electric field lines above the ground plane stay the same. The
metal ground plane is a pool of electrons that adjust so that the voltage at
the surface is zero i.e. tangent E = 0.

Four radials form a counterpoise. The counterpoise has currents induced.
These induced currents then re-radiate, altering the radiation pattern and
inducing currents back in the vertical. The induced currents in vertical
then affect antenna impedance.

A counterpoise is a metal conductor that has currents induced in it by the
radiating element. The currents re-radiate resulting in a field distribution
where the countrpoise is a mirror image or opposite version of the radiating
element.

What surprises me is the claim that the ground plane can mirror a 3D image
e.g. a stacked Yagi.

What are your views on above?

Why do some articles say that the ground plane needs to be connected to the
outer braid of coax, while others says this is not necessary?