Plano Convex /Concave Parabolic Lens

[Narasimham]

This may be viewed as further to the subject of earlier thread:

http://groups.google.com/group/sci.optics/browse_frm/thread/f205baef3e87fd43/558adf5bac15c11f?q=Focussing&rnum=2&hl=en#558adf5bac15c11f

In the above discussion about refraction at aspheric surfaces, I had
derived eccentricity = refractive index for Plano-hyperbolic lens for
constant path length from reference planar section to the other focus
in vacuum. By the same token, a Plano-concave lens should radiate rays
as if emerging from first focus of denser medium. Right?

Now parabolic case is special to the hyperbolic, in that its
eccentricity = 1.

Does this mean that incident rays suffer no defection at all? And the
Plano-convex Parabolic Lens and Plano-concave Parabolic Lens behave
just like a normal incidence thick parallel faced plate? And this was
known from Descartes times? Where could be an error?

Among others, may I request participants in that thread to comment here
also? TIA

Narasimham