Dueling Mirrors: How Many Recursions?

Many old-style barber's shoppes had opposing walls of mirrors that allowed someone sitting in the chair to see an "infinite" number of images of himself, receding into the distance. I am reminded of the dueling mirrors by an idea from a Salerno province high school physics professor to oppose two parabolic mirrors in order to magnify the heat concentrating effect of incident sunlight. Here is the professor's idea:

The design consists of two parabolic mirrors arranged face-to-face. Sunlight first hits the larger mirror and reflects to the smaller mirror placed a short distance away. Then the light from the smaller mirror reflects back, this time being focused into the vertex of the larger mirror. By confining sunlight into this small region, scientists can ideally trap solar radiation. The sunlight is stored in a blackbody, which consists of a cavity with perfectly reflecting inner walls.

"Through a sunlight trap system, solar radiation is first concentrated in a small region of space and then sent into a blackbody, where it can be stored (not for an arbitrary long time, though) for a variety of uses," De Luca told PhysOrg.com. "For example, after having trapped sunlight in a cavity with perfectly reflecting inner walls, what we call a blackbody, one can think of heating water enclosed in a container placed inside the cavity itself. Other uses of this concept are also conceivable." _PO

The European researchers (U. of Salerno) want to use the idea to generate solar thermal electricity, and possibly to desalinate seawater -- among other ideas.

I cannot help but wonder how many times one could repeat the trick, using increasing numbers of opposing parabolic mirrors? Why stop with only 2 mirrors? Each successive nested "zozzaroid" would be smaller than its predecessor, which places limits on your nested array. Alignment would be critical, but could be easily achieved using visible targets or electronic devices. How hot could you make the "black body" target with 6 opposing mirrors? With 12? What about using "fresnel" "parabolic" mirrors for space saving?

The basic idea is similar to a reflector telescope, which "amplifies" the incident starlight from a large area into the small eyepiece optic. It is unlikely that Newton (or even Archimedes) anticipated these particular uses of dueling reflectors.