logarithmic lens?

Theoretical exercise- ASSUMING near perfect transmission/reflection, could one create a logarithmic spiral lens/prism (these always have the same angle of reflection for every ray that enters the system, all the way to the end)? A z-axis could be added (like an elongated snail shell) but I can't visualize what this would do to the image (other than rotate it)- the extra axis allows easier access for an eyepiece.

What the logarithmic spiral (which is very strongly related to the Fibonacci sequence and the Golden Mean, thus everything DaVinci Code (Descartes first mathematically characterized them, and Bernoulli had one engraved on his tombstone!) should be doing is acting both as a light-path shortener (the prism 'angle' if you will..), and a focusing agent.

Problems arise because of large numbers of reflections needed (though can the angle defining the curve be optimized for different glass or other material types- then the entire unit could simply be ground or molded) if simply a mirrored unit, or from absorption and other effects if solid material (and prism-like).

Anyway, apparently people have built a big radio scope using this idea, but I haven't been able to find ANY refs on the WWW to optical telescope potential.

Ideas?

Jess Tauber

No takers, eh? Ok, now I'm talking to myself... According to the experts, things like clam, nautilus, and snail shells all exhibit this sort of logarithmic equal angle growth.

But- how about some sort of GROWN astro-usable mirror? After all, things like nacre in mother of pearl get laid down- anything like dielectrics in biological deposition? Can the process be genetically controlled? Can you get 99% reflection?

So.. you just leave Junior in the well-oxygenated tank, pump him up with growth hormones and the occasional Happy Meal, and you're good to go. Couple of years later you've got your very own logarithmic telescope- of course getting Junior to voluntarily vacate the premises might be another issue, but hey, I like calamari as much as the next guy!

Your kids who've grown to love the big fellow (aperture fever?) may be happy to give him the family bathtub- but you've now been worried for several years that the dog or cat (or little Ricky) might go missing, leaving I guess what counts as the equivalent of a contented smile on his mollusky face (interesting factoid- squid/octo/nautiloid 'arms', snail and clam/oyster 'foot' are all really LIPS. OK- have we got our anatomy straight?).

ATM'ing the beast postmortem could be messy, but as your wife may now be screaming at you that's what kitchens and dispose-all's are for (or not, depending on wife...).

Final figuring and polishing could be touch and go, especially in the deeper parts of the shell (never knew, didya, that the toilet snake could be mobilized this way?).

I have absolutely NO IDEA how one would test the figure. Pretty obvious the usual methods won't work here. I suppose one could make some sort of audio test (you know, hold the shell up to your ear and see if you can hear your kids crying upstairs because you had more 'spine' than your new project, or the neighbors fighting two blocks down).

And the novelty value of your finished logarithmic telescope should keep guest observers coming for considerable time. It could be the ultimate grab and go scope (even when still growing, though in the opposite direction!).

Logarithmic curves come in all shapes and sizes- you can have slow, medium or fast scopes. The slow ones all nicely coiled up. And lightweight, too- you ever held a dry nautilus shell? And you can be grateful you didn't have to shell out an arm or a leg for it- well, actually you DID..
Which leads me to my final issue that will have to be addressed- protests at your dark site by the ASPCA.

Jess Tauber