Wasn't it Stephen who wrote:
>Warp <war### [at] tagpovrayorg> wrote:
>> G?nther Dietrich <gue### [at] despammedcom> wrote:
>> > Have you already tried the intersection of two CSG-speres? That's just
>> > what real spheric optical lenses are.
>>
>>   Are you sure? Can you give a reference?
>>
>>   I have tried to find the exact mathematical function for a convex lens
>> geometry (ie. a lens which focuses perfectly and evenly) but I just can't
>> find it on the net.
>>
>>   As far as I can tell, there are at least two possibilities: The surface
>> of the lens has to be parabolic, or it has to be spherical. It might also
>> be that it has to have some other shape. However, I can't find this info
>> anywhere!
>>
>> --
>>                                                           - Warp
>
>Is this the sort of thing?
>http://www.reference.com/browse/wiki/Lens_(optics)

The lenses in eyeglasses tend to be more complicated than that. Most
eyeglass prescriptions have a spherical and a cylindrical component, and
some (like those for my mother who has one eye that doesn't point in
quite the right direction due to a mild stroke) have a prism component.

Some info here:
http://en.wikipedia.org/wiki/Eyeglass_prescription

Eyeglass lenses never focus mathematically perfectly. In order to do
that they would have to be parabolic, but parabolic lenses are very much
more difficult to grind. The focussing error of spherical lenses
(spherical abberation) is not sufficient to be a problem for eyeglasses. 

I happen to use varifocal lenses, which have regions that warp and twist
the light in strange ways, but it doesn't cause a problem.

If you Google for "parabolic lens" you'll find that you get hits that
are generally for rather exotic applications, such as focussing X-rays
(plus a pile of hits for therapeutic lighting systems, I can't believe
they use optical quality parabolic lenses).

The spherical aberration effect is significant for telescopes: telescope
mirrors are often parabolic, but even for those the additional
complexity of creating a parabolic surface makes some constructors use
spherical mirrors together with other optical components that cancel out
the aberration.

-- 
Mike Williams
Gentleman of Leisure

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