Re: making a magnifying device without a traditional lense.

Hmm, where to start?!

Most optical instruments, such as telescopes, which use lenses
can be redesigned to use mirrors instead to collect and focus light.
This was first done by Newton - reflecting telescopes having some
advantages such as no chromatic aberration and ease of construction;
but some disadvantages such as having to arrange a more complicated
light path so that the observer does to block the light!

Simple ways of magnifying without "traditional" lenses would include
use of a drop of water, or other liquid - quite effective on a small
scale!  Another kind of non-traditional lens is the "fresnel lens" which
consists of concentric rings, a bit like a lens from which the solid
middle has been removed, and the whole thing squashed flat.  Probably
my description isn't very illuminating - but fortunately you can see
examples of such flat lenses in many over-head projectors and eg. devices
to help see the rear of your car while reversing!  The quality isn't very
good, but they are large, cheap and convenient.

I hope that gives you some food for thought!