Magnifying glass I am looking to understand the properties that allow
a magnifying glass to focus sunlight into a hot pin point. 
Specifically I want to know the features of the smallest glass that
will give me a hot enough point to ignite paper.  I have not been able
to get that hot point with a plastic lens only glass but have been
unable to find a small piece under1/2".  As an aside I want to find a
company to provide the right lens.

It is necessary to hold the magnifier at the distance of it's focal length.
Here is some math to explain:
http://www.glenbrook.k12.il.us/gbssci/phys/Class/refrn/u14l5f.html
You can use trial and error to find the right focal lenght (it will
produce the smallest dot).
Use dark paper as it will absorb more light energy.

In order to concentrate the most light with the smallest object you
need curvature....you may wish to look at glass beads (aspheric
lenses) instead....
Link
http://www.frojel.com/Documents/Document03.html

edmunds supplies lenses in the size you are looking for:

http://www.edmundoptics.com/onlinecatalog/DisplayProduct.cfm?productid=2454

Unfortunately, Canadianhelper's comment that "...In order to
concentrate the most light with the smallest object you
need curvature...", is incorrect.

Converging (i.e., convex or magnifying) lenses act to focus parallel
rays of light that are intercepted by their area onto a point (or
line, in the case of cylindrical lenses) lying in the focal plane of
the lens.  See http://hypertextbook.com/physics/waves/lenses/ for a
good explanation.  To increase the amount of energy focused at the
focal point, one needs to increase the amount of sunlight intercepted
by the lens.  Obviously, the easiest way to do this is to increase the
size (aperture) of the lens.   The "light gathering" power of a lens
is directly related to the area of the lens.  This is why larger
telescopes can "see" fainter objects.

Increasing the curvature of the lens changes the "focal length" of the
lens (the distance between the focal plane and the center of the
lens);  it does *not* increase the amount of energy focused at the
focal point.  Higher curvature will decrease the focal length,
bringing the "hotspot" closer to the lens.   Generally, this is not
want you want for your application.  Instead, you would probably
prefer to have the "hotspot" located some conveniently large distance
from the lens itself because this makes it easier to protect the lens,
as well as to manipulate the object being heated.

There are about 1000 watts/(square meter) of sunlight at high noon on
a clear day at the surface of the Earth.  This is roughly the same
power as a heating element on an electric stove.  A circular lens with
a diameter of 7 cm (about 2.75 inches) has an area of about 38.5 cm^2,
or 0.00385 m^2. Assuming a solar insolation of 1000W/m^2, this lens
would concentrate 0.00345*1000 = 3.45 Watts onto the focal point.  A
lens with 10 times that diameter has an area 100 times larger, and
would intercept and concentrate 100 times more energy (345 Watts) onto
the focal point.

Of course, real lenses don't actually focus onto a true "point"; 
optical abberations and diffraction place lower limits on the size of
the "hotspot".  In addition, sunlight is made up of all colors of
light.  All real lenses suffer some degree of chromatic abberation
(resulting from the fact that different colors/wavelengths of light
are refracted different amounts by the lens), so that different colors
are focused onto slightly different focal planes.

You may find the following links of interest:

http://sci-toys.com/scitoys/scitoys/light/marshmallows/solar_roaster.html

http://answers.google.com/answers/threadview?id=525247

hfshaw is correct...however...
The request is for a piece of glass/lens that is less than 1/2 of an
inch big!  You are going to need curvature in order to get a focal
point of any importance no?

And that may be the problem:  a lens of that size may just not gather
enough light to ignite paper.  Perhaps it would work in a controlled
environment or over time, if the lens and paper could move to follow
the sun.

> You are going to need curvature in 
> order to get a focal point of any importance no?

I'm not sure what you mean by a "focal point of any importance", but
in general, the answer is "no".  Increasing the magnifying power of
the lens will neither change the amount of energy available nor change
the power density at the focal point.

A higher quality lens will have a better-defined focal point than a
cheap lens, and a lens that is corrected for chromatic aberations will
also yield better results.  The problem here is that there simply
isn't that much power (in the form of light flux) being collected by
such a small aperture lens.

Your suggestion to use dark-colored paper is a good one.  With white
paper, most of the light (energy) is simply reflected and does not go
into heating the paper.  Dark (ideally matte black) paper will absorb
more of the available energy, and heat up more.

I think you are asking for the "thinest" lens possible.... there is a
type of lens called a fresnel lens. the area of light collected is
irelevant, largely. The standard lens is transfomed into concentric
rings containg lens profiles that duplicate the focus of a larger,
thicker lens enabling a very flat, thin lens to focus light in a
similar fashion. Look in Edmonds Scientific.. for Fresnel Lens