hello, I am trying to make a box which can be placed towards the sun,
and ignite things with the most possible amount of power, concentrated
into one focal point, using only the sun.  the box cannot be more than
2 square feet.  my original thoughts were to put a magnifying glass on
the front, and a mirror in the back, in order to direct other light
into the box.  the box cannot be able to set itself on fire, and holes
can be carved to prevent this, but please take this lack of space into
consideration.

i would like a listing of materials, and a good place to find them
(quality magnifying glasses are suprisingly hard to find), as well as
either schematics or a very good description of how to build this.

if the box could be folded into itself to flatten out, that would be
optimal, and also, preferably, there needs to be a way to make the box
pivot, to line with the direction of the sun, which would leave both
hands free to do other things (like move the flame out of the box)

also, and this is unrelated and would only be a bonus to me:  how can
i easily find out how much space i actually displace?

Just a suggestion:  $2 May not be enough to answer a question of such
detailed scope.  To get a better answer, you may want to consider
upping the price to something more appropriate.

toufaroo has a good suggestion.  At the same time you could define the
size of the box better.  Do you mean the base of the box can not
exceed 2 sq feet?  That would be a square about 17 inches on a side,
but that doesn't say anything about the hight of the box.  You might
be meaning a box that is 2 x 2 x 2 feet, which would have a volume of
8 cubic feet.  Or you could be meaning a box with a volume of 2 cubic
feet, which would be a box about 15 x 15 x 15 inches.

You don't need a particularly high-quality lens for this application. 
A cheap fresnel lens will do just fine.  You might be able to salvage
one from a broken overhead projector, or simply buy one new.  For
instance, good old Edmund Scientific has one for $25 -- see
http://scientificsonline.com/product.asp_Q_pn_E_3052833, or see
http://www.3dlens.com/enter.html?target=Large_Fresnel_Lens.html.  I'm
sure there are lots of other places to buy them online for cheap.

The "depth" of the box will be determined by the focal length of the
lens used.  The focal length, f,  is the distance from the midpoint of
the lens to the point at which incident parallel light rays are made
to converge (i.e., the focal point, which will be your "hot spot"). 
Focal length (expressed in meters) is related to the lens power
(expressed in diopters, d) as:  d = 1/f.

The power density you can achieve at the focal point will depend on
the area of the collector (i.e., the area of the lens in this case),
and the quality of the lens (i.e., how well the lens can focus all the
energy at a single point).  In terms of cost effectiveness and
simplicity, it'll be much easier to use as large a lens as you can,
and sacrifice optical quality (i.e., accept a somehwat "fuzzy" focus.)

The maximum power you'll be able to concentrate is set by the solar
insolation at your location.  Maximum insolation at the Earth's
surface is on the order of 1000 W/m^2, for high noon, no clouds or
dust, and a collector oriented perpendicular to the sun's rays.  One
square foot is equal to about 0.09 square meter, so for every square
foot of collection area, you can "harvest", at most, about 90W of
power under optimum conditions.