moon

The Moon is Earth's only natural satellite and the fifth largest satellite in the Solar System. It is the largest natural satellite of a planet in the Solar System relative to the size of its primary (though Charon?, which orbits the dwarf planet Pluto, is proportionally larger), a quarter the diameter of Earth and 1⁄81 its mass. The Moon is the second densest satellite after Io?. It is in synchronous rotation with Earth, always showing the same face; the near side is marked with dark volcanic maria among the bright ancient crustal highlands and prominent impact craters. It is the brightest object in the sky after the Sun, although its surface is actually very dark, with a similar reflectance to coal. Its prominence in the sky and its regular cycle of phases have since ancient times made the Moon an important cultural influence on language, calendars, art and mythology. The Moon's gravitational influence produces the ocean tides and the minute lengthening of the day. The Moon's current orbital distance, about thirty times the diameter of the Earth, causes it to appear almost the same size in the sky as the Sun, allowing it to cover the Sun nearly precisely in total solar eclipses. Wikipedia Moon (external link)

Moon vs Sun Luminosity
We will assume you will use the full moon to start a fire. Fortunately, the moon has almost exactly the same apparent diameter as the sun and is a sunlit object so that simplifies matters greatly. We shall also ingnore spectral balance differences and only take into account the difference in apparent magnitude. The sun is assigned a magnitude of -26.7 and the full moon about -12.6. As each magnitude is equal to the fifth root of 100 (a change of about 2.5119 times per magnitude) this means the full moon is about 444,631 times dimmer than the sun. So, if we assume you can start a fire with the sun using a magnifier of 1 inch diameter we need a lens (or mirror) of 444,631 times greater area. This gives .785398 X 444,631=349212.
349212/3.1415=111157. Sqrt of 111157=333.4 333.4 X 2 / 12 = 55 foot diameter mirror. from http://bbs.homeshopmachinist.net/threads/5698-Aluminum-telescope-mirrors/page2 (external link)