how did archimedis use mirrors to burn up invaders ships
Archimedes did not use mirrors to burn up the Roman invaders' ships. This myth claims that by focusing the sun's rays, Archimedes' mirrors raised the temperature of the ships enough that they caught fire. While a concave mirror held in one hand can light a paper in the other hand by focusing sunlight, burning a distant wooden ship would require an impractically large mirror. As published in the European Journal of Physics under the title " Reflections on the ‘Burning Mirrors of Archimedes' (http://iopscience.iop.org/0143-0807/13/6/004) ," the scientists A. A. Mills and R. Clift calculate that 440 flat square meter mirrors would be needed to smolder wood at a distance of 50 meters. Even then, smoldering wood can be extinguished easy with a splash of salt water. It would be impractical for the Greeks to produce, perfectly align, and effectively use 440 mirrors in 214 BC.
