Archimedes' Burning Mirror Problem Solved (cont.)
By Christopher Jordan

Parabolic concentrators

The problem of how to make powerful solar concentrators has plagued historians and scientists from Archimedes' time to Newton's. The reasons for this interest are not abstract, but the practical uses of the ideal curve. A perfect parabola will concentrate sunlight infinitely, which can be very useful, alas, perfection is impossible to engineer.

A hemisphere is easy to make, but it is thought that it proves a poor parabola. The paper above shows explicitly that if smaller and smaller sections of a sphere are used, the approximation to a parabola increases exponentially. If a twentieth of a spherical surface is used, it concentrates sunlight by several thousand times. If a hundredth of the surface is used, it has an incredible concentration ratio of several million. See the math paper for the detailed calculations.

Concentration ratio for a 1 m dish as the pendulum length increases

The math that underpins the idea is indisputable, but it is the physical proof that persuades most people. There is also the matter of whether the ancients had the technology to build such devices. To address these issues, the mirrors have to be made, tested, found in the archaeological record along with explicit evidence of ancient use.