The question was:

**The legend has it that Greeks, on the advice of Archimedes, have burned the
Roman ships by focusing the sunlight (reflected from their shields) on the
ships. Is it possible?**

The answer is **YES**, but just barely...

Dry wood can be lighted by focusing the sunlight by a lens of diameter *d*=3cm
and focal length *f*=10cm (the "regular" variety of a lens...).
The angular diameter of the sun is *a*=0.01rad. The flux of light through
such a lens is:

*F=E({pi}/4)d^2*,

where E is the flux of the sunlight on the surface of earth. The area of the
image of sun created by such a lens is

*S=({pi}/4)(af)^2*.

Thus the illumination required to light the wood is

*I=F/S=Ed^2/(af)^2=900E*.

If the shields of Greek soldiers were flat and the ships were close to shore
we can neglect the widening of the reflected beams of light. If we further
assume 50% reflectivity of the shields, we can see that 1800 soldiers can
create illumination of 900E required to light the wood, provided they all
direct their shields in such a way that the reflected light falls at the same
spot.

Comment: There is a beautiful and very informative web-site
dedicated to Archimedes:

http://www.mcs.drexel.edu/~crorres/Archimedes/contents.html

p.s. (4/2000) We received an interesting email from Jim Hunt detailing the
history of the inquiry into the subject of ship burning.