I don’t think Archimedes Death Ray was realized, at least not in the way it is described by ancient historians, or the hypotheses of numerous individuals appearing on Mythbusters.
In theory, though, one can burn almost anything if one can manage to focus enough of the sun’s rays on a small area. I offer the following excerpt:

This is from http://e360.yale.edu/content/feature.msp?id=2144
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A Potential Breakthrough
In Harnessing the Sun’s Energy
by David Biello

“In the high desert of southern Spain, not far from Granada, the Mediterranean sun bounces off large arrays of precisely curved mirrors that cover an area as large as 70 soccer fields. These parabolic troughs follow the arc of the sun as it moves across the sky, concentrating the sun’s rays onto pipes filled with a synthetic oil that can be heated to 750 degrees Fahrenheit. That super-heated oil is used to boil water to power steam turbines, or to pump excess heat into vats of salts, turning them a molten, lava-like consistency.”
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What do you think would happen to those metal pipes if there were no liquid passing through them?

I wonder how much one could scale down the above described array and still be able to ignite wood, or, perhaps scaling down even further, simply ignite the enemy ships’ sails? Maybe the “Death Ray” would be enough of a weapon if it was just powerful enough to blind the ships crew…but that’s much less than what we’re told, at least by historians–only reliable to a point.

One more note: Polycarbonate sheets from your local plastics store, or even Lowe’s and similar home improvement sites, have polycarbonate available that will stop bullets, if you use a thick enough “laminate” tape or glue. Tape might help by the first bullet slug creating an air space between the layers, so subsequent shots tumble as the past through it and are even more easily defeated.

I took FOUR 6 by 8 inch pieces of quarter inch-thick polycarbonate, taped them together with Gorilla tape, and shot that 1 inch thick piece FOUR times with a .357 magnum (jacketed but lead pointed rounds, aka JSP), with the holes all within a 3 in. diameter circle, and with two rounds an inch apart. Not one of those rounds made it past the 3/4 in. panel. The last panel was, with the exception of very slight surface marks from the dents, completely untouched and undeformed, and able to be used in another application. All shots were made with the muzzle 3 to 4 feet away from the target.

Any mispellings, I’m terribly sorry. syntax, errors. too.