The Death Ray Debate
The content of this page is an excerpt from http://www.mlahanas.de/Greeks/Mirrors.htm. Checkout this site for additional, interesting historical context.
A Burning Question by J. L. Hunt
The Greek historian Lucian has recorded that during the siege of Syracuse,
Archimedes constructed a burning glass" to set the Roman warships afire.
The story has long been dismissed as fantasy and was particularly attacked
by the French philosopher-mathematician Rene Decartes, who sought to discredit
all claims from antiquity. This story was the subject of an interesting
correspondence in the scientific journal Applied Optics in 1976 where arguments
pro and con were advanced.
A.C. Claus of Loyola University in Chicago opened the argument by pointing
out that a persistent problem with the story was how Archimedes was able
to align many mirrors in an array to accomplish this feat. Claus provided
a simple method by which this could be done quickly and efficiently by sighting
along a stick attached to the mirror.
This letter prompted an immediate response from O.N. Stavroudis of the Optical
Sciences Center, University of Arizona, who argued that Claus' explanation
was unnecessary because the story was obviously false on physical principles.
in support of this he argued that the instrument would have to have a long
focal length which was variable, and to have an area sufficient to collect
enough energy to do the job.
He calculated that a one foot mirror would provide only 2000 calories per
minute even at 100 percent reflection and, argues Stavroudis, this will
only raise the temperature by a few degrees per minute.
This argument is incomplete since he said nothing about the nature of the
object receiving the focused energy. The total heat delivered by the mirror
is not the point. What is important is the size of the image produced by
the mirror and the characteristics of the surface being heated, particularly
as to how it absorbs and conducts heat. in the ideal case of a perfectly
black surface which loses no heat, then the surface temperature will rise
to the same temperature as that of the Sun. This is well above the flash-point
of wood which as all readers of Science Fiction know is "Fahrenheit
451". All children know that they can set fire to a piece of wood with
a magnifying glass. They can do this because the small image of the Sun,
which focuses on the wood acquires a high temperature; that amount of heat
delivered is of lesser consequence.
Stavroudis addressed himself to the wrong problem and, even so, came up
with an incorrect answer. K.D. Mielenz pointed out that Stavroudis's view
was negated by experiments done by George Louis LeClerc, Comte de Buffon,
in 1747. Buffon recognized that the real problem was the one of having a
variable focal length and so the mirror must be an array of individual adjustable
elements. What does such an array do to the image quality? The answer is
"surprisingly little". Let us look at Buffon's own numbers. He
assumed a mirror of 400 feet radius of curvature and a diameter of 10 feet.
Such a spherical mirror will produce an image of the Sun about two feet
in diameter. if the mirror is made of plane elements of diameter d, then
the image is increased in size by about d. If the elements are six inches
in diameter then the two foot image is smeared out to two and one half feet.
Buffon assembled 168 mirrors 8 in. by 10 in adjusted to produce the smallest
image 150 feet away. The array turned out to be a formidable weapon. At
66 feet 40 mirrors ignited a creosoted plank and at 150 feet, 128 mirrors
ignited a pine plank instantly. in another experiment 45 mirrors melted
six pounds of tin at 20 feet.
If there is doubt about Buffon's experiment consider the following newspaper
report from 1975:
A Greek scientist, Dr. Ioannis Sakkas, curious about whether Archimedes
could really have used a "burning glass" to destroy the Roman
fleet in 212 BC lined up nearly 60 Greek sailors, each holding an oblong
mirror tipped to catch the Sun's rays and direct them at a wooden ship 160
feet away. The ship caught fire at once.....Sakkas said after the experiment
there was no doubt in his mind the great inventor could have used bronze
mirrors to scuttle the Romans.
See this document in its original web page.
