Archimedes and his Burning Mirrors

Michael Lahanas

Αρχαία Ελληνικά όπλα : Τα καυστικά κάτοπτρα του Αρχιμήδη

Archimedes: Brennspiegel als Strahlenwaffen, Theorie und Praxis

STREPSiADES Have you ever seen a beautiful, transparent stone at the druggists', with which you may kindle fire?
SOCRATES You mean a crystal lens.
STREPSiADES That's right. Well, now if i placed myself with this stone in the sun and a long way off from the clerk, while he was writing out the conviction, i could make all the wax, upon which the words were written, melt.

Diocles in burning mirrors, late 2nd century BC, proved that the surface that reflects the rays from the Sun to a single point is a paraboloid of revolution. Constructions of such devices remained of interest as late as the 6th century AD, when Anthemius of Tralles, the architect of the Hagia Sophia at Constantinople, compiled a survey of remarkable mirror configurations.

According to Roman writers who chronicled the life of Archimedes, the mathematician was a devoted subject of Hiero ii, ruler of Syracuse, and spent part of his career designing and building weapons to defend Syracuse -- catapults, pulley hoists and levers for disabling enemy ships and siege towers. The ancient historians Polybius, Plutarch and Pliny the Elder all mention such inventions, although none was alive in Archimedes' lifetime. Some Greco-Roman historians also assert that during the Roman siege of Syracuse from 214 to 212 B.C., at the height of the Second Punic War, Archimedes used bronze mirrors to focus sunlight on Roman ships and set them on fire.

The Burning mirrors are mentioned by Lucian of Samosata and Galen. Anthemius of Tralles (474-534), the Architect of the Hagia Sophia, tells us that Archimedes used many mirrors. Johannes Zonaras in 1118 says that first Archimedes used the "iron Hand" against the ships and then he burned these with mirrors.

Proclus used a similar method in 514 against the ships of Vitellius. Fire was emitted from the mirrors that looked like a flash. Johannes Tzetzes says that hexagonal mirrors were used. Zonaras and Tzetzes used sources from Cassius Dio and Diodorus Siculus. Girolamo Cardano discussed the possibility of using spherical mirrors for ships in 1.5 km distance. Cardano proposed a mirror with only 1/60 of the total spherical perimeter that still is around 300 m!

When Marcellus withdrew them [his ships] a bow-shot, the old man [Archimedes] constructed a kind of hexagonal mirror, and at an interval proportionate to the size of the mirror he set similar small mirrors with four edges, moved by links and by a form of hinge, and made it the center of the sun's beams – its noon-tide beam, whether in summer or in mid-winter. Afterwards, when the beams were reflected in the mirror, a fearful kindling of fire was raised in the ships, and at the distance of a bow-shot he turned them into ashes. in this way did the old man prevail over Marcellus with his weapons. Johannes Tzetzes

Since sails were not used by the attacking ships it is at least necessary to set wood in fire by the mirrors.

is the story true? The following report by J. L. Hunt tells us that it is not unlikely even if it is not clear how the motion of ships is considered in the experiments by Buffon and others.


Lucian Samosata, Hippias.
Claudius Galen, De temperamentis.
Johannes Tzetzes, Chiliades.
Girolamo Cardano, De subtilitate

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: (probably 1973)

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

(image of the Sakkas Experiment from a Spanish Webpage)

There seems to be ample evidence that the optics to do this was well known to Archimedes who was apparently centuries ahead of his time in this as in many other areas of science.

E.A. Phillips pointed out that the Science Fiction writer, Arthur C. Clarke, has the last word in his story "A Slight Case of Sunstroke". A South American country sends 50000 well trained soldiers as a cheering section with their soccer team as a big international game. Each soldier has an expensive aluminized program two feet square. When a biased referee makes an unfavorable call, a bugle sounds and 50000 well-trained programs are raised. Zap!

The burning of the Ships, Thesaurus Opticus, Alhazen

The study of Mills and Clift

Mills and Clift considered the reflective surface that is required to concentrate energy enough to ignite wood in 50 m distance. Their conclusion is:

This calculation necessitated an initial investigation of the way in which sunlight is reflected by a plane mirror when the divergence induced by the real angular diameter of the Sun is taken into account. it is established that the patch of reflected sunlight is always greater in size than the mirror, and so (apart from reflection loss) must always be of less intensity than the incident radiation. This patch becomes essentially circular when the equivalent 'f number' of the system is >or=500. its diameter is then given by 0.009* separation between mirror and receiving surface, with the intensity controlled by the area of the mirror. As a result of this divergence, the reflectivity of bronze mirrors, and the angles involved, it is concluded that the combined effort of some 440 men, each wielding a 1 m2 metal mirror, would only just begin to ignite a 1*0.5 m area of a wooden hull at a distance of 50 m. This is such a poor use of manpower and resources that it is concluded this classic story is no more than a myth. Nevertheless it appears that a much smaller minor corps-say 50 men- could inflict severe burns upon selected enemy personnel. A A Mills and R Clift, Reflections of the 'Burning mirrors of Archimedes'. With a consideration of the geometry and intensity of sunlight reflected from plane mirrors, Eur. J. Phys. 13 (November 1992) 268-279

An Experiment was recently performed in Germany (Osnabrück, Bramsche-Kalkriese) in 15 September 2002. it was possible with 500 persons carrying mirrors (each 45cm*45cm ) to ignite a sail of a ship in 50 meter distance in seconds with an estimated 100 KW at the focal point. The visitors of the event called “Mythen & Magie” (Myths and Magic) were excited by the success of the experiment who were instructed by the German Engineer Peter Richter how to align the mirrors. The calculations were performed by the physicist Jörg Buchholz.

My opinion is that there is some truth in the Story of Archimedes and the burning mirrors, it is not fiction but we do not know the exact details of this story. Archimedes was a legend because he produced with the claw (or iron hand), the largest ever build Catapults in antiquity and the burning mirrors amazing war machines for his time. The interesting story is that he finally was not so interested in these devices among which devices similar to the Antikythera planetarium, but he was mainly proud for his mathematical discoveries, maybe because he knew that technology changes and evolves but mathematical truths remain true forever. Was it a practical weapon or a special case used in Syracuse? The Romans took all the military technology they could from the Greeks. There is also the example of the repeating Ballista technology from the Greeks that was known to the Romans but the machine was too complex. So it is possible that for the same reason the use of the technique of Archimedes, his burning mirrors, was not used.

Carlo Rubbia and Archimedes

Recently Carlo Rubbia the Nobel Physics prize winner proposed in Sicily the use of 360 Parabolic mirrors for the production of electric energy from solar energy. Such devices are used in many places, but Rubbia proposed some new ideas and called the project "Archimedes". Even if the idea of Archimedes is not used as a weapon today it is used for the electric energy production.

See also:

A rare Arabic manuscript from AD 902, a translation of a Greek manuscript on the code of research of burning mirrors!



...Some o the inventions of this great man (Archimedes) have appeared so far to surpass human ability and imagination, that some celebrated philosophers have called them in question, and even gone so far as to pretend to demonstrate their impossibility. I intend in this chapter, to examine into the subject of the burning glasses, employed by Archimedes, to set fire to the Roman fleet, at the siege of Syracuse. Kepler, Naudeus and Descartes, have treated it as a mere fable, though the reality of it bath been attested by Diodorus Siculus, Lucian, Dion, Zonaras, Galen, Anthemius, Eustathias, Tzetzes and others. Nay, some have even pretended to demonstrate by the rules of catoptrics, the impossibility of it, notwithstanding the asseveration of such respectable authors, who ought to have prevented them from rejecting so lightly, a fact so well supported.

Yet all have not been involved in this mistake. Father Kircher attentively observing the description which Tzetzes gives of the burning glasses of Archimedes, resolved to prove the possibility of this; and having by means of a number of plain mirrors, collected the sun’s rays into one focus, he so augmented the solar heat, that at last by increasing the number of mirrors, he could produce the most intense degree of it. Tzetzes’ description of the glass Archimedes made use of, is indeed proper to raise such an idea as Kircher entertained. That author says, Archimedes set fire to Marcellus’ navy, by means of a burning glass, composed of small, square mirrors, moving every way upon hinges; which, when placed in the sun’s rays, directed them upon the Roman fleet, so as to reduce it to ashes, at the distance of a bow-shot. it is probable, Mr. de Buffon availed himself of this description, in constructing his burning glass, composed of one hundred and sixty-eight little plain mirrors, which produced so considerable a heat as to set wood in flames at the distance of two hundred and nine feet; melt lead, at that of one hundred and twenty; and silver, at that of fifty. Another testimony occurs, which leaves not the least doubt in this case. Anthemius, of Tralles, in Lydia, a celebrated architect, able sculptor, and learned mathematician, who in the emperor Justinian’s time, built the church of St. Sophia, at Constantinople, wrote a small treatise in Greek, which is extant only in manuscript, entitled, “Mechanical Paradoxes.” That work, among other things, has a chapter respecting burning glasses, where we meet with the most complete description of the requisites that Archimides must have been possessed of, to enable him to set lire to the Roman fleet. He begins with this inquiry, "How in any given place at a bow-shot’s distance, a conflagration may be raised by means of the sun’s rays ?“ And immediately lays it down as a first principle. “The situation of the place must be such, that the rays of the sun may be reflected upon it in an oblique, or even opposite direction, to that in which they came from the sun itself.” And he adds, “that the assigned distance being so considerable, it might appear at first impossible to effect this, by means of the reflection of the sun’s rays; but as the glory Archimides had gained by thus setting fire to the Roman vessels, was a fact universally agreed in, he thought it reasonable to admit the possibility of it, upon the principle he had laid down.” He afterward advances farther in this inquiry, establishing certain necessary propositions in order to come at a solution of it. “To find out therefore, in what position a plain mirror should be placed, to carry the sun’s rays by reflection to a given point, he demonstrates that the angle of incidence is equal to the angle of reflection; and having shown, that in so just a position of the glass, the sun’s rays might be reflected to the given place, he observes, that by means of a number of glasses, reflecting the rays into the same focus, there must arise the given place, the conflagration required, for inflaming heat is the result of thus concentrating the sun’s rays; and that when a body is thus set on fire, it kindles the air around it, so that it comes to be acted upon by the two forces at once; that of the sun, and that of the circumambient air, reciprocally augmenting and increasing the heat ;“ whence continues lie, “it necessarily results, that by a proper number of plain mirrors duly disposed, the sun’s rays might be reflected in such quantity into a common focus at a bow shot distance as to set all in flames around it.” “As to the manner of putting this in practice,” he says “it might be done by employing many bands to bold the mirrors in the described position; but to avoid the confusion that might thence arise, twenty-four mirrors at least, being requisite to communicate flame at such a distance, lie fixes upon another method, that of a plain hexagon mirror, accommodated on every side by lesser ones, adhering to it by means of plates, bands, or hinges, connecting them mutually together, so as to be moved or fixed at pleasure in any direction. Thus having adapted the large or middle mirror to the rays of the sun, so as to point them to the given place, it will be easy in the same manner to dispose the rest, so that all the rays together may meet in the same focus : and multiply compound mirrors of this kind, and giving them all the same direction, there must thence infallibly result, to whatever degree or intenses, the conflagration required at the place given.”

“The better to succeed in this enterprise, there should be in. readiness,” he adds, “a considerable number of these compound mirrors to act all at once, from four at least to seven.” He concludes his dissertation with observing, “that all the authors who mention the burning machine of the divine Archimedes, never speak of it as one compound mirror, but as a combination of many.” So large and accurate a description is more than sufficient to demonstrate the possibility of a fact, so well attested in history, and by such a number of authors, that it would be the highest arrogance to refuse our suffrage to such invincible testimony. Vitellion, who lived about the 13th century, speaks of a work of Anthemius of Tralles, who had composed a burning glass, consisting of twenty-four mirrors, which conveying the rays of the sun into a common focus, produced an extraordinary degree of heat. And Lucian, speaking of Archimedes, says,. “that at the siege of Syracuse, he reduced by a singular contrivance, the Roman ships to ashes.” And Galen, “that with burning glasses, he fired the ships of the enemies of Syracuse.” Zonoras also speaks of Archimedes’ glasses, in mentioning those of Proclus, who, he says, “burnt the fleet of Vitellius, at the siege of Constantinople, in imitation of Archimedes, who set fire to the Roman fleet at the siege of Syracuse.” He intimates, that the manner in which Proclus effected was by launching upon the enemies’ vessels, from the surface of reflecting mirrors, such a quantity of flame, as reduced them to ashes. Eustathias, in his commentary upon the iliad, says, that “Archimedes, by a catoptric machine, burnt the Roman fleet, at a bow shot's distance." insomuch, that there is scarcely any fact in history, warranted by more authentic testimony; so that it would be difficult not to surrender to such evidence, even although we could not comprehend how it were possible for Archimedes to have constructed such glasses: but now that the experiment of father Kircher, and Mr. de Buffon, have made it apparent, that nothing is more easy in the execution, than what some gentlemen have denied the possibility of; what ought they to think of the genius of that man, whose inventions even by their own accounts, surpass the conception of the most celebrated mathematicians of our days, who think they have done something very extraordinary, when they have showed themselves capable of imitating in some degree the sketches of those great masters, of whom, however, they are very unwilling to be thought the disciples!

Again, it appears that the ancients were acquainted with refracting burning glasses; for we find in Aristophanes’ comedy of the clouds, a passage which clearly treats of the effects of those glasses. The author introduces Socrates as examining Strepsiades, about the method he had discovered for getting clear forever of his debts. He replies, that” he thought of making use of a burning glass, which he bad hitherto used in kindling his fire; for,” says he,” should they bring a writ against me, I’ll immediately place my glass in the sun, at some little distance from the writ, and set it on fire.” Where we see he speaks of a glass which burned at a distance, and which could he no other than a convex glass. Pliny and Lactantius have also spoken of glasses that burnt by refraction. The former calls them balls or globes of glass, or crystal, which exposed to the sun, transmit a heat sufficient to set fire to cloth, or corrode away the dead flesh of those patients who stand in need of caustics; and the latter, after Clemens Alexandrinus, takes notice, that fire may be kindled, by interposing glasses filled with water, between the sun and the object, so as to transmit the rays to it.

German Reports


Archimedes-Test in Kalkriese gelungen: 500 Besucher spiegeln Segel in Brand

Teilnehmer und Zuschauer begeistert: „Spannend wie ein Krimi“ Bramsche-Kalkriese, 15. September 2002

Die Sonne ließ sich lange bitten, versteckte sich immer wieder hinter Wolken. Doch nach gut einer Stunde, um 14.06 Uhr, schallen laute Jubelrufe über das Gelände der Varusschlacht im Osnabrücker Land: Das Segel brennt. Den 500 teilnehmenden Besuchern der Veranstaltung „Mythen & Magie“ war es gelungen, mit 500 Spiegeln das Sonnenlicht zu reflektieren, zu bündeln und damit ein 50 Meter entferntes, 4 mal 5,5 Meter großes Segel in Brand zu setzen. Wissenschaft zum Mitmachen und Miterleben – die Besucher waren begeistert: „Spannend wie ein Krimi“.

Geduldig hatten die Teilnehmer des Experiments jeden kleinen Sonnenstrahl genutzt und auf Anweisung des 50-jährigen Ingenieurs Peter Richter aus Ostercappeln-Venne, dem Initiator des Archimedes-Tests „Spiegel wie in Syrakus“, die Spiegel immer wieder ausgerichtet und den Lichtpunkt auf das Segel konzentriert. Die Teilnehmer waren nach den Berechnungen von Diplom-Physiker Jörg Buchholz höhenversetzt in fünf Reihen zu einem Halbrund gruppiert worden. Mit den 45 mal 45 Zentimeter großen Kristallglasspiegeln in den Händen, gestiftet eigens für diesen Versuch von dem Georgsmarienhütter Unternehmer Günther Zierath (Firma Spiegel-Design), bildeten sie einen Hohlspiegel von 108 Grad. Das auf den Brennpunkt des Parabolspiegels ausgerichtete Sonnenlicht erreichte eine Energie von rund 100 Kilowatt. Gebündelt durch eine Fresnel-Linse und gesammelt auf einem Stück schwarzen Leinens, ließ das Sonnenlicht den unbehandelten Nesselstoff in Sekunden in Flammen aufgehen – wohl beobachtet von der Freiwilligen Feuerwehr Engter.

Das einmalige Experiment geht zurück auf eine historische Begebenheit: Der griechische Mathematiker, Mechaniker und Erfinder Archimedes hat nicht nur den Näherungswert für die Zahl Pi (= 3,141...) und den Auftrieb des Wassers entdeckt, er entwickelte auch zahlreiche Kriegsmaschinen, zum Beispiel Schleudern und Hebewerke, und er erfand den Brennspiegel – eine Technik, mit der noch heute alle vier Jahre das olympische Feuer entzündet wird.

Archimedes lebte von 285 bis 212 vor Christus in Syrakus, der bedeutenden griechischen Kolonie im heute italienischen Sizilien. Die Römer versuchten mehrfach, Sizilien zu erobern. Ein nach dem 1. Punischen Krieg geschlossenes Bündnis mit Rom zerfiel nach dem Tod des sizilianischen Herrschers Hieron dem Zweiten im Jahr 214 vor Christus, die Römer belagerten Sizilien und Syrakus, sie eroberten die Stadt 212 vor Christus, Archimedes kam dabei zu Tode. Die Legende erzählt, Archimedes habe mit Hilfe des von ihm erfundenen Brenn- oder Hohlspiegels und der Bürger von Syrakus die Segel der heran rollenden römischen Flotte in Brand gesetzt und die Schiffe damit kampfunfähig gemacht. Der Erfinder gruppierte der Überlieferung nach die mit Spiegeln ausgestatteten Syrakusaner auf einer Anhöhe zu einem großen Hohlspiegel, ließ sie mit den Spiegel das Sonnenlicht reflektieren und auf einen Brennpunkt lenken, so dass ein energiereicher, gebündelter Lichtstrahl entstand.

Ob dieser Versuch damals gelungen ist und die Segel tatsächlich brannten, ob dieses Experiment überhaupt gelingen kann, darüber sind die Chronisten von einst und die Wissenschaftler von heute geteilter Meinung. In Kalkriese jedenfalls hat der Archimedes-Test gestern geklappt. Auch Varusschlacht-Geschäftsführer Christian Jaletzke war begeistert: „Das machen wir zu den internationalen Römertage zu Pfingsten 2003 noch einmal“.


Simms, D.L., Archimedes and the Burning Mirrors. Technology and Culture, Vol. 18, No. 1, pp. 1-24

Experiment of Ioannis Sakkas: The Times 11-Nov-1973; The NY Times 11-Nov-1973; International Herald Tribune 8-Nov-1973; Newsweek 26-Nov-1973 (Information from Antreas P. Hatzipolakis)

E. Kreyszig, Archimedes and the invention of burning mirrors : an investigation of work by Buffon, in Geometry, analysis and mechanics (River Edge, NJ, 1994), 139-148

G L Huxley, Anthemius of Tralles, Cambridge, Mass., 1959.


a)Burning Mirrors, History, images , An old film Cabiria with scenes of Archimedes burning mirrors
Archimedes and burning mirrors
Diocles, Cissoid and burning mirrors !!!
Heliostats as death-rays
LEONARDO DA ViNCi - Studies of reflection in burning-mirrors (image only low resolution!)

See also:

Archimedes Mathematics
Archimedes cubic and bi-quadratic equations and a method for angle trisection
Archimedes and Combinatorial Problems (The loculus of Archimedes)
Archimedes the Arbelos and the Salinon
Archimedes and the Palimpsest
Archimedes semi-regular Convex Solids

Biography of Anthemius of Tralles

Ancient Greek Military Technology (Armor, Ships, Catapults, Polybola, Siege and Radiation Weapons)

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