Burning Mirrors
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Refuting the Legend       

The legend of Archimedes’ burning mirrors is too good to die, regardless of how much evidence is presented to refute it. The legend is ever captivating—even after 2300 years: a city under attack, a solitary genius who rescues the city, a spectacular military weapon, and the reduction of the attacking forces to ashes.

Over the centuries many attempts have been made to demonstrate how Greek forces under Archimedes might have used mirrors to set aflame invading Roman ships that were attacking their city of Syracuse in 213 BC. Most such reenactments have involved the use of flat mirrors individually aimed by “Greek soldiers” to reflect the sun’s rays onto a single point on a small wooden boat. Such reconstructions are now proliferating because of the ease of worldwide communication through television and the internet.

These reconstructions always portray the invading Roman ships attacking under ideal conditions for the Greek defenders. Also, the Roman soldier-enactors, if any are present, do not ever attempt to extinguish even a small, smoldering flame that could grow and slowly reduce the vessel to ashes.

Following is a list of diverse reasons (historical, military, mathematical and other) why Archimedes did not use burning mirrors in the Siege of Syracuse.

  • The three earliest and most reliable historians—Polybius (Greek, c. 200-118 BC), Livy (Roman, 59 BC-AD 17), and Plutarch (Greek, c. AD 45-120)—did not write a word about burning mirrors or fire of any kind during the siege of Syracuse. Polybius, the earliest historian, born about a dozen years after the siege, gives a very detailed account of the siege and would have been able to interview survivors of that siege. He certainly would have mentioned burning mirrors if they were used, since they would have produced the most spectacular episode of the siege. Polybius’s silence on this matter is one of the strongest historical refutations of the legend.
  • The Greek geometer Diocles (c. 240-180 BC) was born about 50 years after Archimedes and wrote a work entitled “On Burning Mirrors”. This work contains the first known proof of the focal property of a parabolic mirror, although Diocles mentions that a contemporary of Archimedes by the name of Dosithius was aware of this fact. Archimedes does not mention the focal property of the parabola in any of his extant works nor has any work of his on burning mirrors survived.

    In his work Diocles mentions Archimedes in connection with a certain geometric problem, but makes no reference to him in connection with burning mirrors or the burning of Roman ships. (Diocles would have been around thirty years old when the Siege of Syracuse took place.) His silence on this matter is as damning as Polybius’s silence.

  • Lucian of Samosata and Galen of Pergamon, both of the second century AD, are often given as sources of Archimedes’ burning mirrors. But both simply state, in passing, that Archimedes set fire to the Roman fleet without precisely describing how. The key quotations are these:

    Lucian (Hippias, or The Bath):

    The former [Archimedes] burned the ships of the enemy by means of his science.

    . . . τὸν δὲ τὰς τῶν πολεμίων τριήρεις καταφλέξαντα τῇ τέχνῃ.

    Galen (De Temperamentis 3.2. The meaning of the Greek word pyreia (πυρεία) is not clear.):

    In some such way, I think, Archimedes too is said to have set on fire the enemy’s triremes by means of pyreia.

    οὕτω δέ πως, οἶμαι, καὶ τὸν Ἀρχιμήδην φασὶ διὰ τῶν πυρείων ἐμπρῆσαι τὰς τῶν πολεμίων τριήρεις.

  • The earliest source that unequivocally states that Archimedes employed burning mirrors was written by Anthemius of Tralles (Greek, c. AD 500) some 700 years after the fact. In his treatise entitled On Burning-Glasses he mentions offhandedly that Archimedes may have used a parabolic mirror to focus the sun’s rays on the invading Roman ships. He also gives a description of what Archimedes’ burning mirrors might have looked like, but, as he states, his description is strictly his own creation.
  • John Tzetzes and John Zonaras, Byzantine Greeks of the twelfth century, give purported descriptions of Archimedes’ burning mirrors. However, both men are generally regarded as unreliable sources and were clearly quoting Anthemius’ description of the mirrors.
  • Two of the earliest historians, Polybius and Plutarch, state that the second and final attack on the sea walls of Syracuse occurred at night, rendering burning mirrors useless. The night attack was ordered because the first attack in the daytime was driven off far from the sea walls by catapults throwing stones. Here are the specific quotations:

    Polybius (Universal History, Book VIII.5)

    In the end Marcellus was reduced in despair to bringing up his ships secretly under cover of darkness.

    ἓως ὁ Μάρκος δυσθετούμενος ἠναγκάσθη λάθρᾳ νυκτὸς ἒτι ποιήσασθαι τὴν παραγωγήν.

    Plutarch (Parallel Lives: Marcellus)

    They then took a resolution of coming up under the walls, if it were possible, in the night.

    Βουλενομένοις δὲ ἒδοξεν αὐτοῖς ἒτι νυκτός, ἂν δύνωνται, προσμῖξαι τοῖς τείχεσι.

  • There is no reliable historical record of the use of burning mirrors in any battle before or after Archimedes’ time. If burning mirrors were an effective weapon, this would not be the case. In particular, why did the Romans never make use of burning mirrors even though, if the legend were true, they would have observed the destructiveness of this weapon firsthand and had access to Archimedes’ original mirrors and designs when they looted Syracuse?


  • To be vulnerable to burning mirrors, the invading Roman ships must have attacked when the sun was visible and high in the sky. The ships must also have attacked from a precise direction so that the sun was at an advantageous angle for the Greek defenders. Consequently, the Romans could easily have overcome burning mirrors by attacking at dawn, dusk, night, on a cloudy or rainy day, or from a disadvantageous direction. Defensive weapons that are so easily overcome are of little value.
  • The Romans ships would need to be stationary for many minutes while the Greek defenders aimed their mirrors waiting for a flame to start. But the ships were bouncing in the waves and jockeying for position along a 900-meter stretch of the city walls. Sixty Roman ships attacked Syracuse along the city walls with some carrying ladders so that about 150 soldiers on each of the ships could scale the walls. Meanwhile, these soldiers were shooting arrows, throwing javelins, and slinging rocks at the Greek defenders on the walls. Such a fast-moving, chaotic battle scene is hardly the place to preform what is basically a science experiment to start a fire at a distance with mirrors.
  • If water is splashed on the spot at which the mirrors are aimed, then no flame can get started. Any flame that does get started is easily extinguished by the sea waves or by men with splashing oars or with buckets of water. Men on ships were trained to put out fires in battle (from fire pots and flaming arrows, for example) and so would not panic if mirrors actually started a small, smoldering flame.
  • Using many men, a hundred or more, to set a ship on fire using burning mirrors is a very poor use of resources. Flaming arrows and fire pots (clay pots filled with tar, pitch, sulfur and other flammable substances set aflame) are much more effective devices to set a ship on fire. They are usable in the dark and on cloudy and rainy days. They do not require the target ship to be stationary. They spread the fire immediately throughout the ship (into the hull for example) and the fires they start are more difficult to put out because of the materials set afire (tar, pitch, sulfur, etc.). It is not just the wood of the ship that is in flames, but also the splattered material from the fire pots. One hundred men could dispatch literally thousands of flaming arrows and fire pots onto a ship in the time that it would take them to start a single small, smoldering fire using burning mirrors.
  • Some reconstructions have attempted to set the invading ships’ sails on fire. However, sails were never used in the attack of a city; sails were only used to transport a ship from one port or battle location to another. The Roman ships used in the invasion, called quinqueremes, had about 270 rowers each to propel and steer the ships in battle.

  • It is difficult for many men to simultaneously aim mirror reflections onto a common target. Each man does not know which of the many reflections swarming around the target is his. If the men aimed their mirrors sequentially, each covering his mirror after aiming it, the ship and the sun will have moved by the time all of the mirrors were aimed.

    Although mirrors with practical, built-in aiming devices were developed during World War II (for downed pilots and sailors to signal rescuers), there is no record of such mirrors before then.

  • Some defenders of the burning-mirror legend have attempted to rescue a portion of the legend by suggesting that mirrors were used to blind or confuse the Roman soldiers or were used to generate steam for “steam cannons”. But whatever arguments are used to dispel a part of the legend are enough to dispel the entire legend. This is simply piling a new legend on top of an old legend. Just because something can be done is hardly proof that it was done.
  • There is no mystery about how the Greek forces under Archimedes repulsed the Roman sea attack. The earliest historians (Polybius, Livy, and Plutarch) give a consistent, believable, and complete description of the weapons deployed by the Greeks and their success in forcing the Romans to call off their siege. These weapons included catapults of various ranges, powerful ballistic machines (“scorpions”) stationed behind the walls that shot huge darts through slits in the walls, machines mounted on top of the walls that dropped rocks and rubble on the ships below, and cranes with grappling hooks (“Archimedes’ Claws”) that snagged and overturned the attacking ships.

    The burning-mirror legend is an unsatisfactory solution to a nonexistent problem.



Some proponents of the burning-mirrors legend propose that a single large parabolic mirror was used rather that many individual flat mirrors. Usually a paraboloid with a focal length of about 50 meters (164 feet; the approximate range of a “bowshot”) is taken. This proposal, however, is based on a misunderstanding of the focal properties of parabolic mirrors. Below are some discussion points on this matter:

  • A parabolic mirror focuses rays parallel to its axis of symmetry onto a unique focal point that lies on that axis of symmetry. Rays that are not parallel to the axis of symmetry are not reflected through the focal point. Consequently, if a parabolic mirror is to set fire to a ship, its axis of symmetry must be pointed towards the sun and the ship must be situated on that axis at the focal point. The vertex of the parabola must then be below sea level since the vertex, ship and sun in that order must lie along the parabola’s axis of symmetry. Because the mirror would be situated above sea level on the wall surrounding Syracuse, the mirror must constitute a segment of the parabola that does not contain its vertex. Such parabolic mirrors are called off-axis parabolic mirrors (as opposed to the usual right parabolic mirrors) and are quite difficult to design and construct.

    The important point here is that a parabolic mirror cannot be aimed by tilting it the way a flat mirror can. Once the parabolic mirror is constructed, situated on the wall, oriented with its axis of symmetry pointing towards the sun, and rotated about a line parallel to that axis so that the focal point is at sea level, then the focal point is fixed. If the ship is not located near that focal point, then the burning mirror is useless.

    To complicate things further, as the sun moves along its daily path the orientation of the off-axis mirror must be continuously adjusted so that its axis of symmetry remains parallel to the sun’s rays and it must be rotated so that the focal point is at sea level. The Roman ship must then follow this wandering focal point if it is to be set on fire.

  • A parabolic mirror does not focus the sun’s rays to a single point because the sun is not a point source of light situated at infinity; it is a spherical body situated a finite distance away from the earth. A right parabolic mirror is the basic component of a reflecting telescope and as such focuses the sun’s rays onto a small image of the sun. The diameter of this image is given by the formula ƒ/107 where ƒ is the focal length of the mirror. That is, the mirror concentrates the sun’s rays onto a disk whose diameter is about one-hundredth of the mirror’s focal length. This formula comes from basic optical theory and the fact that the sun subtends an angle of approximately ½° as viewed from the earth (more precisely, 31.6 to 32.7 arc-minutes). The number 107 is the reciprocal of the average angle subtended by the sun in radians.

    For example, the Hale telescope at the Palomar Observatory in California contains a parabolic mirror with a focal length of 666 inches (16.9 meters) and so focuses the sun’s rays onto a disk of diameter 6.22 inches (15.8 centimeters). If Archimedes’ parabolic mirror had a focal length of 50 meters (164 feet), then it would focus the sun’s rays onto a disk of diameter 46.7 centimeters (18.4 inches).

  • The temperature at which a parabolic mirror can raise a target at its focal point is dependent on how much it concentrates the sun’s rays there. If D is the diameter of a right parabolic mirror and ƒ is its focal length, then the concentration factor is given by (107D/ƒ)2. For a small parabolic shaving mirror with a diameter of 15 centimeters and focal length of 30 centimeters—a typical situation—this concentration factor is 2860. But for a proposed Archimedes’ right parabolic mirror with the diameter of the Hale telescope (200 inches or 5.08 meters) and a focal length of 50 meters, this concentration factor is only 118. A shaving mirror can thus achieve much higher temperatures at its focal point than the type of large parabolic mirror proposed to burn invading ships.

    Notice that if the focal length of a parabolic mirror is greater than 107 times its diameter (in optical terms, if the ƒ-number or ƒ-stop of the mirror is greater than ƒ/107), then its concentration factor is less than one, so that a target at its focal point will be illuminated less that it would directly by the sun. This fact was first observed by Descartes in 1637.

  • If D is the diameter of a right parabolic mirror and ƒ is its focal length, then its depth is given by D2/(16ƒ). For our proposed Archimedes’ right parabolic mirror this is (5.08)2/(16x50) meters or 3.23 centimeters (1.27 inches). For an off-axis mirror the formula for the depth is rather complicated but its depth would always be less than the depth of the corresponding right parabolic mirror. The ability to design and construct an off-axis parabolic mirror with a diameter of 5.08 meters and a depth of less than 3.25 centimeters was far beyond the capabilities of the technology of Archimedes’ time. And as mentioned above, there would be only one fixed spot in the sea where it could potentially set a ship on fire.
  • As a minor point, it can be remarked that the mirror should actually have an elliptical rather than parabolic shape, with the ship located at one of the foci of the ellipse and the sun located at the other. But because the distance from the sun to the mirror is so much larger than the distance from the ship to the mirror, the difference between the elliptical shape and the parabolic shape is completely negligible. This is equivalent to assuming that the sun’s rays are all parallel to each other, which is not quite the case, but negligibly so.

All of the above considerations show why a single large parabolic mirror would be hopelessly impractical. Many individual, tiltable flat mirrors are a much more practical solution to setting a fire at a distance. Individual flat mirrors would constitute a disconnected segmentation of a paraboloid whose focal length and axis of symmetry can be varied by adjusting the orientations of the flat mirrors. Additionally, they would be just as effective if the combined surface area of the flat mirrors is equal to the surface area of the single parabolic mirror. The optimal utilization of flat mirrors requires that they be elliptical in shape and of a size that a Roman soldier situated at the target on his ship should see a reflection of the complete solar disk filling each of the tilted mirrors aimed at the ship. If a hundred flat mirrors were aimed at him, he should be able to see a hundred reflections of the sun.


  1. The television show MythBusters devoted three episodes to testing the myth of the “Archimedes Death Ray” (29-September-2004, 25-January-2006, 8-December-2010). The last episode featured a guest appearance by United States President Barack Obama and the use of 500 large, flat, modern mirrors. In all three episodes the myth was declared implausible (“Busted”).
  2. For more information read the articles on burning mirrors written by Dennis L. Simms, which are listed on this web site. During his professional career Dr. Simms lectured and published numerous scientific articles refuting the burning-mirrors legend, apparently to little effect since belief in the legend seems to now be stronger than ever.