Ancient Greece: Optics

Michael Lahanas

Αρχαία Ελληνική Οπτική

Optik im antiken Griechenland

Antisthenes: Plato, I see particular horses, but not horseness.
Plato: That is because you have eyes but no intelligence.

Are the columns rectangular? Are there two or three columns? © Sandro Del-Prete.

What is Optics?

The word comes from the Greek for eye, οψ , but the study of the eye itself is physiology and neurology, the study of vision a branch of psychophysics, and the study of illumination and color an applied field of its own. Optics is descended from the ancient Greek science of mathematical perspective, in which the behavior of the rays of vision was discussed by deductive geometry.

Epicharmus of Cos c.(540 - 450 BC)

(son of Elothales, a physician of Cos, a member of the Asclepiad clan), author and physician, "It is the spirit that sees, it is the spirit that hears, all the rest is deaf and blind".

Epicur or Epicurus (Επίκουρος ο Σάμιος)

Epicur describes that the color of an object depends on the color of the irradiated light

Besides this, remember that the production of the images is as quick as thought. For particles are continually streaming off from the surface of bodies, though no diminution of the bodies is observed, because other particles take their place. And those given off for a long time retain the position and arrangement which their atoms had when they formed part of the solid bodies, although occasionally they are thrown into confusion. Sometimes such films are formed very rapidly in the air, because they need not have any solid content; and there are other modes in which they may be formed. For there is nothing in all this which is contradicted by sensation, if we in some sort look at the clear evidence of sense, to which we should also refer the continuity of particles in the objects external to ourselves.

We must also consider that it is by the entrance of something coming from external objects that we see their shapes and think of them. For external things would not stamp on us their own nature of color and form through the medium of the air which is between them and use or by means of rays of light or currents of any sort going from us to them, so well as by the entrance into our eyes or minds, to whichever their size is suitable, of certain films coming from the things themselves, these films or outlines being of the same color and shape as the external things themselves. They move with rapid motion; and this again explains why they present the appearance of the single continuous object, and retain the mutual interconnection which they had in the object, when they impinge upon the sense, such impact being due to the oscillation of the atoms in the interior of the solid object from which they come. And whatever presentation we derive by direct contact, whether it be with the mind or with the sense-organs, be it shape that is presented or other properties, this shape as presented is the shape of the solid thing, and it is due either to a close coherence of the image as a whole or to a mere remnant of its parts. Falsehood and error always depend upon the intrusion of opinion when a fact awaits confirmation or the absence of contradiction, which fact is afterwards frequently not confirmed or even contradicted following a certain movement in ourselves connected with, but distinct from, the mental picture presented - which is the cause of error. Epicurus: Letter to Herodotus (a summary of his atomic theory)


Plato (427-347 BC) (Πλάτων ο Αθηναίος)

Plato says that that the soul is the source of vision that is possible from light rays emitted from the eyes. The question is why we cannot see nothing in a completely dark room? Like the light which is necessary for vision Plato says the “Good” is like an intellectual light that allows us to “see” the invisible “forms”.

Philippus of Opus (Φίλιππος ο Οπούντιος) (4th century BC)

from Opus, or Medma in Locris, a disciple of Plato and a contemporary of Eudoxus. He is cited by Vitruvius, Stobaeus, Eudemus, Diogenes Laertius, Suidas and Stephen of Byzantium. He wrote many books but only fragments survived, among his books are:

Optics, 2 books
Enoptrics
, 2 books
The rainbow as a phenomenon of diffraction

(Information from the Technology Museum of Thessaloniki)


The ancient Greeks studied the geometric properties of light. According to a optics text book they considered only rays inside the cone of visibility. Such light cones from an optical source in the study of sundials could probably also be the reason of the discovery of conic sections.


Aristophanes

Aristophanes in The clouds (420 BC) describes the light focus effect of a lens:

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.

Aristotle (Αριστοτέλης ο Σταγειρίτης) (or Pseudo-Aristotle ?) (384-322 BC)

All men by nature desire to know. An indication of this is the delight we take in our senses; for even apart from their usefulness they are loved for themselves; and above all others the sense of sight. For not only with a view to action, but even when we are not going to do anything, we prefer seeing (one might say) to everything else. The reason is that this, most of all the senses, makes us know and brings to light many differences between things. Aristotle, Metaphysics

The earliest known written evidence of a camera obscura can be found in Aristotle's documentation of a device in 350 BC in Problemata" (Patti, 1993). Aristotle's apparatus contained a dark chamber that had a single small hole to allow for sunlight to enter. With this device, he made observations of the sun. He noted that no matter what shape the hole was, it would still display the sun correctly as a round object. Another observation that he made was that when the distance between the aperture (the tiny hole) and the surface with the image increased, the image would become amplified. Although no one is perfectly sure, many attribute the invention of the camera obscura to Aristotle. He rejected the vision theory of Plato of light rays emitted from the eyes.

The first casual reference [to the Camera Obscura] is by Aristotle (Problems, ca 330 BC), who questions how the sun can make a circular image when it shines through a square hole. Euclid's Optics (ca 300 BC), presupposes the camera obscura as a demonstration that light travels in straight lines. Egnacio Danti in commentary on his translation of Euclid's Optica (1573), adds a description of the camera obscura... Aristotle (384 - 322 B.C.) observed the crescent shape of the partially eclipsed sun projected on the ground through the holes of a strainer, and the gaps between the leaves of a tree. He also noticed that the smaller the hole, the sharper the image. In modern cameras, this is analogous to the diaphragm. http://www.acmi.net.au/AIC/CAMERA_OBSCURA.html

Pseudo-Aristotle Problemata Mechanica 1831 Edition in Greek

Archimedes (Αρχιμήδης ο Συρακούσιος)

He was involved in catoptrics (reflections from surfaces) and in refraction, but his writings in this field are lost. He is known from using burnig mirrors to set Roman ships in fire. Although assumed a legend experiments showed that this is possible. According to some reports on the net I have seen Archimedes used a box with a little hole on one side and a piece of papyrus on the other. The image was passing through the hole and was shaping an image on the papyrus. I do not have found more details and references for this story of a camera obscura used by Archimedes.

According to Aristotle: “sight is the noblest faculty of man.”

An old film: Cabiria with scenes of Archimedes burning mirrors

See also:

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

Ptolemy (Claudius Ptolemaeus)(Πτολεμαίος Κλαύδιος)(85 – 170) AD

Optics (Οπτική πραγματεία), five books, of which Book I and the end of Book V are missing, known from a Latin version of a lost Arabic version of the original Greek work. Books III and IV are on catoptrics. Book V deals with refraction. He considered refraction and obtained the small angle approximation to Snell’s law, concluding that the ratio of the angles of incident and refracted light were constant. He also discussed the refraction of starlight by the atmosphere but held to the wrong theory that vision is due to rays emitted from the eye touching the object. (One could ask why then we are not able to see in the dark?)

According to Snell's Law of the Physicist Willebrord Snell van Roijen from Holland (or Snellius) (1580-1626) :

sin a1 / sin a2 = n2 / n1

Where a1 and a2 are the angles of the incident and refracted rays and n1, n2 are the material refractive indices. Note that the this assumes that Ptolemy performed experiments as it is less probably that Ptolemy derived this law by “first principles”

The refraction of glass and Ptolemy and Refracted Images

Euclid of Alexandria (Ευκλείδης ο Αλεξανδρεύς)

The Arabic Version of Euclid's Optics: (Kitab Uqlidis Fi Ikhtilaf Al-Manazir) ,Springer-Verlag New York Inc.

Abram Klooswyk writes about the stereoscopic depth perception assumed to be known by the ancient Greeks:

Sir David Brewster was a great man in science and his virtues for early stereoscopy are unsurpassed. However, he is the origin of some serious errors in the history of stereoscopic depth perception that still can be found in many articles and books today. He apparently was not fully aware of the changes of the world image through the centuries. It seems also that rivalry with Wheatstone blurred his judgment in these matters.

To be more specific, one of the most widespread errors is the idea that Euclid knew of binocular depth perception. Two examples:

1) Time magazine once had printed on its front cover the slogan: "3D - Euclid had a word for it".

2) The Web pages of the "Turing institute" (actually a commercial company) even today have a section on the history of stereo photography (also to be found on the otherwise so excellent 3D-CD ROM of Dan Shelley and friends) which says:

"In 280 A.D., Euclid was the first to recognize that depth perception is obtained when each eye simultaneously receives one of two dissimilar images of the same object."

I have seen dozens of similar statements "all over the place" (but, for the record, not in the Burder & Whitehouse booklet "Photographing in 3-D", publ. Stereoscopic Soc. UK). The erroneous statements are all (directly or indirectly) based on Brewster's 1856 book "The Stereoscope" and some of his other writings.

Euclid, author of The Elements also wrote other treatises, among which one on Catoptrics and one on Optics. Catoptrics is about mirrors, I don't know if it is translated in English, I have seen a French translation. (by Paul Ver Eecke, "Euclide, l'Optique et la Catoptrique", Paris 1959). In the Catoptrics a few propositions are on looking in spherical concave mirrors with two eyes, but Euclid only discusses whether one eye can see the other or not, in different positions of the eyes. He doesn't mention binocular vision (looking with both eyes at the same object(s)) in that treatise.

An English translation of the Optics was published by Harry E. Burton in the Journal of the Optical Society of America 1945, vol. 35 Nr. 5, pages 357-372, so it is only 16 pages long (A4). The "Optics" is in fact a treatise on perspective, it contains many of the basic concepts which artists would need for using central perspective, although it doesn't specifically discuss the projection of images on surfaces. Also, the Optics is not about lenses or prisms. This treatise again is composed of a short list of postulates and several propositions (theorems) each followed by geometrical proof.

In ancient Greece there were several theories of vision, one of them (advocated by Plato) was that the eyes EMIT visual rays, these rays mix with the luminous rays from the sun (or other sources), and give the visual sensation (what exactly was meant remains unclear).

Aristotle had a different theory, but it seems that Plato's ideas were followed by Euclid, but he doesn't mention any specific theory.

The theory Euclid adhered to seems to follow from a number of phrases. In one postulate he says "those things upon which the vision falls are seen". And the first theorem states: "nothing is seen at once in its entirety", and he explains that the rays of vision diverge and are not contiguous, but "(the object) seems to be seen all at once because the rays of vision shift rapidly".

That eyes emit rays may sound strange to adults in this century, but most of us do believe in the existence of X-rays, gamma-rays, RADAR, ultrasound and radiowaves, all invisible and not directly percepted. And when an eye is hit, or with gentle pressure sideways on a closed eye, don't you actually "see light" which has its origin in the eye itself?

(Disclaimer: this is potentially harmful for the eye - NOT a joke).

Moreover, in recent psychological studies it has been demonstrated that many children and even college students (OK, at Ohio State University, but still a university :-)) believe that something goes out of the eyes. A psychologists group at Ohio State has published several papers on this subject. In one study for example some of the questions were "when people look at something, do you think waves or rays or anything else goes out of their eyes?", and also "... into there eyes?" and "... both into and out of their eyes?".

Of 67 grade 6 children (about 11.5 years old) only 6 answered 'in', 18 'out' and 39 'both'. Of 98 college students (mean age 21.8 years) 58 said 'in', still 4 answered 'out' and no less than 32 'both'! When they were told in debriefing that there exist no emissions from the eyes many children protested vigorously. Embarrassing was also that some of the *psychology* students trained to do the testing asked to tell them the right answers first. (Jane E. Cottrell and Gerald A. Winer "Development in the Understanding of Perception: The Decline of Extramission Perception Beliefs", Developmental Psychology 1994 Vol 30 No 2 pp 218-228)

* On the ONE eye or BOTH eyes issue. Several theorems of the "Optics" involve seeing different distances, but none of them mention seeing different distances with two eyes.

On the contrary, ALL theorems (or their proofs), except the few I will quote further on, invariably speak of "the eye" (singular). Euclid's phrasing leaves no doubt: it is always clear whether one eye or both eyes are meant.

Some examples, also to give an idea of the treatise's contents: (Theorem 2) "Objects located nearby are seen more clearly than objects of equal size located at a distance". "Let B represent the eye and ...etc". ('Clearly' obviously means 'with higher definition', the proof says that the closer one of two equal and parallel lines is seen by more rays; we would say seen by more retinal cones.) (5) "Objects of equal size unequally distant appear unequal and the one lying nearer to the eye always appears larger". (6) "Parallel lines, when seen from a distance, appear not to be equally distant from each other". "Let there be two parallel lines, AB and GD, and let the eye... etc" (10) "In the case of flat surfaces lying below the level of the eye, the more remote parts appear higher." And of course: (11) "In the case of flat surfaces located above the level of the eye, the more remote parts appear lower." (36) "The wheels of the chariots appear sometimes circular, sometimes distorted." "(...) but if the line drawn from the eye to the center is not at right angles to the plane (...) the diameters appear unequal (...)" (54) "When objects move at equal speed, those more remote seem to move slowly". "For let B and K move at equal speed, and from the eye, A, let rays be drawn ...etc".

A number of theorems state how much is seen of the surface of various objects in different cases. Theorem 23, on vision with one eye says: "Of a sphere seen in whatever way by one eye, less than a hemisphere is always seen, and the part of the sphere that is seen itself appears as an arc". (The Burton translation says "arc", Ver Eecke has "circonference de cercle", circle circumference, which seems closer to the Greek original which says kuklou perifereia). The theorem is proven by drawing lines from the eye touching the sphere, the circle of all contact points cuts off a part from the sphere which is less than a hemisphere. (24) "When the eye approaches the sphere, the part seen will be less, but will seem to be more." (A smaller amount of the surface is seen under a greater visual angle).

Heron of Alexandria (Ηρων ο Αλεξανδρεύς)

He divided vision into 1) optics, the study of vision proper; 2) dioptrics, the study of dioptras and sighting instruments and 3) catoptrics or the study of mirrors. The straight line is the shortest route between two points, while the circle is the shortest periphery for a given area.

The principle was then applied by Heron of Alexandria to prove that in a mirror, the angle of reflection is equal to the angle of incidence. Fifteen centuries later, Fermat (1601- 1665) used the same principle of the fastest route or minimal travel-time for the transition of light between two media, i.e. for the derivation of Snell's law.

Kim H. Veltman Perspective and the Scope of Optics Unpublished, Toronto, 1992 PDF File

Optical Illusions, Perception

Cleomedes (Kleomedes) (Κλεομήδης) (1st century AD?) produced what is probably the earliest extant statement of size-distance invariance. He supported the Stoic philosophy and was concerned to discredit the Epicurean position that we perceive objects as having their true size. He explained the celestial illusion (the apparent enlargement of the sun near the horizon) in two ways: partly as a refractive effect of the atmosphere similar to angular enlargement when looking into water; and partly as a linear enlargement due to increased apparent distance in a misty atmosphere. He is the earliest extant author to offer apparent distance as a clear explanation of the celestial illusion. He attributed these views to Posidonius (c. 135-51 BC). His explanations remained at the geometrical level, and he did not speculate on sensory mechanisms, Helen E Ross, Perception 2000, volume 29, number 7, pages 863-871

The full moon rising in the east at sunset appears huge and close, especially over a flat horizon, as does the red setting sun in the west. At midnight, the moon sailing high seems small and distant. Of course, the size of the moon as measured by the angle subtended at the eye is the same in both cases (except as slightly modified by refraction). The difference is in the mental perception of size. This is possibly the most commonly recognized optical illusion, although it is different from the usual ones. It has received extensive study. Minnaert discusses it at length in The Nature of Light and Colour in the Open Air, pp. 155-166. The effect is most striking seen over flat land, such as the Flanders coast or the Llano Estacado of Texas, and is weaker over the sea or in the mountains...

The horizon illusion was known and remarked from antiquity. The rising moon seemed four times as large as the moon in the zenith. At first it seemed close, almost an earthly thing, but later its celestial nature took hold. Ptolemy explained that this was only apparent; the objective size of the moon was no different on the horizon than in the zenith. He said that although the celestial sphere was, indeed, a sphere, it appeared farther from the observer at the horizon, and bodies subtending the same angle appeared larger when presumed to be at a greater distance. A man at 1000 yards subtending the same angle as a man at 100 yards, would indeed appear to be a giant. It was the misjudgment of distance that caused the illusion. I feel that this explanation, though incomplete and unsatisfying, is still rather close to the best that can be said given our state of knowledge. There have been very many explanations and analyzes of the horizon illusion, many which accept Ptolemy's foundation, and seek to understand why distances to the horizon are misjudged, and others that look for some different cause. In fact, there is a book on the horizon illusion, and it has been the subject of more scientific papers than any other optical illusion. (J. B. Calvert)

Plateau's Phenakistoscope and other Optical Toys

Phenakistoscope.

The Phenakistoscope uses the persistence of motion principle to create an illusion of motion. Although this principle had been recognized by the Greek mathematician Euclid and later in experiments by Newton, it was not until 1829 that this principle became firmly established by Joseph Plateau.

About Visual perception and Ptolemy a comment by Helen Ross:

Ptolemy (Optics, Book 2) discusses slant and shape constancy, and the perception of convexity/concavity. He also says (paragraph 73): "Distortion in visual perceptions of this kind [i.e. slant/shape distortions] depends on the orientation of the figures and on the displacement of the viewers, but it is impossible for one, single case of such distortion to represent every one. If, however, one is disposed to examine many such cases together, the more carefully [he does so, the more] miraculous the natural capacity of the visual flux to arrange visual information turns out to be..... Moreover, it does this swiftly, without delay or interruption, and it carries out a careful scrutiny with a marvelous, nearly incredible power, and it does this unconsciously because of its speed." (Translated by A. Mark Smith *) Thus Ptolemy was aware that viewing distance was a factor in shape perception that was in need of explanation. However, he did not offer an explanation, but merely asserted that the visual processing was swift and unconscious.”

Helen E. Ross PSYCHOPHYSICAL TERMINOLOGY: SHOULD WE REGULATE IT? (PDF File )

A. Mark Smith The psychology of visual perception in Ptolemy's Optics. Isis. Jun;79(297):189-207. 1988

*A. Mark Smith: Ptolemy's Theory of Visual Perception, Transactions of the American Philosophical Society, Vol. 86, Part 2, 1996 p 101-102


Optical lenses


From the book "Ancient Inventions" by Peter James & Nick Thorpe, published by Ballantine Books in 1994

Two lenses of optical quality are on display at the Heraklion Museum of ancient Cretan civilization. As many as fifty were reported as having been found in the excavations of Troy, though only a handful have been properly published.

Some lenses from these sites have impressive magnifying powers. One lens, probably of the fifth century B.C., found in Crete, can magnify with perfect clarity up to seven times. If it is held farther away from the object viewed, it will actually magnify up to twenty times, though with considerable distortion.


COLORS



EXTRACT OF MR. DUTEN’S INQUIRY INTO THE ORIGIN OF THE DISCOVERIES ATTRIBUTED TO THE MODERNS

from http://wesley.nnu.edu/JohnWesley/Wesley_Natural_Philosophy/index.htm


CHAPTER XI, NEWTON’S THEORY OF COLOURS, INDICATED BY PYTHAGORAS AND PLATO.


That the wonderful theory, whereby is investigated and distinguished from one another, all that variety of colours, which enters into the composition of that uniform appearance, light, might of itself suffice to establish forever the glory of Sir Isaac Newton, and be an eternal monument of the extraordinary sagacity of that great man. That discovery seems, by its importance, to have been reserved for an age when philosophy had arrived at its fullest maturity ; and yet it is to be found among some of the eminent men of the first antiquity, whose genius had no occasion for the experience of many ages to form it, as is strikingly evident from their having given birth to the sciences. Of this number are Pythagoras and Plato. The former of whom, and. his disciples after him, entertained sufficiently just conceptions of the formation of colours. They taught that they resulted from the different modifications of reflected light; or as a modern author, in explaining the sentiments of the Pythagoreans, expresses it, light reflecting itself with more or less vivacity, forms by that means our different. sensations of colour. Those same philosophers of the Pythagoric school, in assigning the reason of the difference in colours, ascribe it to a mixture of the elements of light ; and divesting the atoms, or small particles of light, of all manner of colour, impute every sensation of that kind to the motions excited in our organs of sight. The disciples of Plato contributed not a little to the advancement of optics, by the important discovery they made, that light emits itself in straight lines, and that the angle of incidence is always equal to the angle of reflection. Plato also seems to have apprehended the Newtonian system of colours; for he calls them the effect of light transmitted from bodies, the small particles of which were adapted to the organs of sight. Now is not this precisely the same with what Sir Isaac teaches, “that the different sensations of each particular colour are excited in us by the difference of size in those small particles of light which form the several rays; those small particles occasioning different images of colour, as the vibration is more or less lively with which they strike our sense?” The same philosopher hath gone further: lie bath entered into a detail of the composition of colours, and inquired into the visible effects that must arise from a mixture of the different rays of which light itself is composed. And what he advances a little farther on, that it was not in the power of man exactly to determine what the proportion of this mixture should be in certain colours, sufficiently shows, that lie bad an idea of this theory, though he judged it almost impossible to unfold it; which makes him add, that “should any one arrive at the knowledge of this proportion, he ought not to hazard the discovery of it, since it would be impossible to demonstrate it by clear and convincing proofs ;“ and yet he thought “certain rules might be laid down” respecting this subject “if in following and imitating nature, we could arrive at the art of forming a diversity of colours, by the combined intermixture of colours.” And he afterward adds, what may be regarded as the noblest eulogium that ever was made on Sir Isaac Newton: “yea, should ever any one,” exclaims that fine genius of antiquity, “attempt by curious research to account for this admirable mechanism, he will, in doing so, but manifest how entirely ignorant he is of the difference between Divine and human power. It is true, God can intermingle those things one with another, and then sever them at his pleasure, because he is, at the same time, all-knowing and all. powerful; but there is no man now exists, nor ever will perhaps, who shall ever be able to accomplish things so very difficult.” What an eulogism are these words in the mouth of such a philosopher as Plato, and bow glorious is he who hath successfully accomplished what appeared impracticable to that prince of philosophers! And what elevation of genius, what piercing penetration into the most intimate secrets of nature, displays itself in what we have just now recited from Plato, concerning the nature and theory of colours, at a time when philosophy was but yet in its infancy.

Comments of Plutarch

about:

OUR SIGHT, AND BY WHAT MEANS WE SEE.

Democritus and Epicurus suppose that sight is caused by the insertion of little images into the visive organ, and by the reception of certain rays which return to the eye after meeting the object. Empedocles supposes that images are mixed with the rays of the eye; these he styles the rays of images. Hipparchus, that the visual rays extend from both the eyes to the superficies of bodies, and give to the sight the apprehension of those same bodies, after the same manner in which the hand touching the extremity of bodies gives the sense of feeling. Plato, that the sight is the splendor of united rays; there is a light which reaches some distance from the eyes into a cognate air, and there is likewise a light shed from bodies, which meets and joins with the fiery visual light in the intermediate air (which is liquid and mutable); and the union of these rays gives the sense of seeing. This is Plato’s corradiancy, or splendor of united rays.

THOSE IMAGES WHICH ARE PRESENTED TO OUR EYES IN MIRRORS.

Empedocles says that these images are caused by certain effluxes which, meeting together and resting upon the superficies of the mirror, are perfected by that fiery element emitted by the said mirror, which transforms withal the air that surrounds it. Democritus and Epicurus, that the specular appearances are made by the subsistence of the images which flow from our eyes; these fall upon the mirror and remain, while the light returns to the eye. The followers of Pythagoras explain it by the reflection of the sight; for our sight being extended (as it were) to the brass, and meeting with the smooth dense surface thereof it is forced back, and caused to return upon itself: the same takes place in the hand, when it is stretched out and then brought back again to the shoulder. Any one may use these instances to explain the manner of seeing.

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