"Feynman uses Dirac's notation to describe the quantum mechanics of stimulated emission... he applies that physics to... dye molecules... In this regard, Feynman could have predicted the existence of the tunable laser."

"Regardless of the prophetic value of Dirac’s description [on interference] his was probably the first discussion... including a coherent beam of light. In other words, Dirac wrote the first chapter in laser optics."

"Fermat had recourse to the principle of the economy of nature. Heron and Olympiodorus had pointed out in antiquity that, in reflection, light followed the shortest possible path, thus accounting for the equality of angles. During the medieval period Alhazen and Grosseteste had suggested that in refraction some such principle was also operating, but they could not discover the law. Fermat, however, not only knew (through Descartes) the law of refraction, but he also invented a procedure—equivalent to the differential calculus—for maximizing and minimizing a function of a single variable. … Fermat applied his method … and discovered, to his delight, that the result led to precisely the law which Descartes had enunciated. But although the law is the same, it will be noted that the hypothesis contradicts that of Descartes. Fermat assumed that the speed of light in water to be less than that in air; Descartes' explanation implied the opposite."

"Descartes maintained his confidence in the instantaneity of light. ...Yet in his derivation of the law of refraction, Descartes reasoned that light traveled faster in a dense medium than in one less dense. He seems to have had no qualms about comparing infinite magnitudes!"

"(Ptolemy) left in his Optics, the earliest surviving table of angles of refraction from air to water. ...This table, quoted and requoted until modern times, has been admired... A closer glance at it, however, suggests that there was less experimentation involved in it than originally was thought, for the values of the angles of refraction form an arithmetic progression of second order... As in other portions of Greek Science, confidence in mathematics was here greater than that in the evidence of the senses, although the value corresponding to 60° agrees remarkably well with experience."

"Hooke's theoretical investigations on light were of great importance, representing as they do the transition from the Cartesian system to the fully developed theory of undulations. He begins by attacking Descartes' proposition, that light is a tendency to motion rather than an actual motion. "There is," he observes, "no luminous Body but has the parts of it in motion more or less"; and this motion is "exceeding quick." Moreover, since some bodies (e.g. the diamond when rubbed or heated in the dark) shine for a considerable time without being wasted away, it follows that whatever is in motion is not permanently lost to the body, and therefore that the motion must be of a to-and-fro or vibratory character. The amplitude of the vibrations must be exceedingly small, since some luminous bodies (e.g. the diamond again) are very hard, and so cannot yield or bend to any sensible extent."

"Hooke, who was both an observer and a theorist, made two experimental discoveries which concern [us]... but in both of these, as it appeared, he had been anticipated. The first was the observation of the iridescent colours which are seen when light falls on a thin layer of air between two glass plates or lenses, or on a thin film of any transparent substance. These are generally known as the "colours of thin plates," or ""; they had been previously observed by Boyle. Hooke's second experimental discovery, made after... Micrographia, was that light in air is not propagated exactly in straight lines, but that there is some illumination within the geometrical shadow of an opaque body. This observation had been published in 1665 in a posthumous work of Francesco Maria Grimaldi... who had given to the phenomenon the name ."

"Euler observed, that a combination of lenses which does not colour the image must be possible, since we have an example of such a combination in the human eye; and he investigated mathematically the conditions requi site for such a result. Klingenstierna... also showed that Newton's rule could not be universally true."

"The discovery that the laws of refractive dispersion of different substances were such as to allow of combinations which neutralized the dispersion without neutralising the refraction, is one which has hitherto been of more value to art than to science."

"Sir David Brewster... contests Newton's opinion, that the coloured rays into which light is separated by refraction are altogether simple and homogeneous, and incapable of being further analysed or modified. For he finds that by passing such rays through coloured media, (as blue glass for instance,) they are not only absorbed and transmitted in very various degrees, but that some of them have their colour altered; which cannot be conceived otherwise than as a further analysis of them, one component colour being absorbed and the other transmitted. ...The whole subject of the colours, of objects both opake and transparent, is still in obscurity. Newton's conjectures concerning the causes of the colours of natural bodies, appear to help us little; and his opinions on that subject are to be separated altogether from the important step which he made in optical science, by the establishment of the true doctrine of refractive dispersion."

"Göthe not only adopted and strenuously maintained the opinion that the Newtonian theory was false, but he framed a system of his own to explain the phenomena of colour. ...Göthe's views are, in fact, little different from those of Aristotle and Antonio de Dominis though more completely and systematically developed. ...it is not difficult to point out the peculiarities in Göthe's intellectual character which led to his singularly unphilosophical views on this subject. ...[H]e appears, like many persons in whom the poetical imagination is very active, to have been destitute of the talent and the habit of geometrical thought. In all probability, he never apprehended clearly and steadily those relations on which the Newtonian doctrine depends. ...[P]robably ...he had conceived the "composition" of colours in some way altogether different from that which Newton understands by composition. What Göthe expected to see, we cannot clearly collect; but we know... his intention of experimenting with a prism arose from his speculations on the rules of colouring in pictures; and we can easily see that any notion of the composition of colours which such researches would suggest, would require to be laid aside before he could understand Newton's theory of the composition of light."

"The doctrine of the unequal refrangibility of different rays is clearly exemplified in the effects of lenses, which produce images more or less bordered with colour, in consequence of this property. The improvement of telescopes was, in Newton's time, the great practical motive for aiming at the improvement of theoretical optics. Newton's theory showed why they were imperfect... The false opinion... that the dispersion must be the same when the refraction is the same led him to believe that the imperfection was insurmountable, and made him turn his attention to the construction of reflecting instead of refracting telescopes. But the rectification of Newton's error was a further confirmation of the general truth of his principles in other respects; and since that time, the soundness of the Newtonian law of refraction has hardly been questioned among physical philosophers."

"Newton was attacked by... Hooke and Huyghens. These philosophers, however, did not object so much to the laws of refraction of different colours, as to some expressions used by Newton, which, they conceived conveyed false notions respecting the composition and nature of light. Newton had asserted that all the different colours are of distinct kinds, and that, by their composition they form white light. ...Hooke maintained that all natural colours are produced by various combinations of two primary ones, red and violet; and Huyghens held a similar doctrine, taking, however, yellow and blue for his basis. ...These writers also had both of them adopted an opinion that light consisted in vibrations; and objected to Newton... involving the hypothesis that light was a body. Newton appears to have had a horror of the word hypothesis, and protests against its being supposed that his "theory" rests on such a foundation."

"[Anthony] Lucas of Liege repeated Newton's experiments, and obtained Newton's result, except that he never could obtain a spectrum whose length was more than three and a half times its breadth. Newton... persisted in asserting that the image would be five times as long as broad... We now know that the dispersion, and consequently the length, of the spectrum, is very different for different kinds of glass, and it is very probable that the Dutch prism was really less dispersive than the English one. The erroneous assumption which Newton made in this instance, he held by to the last; and was thus prevented from making [another] discovery."

"When Newton produced a bright spot on the wall of his chamber, by admitting the sun's light through a small hole in his window-shutter, and making it pass through a prism, he expected the image to be round; which, of course, it would have been, if the colours had been produced by an equal dispersion in all directions, but to his surprise he saw the image, or spectrum, five times as long as broad. He found that no consideration of the different thickness of the glass, the possible unevenness of its surface, or the different angles of rays proceeding from the two sides of the sun, could be the cause of this shape .He found, also, that the rays did not go from the prism to the image in curves; he was then convinced that the different colours were refracted separately, and at different angles; and he confirmed this opinion by transmitting and refracting the rays of each colour separately. ...Newton's opinions were not long in obtaining general acceptance; but they met with enough of cavil and misapprehension to annoy extremely the discoverer... impatient alike of stupidity and of contentiousness."

"[I]n 1672 Newton gave the true explanation of the facts; namely, that light consists of rays of different colours and different refrangibility. ...[T]he impression which this discovery made, both upon Newton and upon his contemporaries, shows how remote it was from the then accepted opinions. There appears to have been a general persuasion that the coloration was produced, not by any peculiarity in the law of refraction itself, but by some collateral circumstance,—some dispersion or variation of density of the light, in addition to the refraction. Newton's discovery consisted in teaching distinctly that the law of refraction was to be applied, not to the beam of light in general, but to the colours in particular."

"Descartes... showed considerable skill in tracing the consequences of the principle when once adopted. In particular we must consider him as the genuine author of the explanation of the rainbow. It is true, that Fleischer and Kepler had previously ascribed this phenomenon to the rays of sunlight which, falling on drops of rain, are refracted into each drop, reflected at its inner surface, and refracted out again. Antonio de Dominis had found that a glass globe of water, when placed in a particular position with respect to the eye, exhibited bright colours; and had hence explained the circular form of the bow, which, indeed, Aristotle had done before. But none of these writers had shown why there was a narrow bright circle of a certain definite diameter; for the drops which send rays to the eye after two refractions and a reflection, occupy a much wider space in the heavens. Descartes assigned the reason for this in the most satisfactory manner, by showing that the rays which, after two refractions and a reflection, come to the eye at an angle of about forty-one degrees with their original direction, are far more dense than those in any other position. He showed, in the same manner, that the existence and position of the secondary bow resulted from the same laws."

"The person who did discover the Law of the Sines, was Willebrord Snell, about 1621; but the law was first published by Descartes who had seen Snell's papers. Descartes does not acknowledge this... and after his manner, instead of establishing its reality by reference to experiment, he pretends to prove à priori that it must be true, comparing, for this purpose, the particles of light, to balls striking a substance which accelerates them."

"In Roger Bacon's works we find a tolerably distinct explanation of the effect of a convex glass; and in the work of Vitellio... the effect of refraction at the two surfaces of a glass globe is clearly traced. ...Vitellio had obtained experimentally a number of measures of the refraction out of air into water and into glass. Out of these facts no rule had yet been collected, when, in 1604 Kepler published his "Supplement to Vitellio." ...Kepler attempted to reduce to law the astronomical observations of Tycho,—devising an almost endless variety of possible formulæ, tracing their consequences with undaunted industry, and relating with a vivacious garrulity, his disappointments and his hopes,— ...he proceeded in the same manner with regard to Vitellio's Tables of Observed Refractions. He tried a variety of constructions by triangles, conic sections, &c., without being able to satisfy himself, and he at last is obliged to content himself with an approximate rule, which makes the refraction partly proportional to the angle of incidence, and partly to the secant of that angle. In this way he satisfies the observed refractions within a difference of less than half a degree each way. When we consider how simple the law of refraction is, (that the ratio of the sines of the angles of incidence and refraction is constant for the same medium,) it appears strange that a person attempting to discover it, and drawing triangles for the purpose, should fail; but this lot of missing what afterwards seems to have been obvious, is a common one in the pursuit of truth."

"Alhazen... asserted (lib. vii.), that "refraction takes place towards the perpendicular;" and reference is made to experiment for the proof. On the same ground he states that the quantities of refraction differ according to the magnitudes of the angles which the (primœ lineœ) directions of incidence make with the perpendicular to the surface; and moreover (which shows accuracy as well as distinctness,) that the angles of refraction do not follow the proportion of the angles of incidence."

"[T]he optical philosophers of antiquity had satisfied themselves that vision is performed in straight lines;— ...they had fixed their attention upon those straight lines, or rays, as the proper object of the science;—they had ascertained that rays reflected from a bright surface make the angle of reflection equal to the angle of incidence;—and they had drawn several consequences from these principles. We may add... the art of perspective, which is merely a corollary from the doctrine of rectilinear visual rays... The ancients practised this art, as we see in the pictures which remain to us; and we learn from Vitruvius, that they also wrote upon it. , who had been instructed by Eschylus... was the first author on this subject, and Anaxagoras, who was a pupil of Agatharchus, also wrote an Actinographia, or doctrine of drawing by rays... The moderns re-invented the art in the flourishing times of their painting... about the end of the fifteenth century; and... we have treatises on it."

"The foregoing properties of Reflection and Refraction being discovered and established by repeated experiments upon light and bodies of all sorts both fluid and solid, without any exception yet known; and being the principal foundation of the whole science of Opticks, are called the Laws of Reflection and Refraction; and are expressed by Sir Isaac Newton..."

"But if the ray that came along AC goes into the water at C, it will not proceed straight forward, but being refracted or bent at C, it will describe another straight line CE inclined to the perpendicular CQ at a lesser angle ECQ than the angle ACP; and the line CE will always be so situated, that when any circle, described about the center C, cuts the line CA in A and CE in E, the perpendiculars AD and EF, drawn from A and E to the line PQ shall always bear the same proportion to each other; whatever be the magnitude of the angle ACP. In water the line EF is always three quarters of AD. ... [T]he angle ACP [is] the Angle of Incidence, BCP the Angle of Reflection, ECQ the Angle of Refraction; the line AD the Sine of Incidence, that is, of the angle of incidence; and EF the Sine of Refraction, that is, of the angle of refraction."

"When a ray of light falls obliquely upon a smooth polished surface, it is turned out of its way either by reflection or refraction in the following manner. Imagine the paper upon which this figure is drawn to be perpendicular to the surface of stagnating water, and to cut it in the line RS, and that a ray of light, coming in the air along the line AC, falls upon RS at the point C. Then supposing the line PCQ... to be perpendicular to the surface of the water, if the ray be reflected, or turned back at C into the air again, it will describe a straight line CB, inclined to the perpendicular PC at an angle PCB exactly equal to the angle PCA."

"The least light or part of light, which may be stopt alone, without the rest of the light, or propagated alone, or do or suffer any thing alone, which the rest of the light doth not or suffereth not, is called a Ray of light. That rays of light are straight, is evident enough from the shadows of bodies; or from the appearance of light passing through little holes into a dark room full of dust or smoke; or because bodies cannot be seen through the bore of a bended pipe; or because they cease to be seen by the interposition of other bodies, as the fixt stars by the interposition of the moon and planets; and the parts of the sun by the interposition of the Moon, Mercury or Venus. Rays of light may therefore be represented by straight lines, not Mathematical but Physical, which are described by the motion of the parts or particles of light: and the point which a ray possesses in falling upon any surface may be considered as a Physical Point."

"Whoever has considered what a number of properties and effects of light are exactly similar to the properties and effects of bodies of a sensible bulk, will find it difficult to conceive that light is any thing else but very small and distinct particles of matter: which being incessantly thrown out from shining substances, and every way dispersed by reflection from all others, do impress upon our organs of seeing that peculiar motion, which is requisite to excite in our minds the sensation of light. But for the present purpose it is sufficient to observe that light consists of parts, both successive in the same lines and contemporary in several lines: because in the same place, you may stop that which comes one moment, and let pass that which comes presently after; and at the same time, you may stop it in one place, and let it pass in another. For that part of the light which is stopt cannot be the same with that which is let pass."

"Are not all hypotheses erroneous, in which light is supposed to consist of a Pression or Motion, propagated through a fluid medium? ...If Light consisted only in Pression propagated without actual Motion, it would not be able to agitate and heat the Bodies which refract and reflect it. If it consisted in Motion propogated to all distances in an instant, it would require an infinite force every moment, in every shining Particle, to generate that Motion. And if it consisted in Pression or Motion, propogated either in an instant or in time, it would bend into the Shadow. For Pression or Motion cannot be propogated in a Fluid in right Lines, beyond an Obstacle which stops part of the Motion, but will bend and spread every way into the quiescent Medium which lies beyond the Obstacle. Gravity tends downwards, but the Pressure of Water arising from Gravity tends every way with equal Force, and is propogated as readily, with as much force sideways as downwards, and through crooked passages as through straight ones. The Waves on the Surface of stagnating Water, passing by the sides of a broad Obstacle which stops part of them, bend afterwards and dilate themselves gradually into the quiet Water behind the Obstacle. The Waves, Pulses or Vibrations of the Air, wherein Sounds consist, bend manifestly, though not so much as Waves of Water. For a Bell or a Cannon may be heard beyond a Hill which intercepts the sight of the sounding Body, and Sounds are propogated as readily through crooked Pipes as through straight ones. But light is never known to follow crooked Passages nor to bend into the Shadow. For the fix'd Stars by the Interposition of any Planets cease to be seen. And so do parts of the Sun by Interposition of the Moon, Mercury or Venus. The Rays which pass very near to the edges of any Body, are bent a little by the action of the Body, as we shew'd above; but this bending is not towards but from the Shadow, and is perform'd only in the passage of the Ray by the Body, and at a very small distance from it."

"And so if any one would suppose that Æther (like our Air) may contain Particles which endeavour to recede from one another (for I do not know what this Æther is) and that its Particles are exceedingly smaller than those of Air, or even than those of Light: The exceeding smallness of its Particles may contribute to the greatness of the force by which those Particles may recede from one another, and thereby make that Medium exceedingly more rare and elastick than Air, and by consequence exceedingly less able to resist the motions of projectiles, and exceedingly more able to press upon gross Bodies, by endeavouring to expand it self."

"As Attraction is stronger in small Magnets than in great ones in proportion to their Bulk, and Gravity is greater in the Surfaces of small Planets than in those of great ones in proportion to their bulk, and small Bodies are agitated much more by electric attraction than great ones; so the smallness of the Rays of Light may contribute very much to the power of the Agent by which they are refracted."

"Is not this Medium [æther] much rarer within the dense Bodies of the Sun, Stars, Planets, and Comets, than in the empty celestial Spaces between them? And in passing from them to great distances, doth it not grow denser and denser perpetually, and thereby cause the gravity of those great Bodies towards one another, and of their parts towards the Bodies; every Body endeavouring to go from the denser parts of the Medium towards the rarer? ...And though this Increase of density may at great distances be exceeding slow, yet if the elastick force of this Medium be exceeding great, it may suffice to impel Bodies from the denser parts of the Medium towards the rarer, with all that power which we call Gravity. And that the elastic force of this Medium is exceeding great, may be gather'd from the swiftness of its Vibrations."

"Doth not this Æthereal Medium in passing out of Water, Glass, Crystal, and other compact and dense Bodies into empty Spaces, grow denser and denser by degrees, and by that means refract the Rays of Light not in a point, but by bending them gradually in curve Lines? And doth not the gradual condensation of this Medium extend to some distance from the Bodies, and thereby cause the Inflexions of the Rays of Light, which pass by the edges of dense Bodies, at some distance from the Bodies?"

"Is not the Heat of the warm Room convey'd through the Vacuum by the Vibrations of a much subtiler Medium than Air, which after the Air was drawn out remained in the Vacuum? And is not this Medium the same with that Medium by which Light is refracted and reflected and by whose Vibrations Light communicates Heat to Bodies, and is put into Fits of easy Reflexion and easy Transmission? ...And do not hot Bodies communicate their Heat to contiguous cold ones, by the Vibrations of this Medium propagated from them into the cold ones? And is not this Medium exceedingly more rare and subtile than the Air, and exceedingly more elastick and active? And doth it not readily pervade all Bodies? And is it not (by its elastick force) expanded through all the Heavens?"

"Do not several sorts of Rays make Vibrations of several bignesses, which according to their bigness excite Sensations of several Colours, much after the manner that the Vibrations of the Air, according to their several bignesses excite Sensations of several Sounds? And particularly do not the most refrangible Rays excite the shortest Vibrations for making a Sensation of deep violet, the least refrangible the largest form making a Sensation of deep red, and several intermediate sorts of Rays, Vibrations of several intermediate bignesses to make Sensations of several intemediate Colours?"

"Do not Bodies and Light act mutually upon one another; that is to say, Bodies upon Light in emitting, reflecting, refracting and inflecting it, and Light upon Bodies for heating them, and putting their parts into a vibrating motion wherein heat consists?"

"Do not the Rays of Light which fall upon Bodies, and are reflected or refracted, begin to bend before they arrive at the Bodies; and are they not reflected, refracted, and inflected, by one and the same Principle, acting variously in various Circumstances?"

"Are not the Rays of Light in passing by the edges and sides of Bodies, bent several times backwards and forwards, with a motion like that of an Eel? And do not the three Fringes of colour'd Light... arise from three such bendings?"

"Do not the Rays which differ in Refrangibility differ also in Flexibility; and are they not by their different inflexions separated from one another, so as after separation to make the Colours in the three Fringes... ? And after what manner are they inflected to make those Fringes?"

"Do not Bodies act upon Light at a distance, and by their action bend its Rays; and is not this action (caeteris paribus [all else being equal]) strongest at the least distance?"

"The Sine of Incidence is either accurately or very nearly in a given Ratio to the Sine of the Refraction."

"Refraction out of a rarer Medium into a denser, is made toward the Perpendicular; that is, so that the Angle of Refraction be less than the Angle of Incidence."

"If the reflected or refracted Ray be returned directly back to the Point of Incidence, it shall be refracted into the Line before described as the incident Ray."

"The Angle of Reflexion is equal to the Angle of Incidence."

"The Angles of Refexion and Refraction, lie in one and the same Plane with the Angle of Incidence."

"It was in May 1801 that I discovered, by reflecting on the beautiful experiments of Newton, a law which appears to me to account for a greater variety of interesting phenomena than any other optical principle that has yet been made known. I shall endeavour to explain this law by a comparison. Suppose a number of equal waves of water to move upon the surface of a stagnant lake, with a certain constant velocity, and to enter a narrow channel leading out of the lake. Suppose then another similar cause to have excited another equal series of waves, which arrive at the same channel, with the same velocity, and at the same time with the first. Neither series of waves will destroy the other, but their effects will be combined: if they enter the channel in such a manner that the elevations of one series coincide with those of the other, they must together produce a series of greater joint elevations; but if the elevations of one series are so situated as to correspond to the depressions of the other, they must exactly fill up those depressions, and the surface of the water must remain smooth; at least I can discover no alternative, either from theory or from experiment. Now, I maintain that similar effects take place whenever two portions of light are thus mixed; and this I call the general law of the interference of light. I have shown that this law agrees, most accurately, with the measures recorded in Newton's Optics, relative to the colours of transparent substances, observed under circumstances which had never before been subjected to calculation, and with a great diversity of other experiments never before explained. This, I assert, is a most powerful argument in favour of the theory which I had before revived: there was nothing that could have led to it in any author with whom I am acquainted, except some imperfect hints in those inexhaustible but neglected mines of nascent inventions, the works of the great Dr. Robert Hooke, which had never occurred to me at the time that I discovered the law; and except the Newtonian explanation of the combinations of tides in the Port of Batsha."

"[W]hen, in 1815, a young French military engineer, named Augustin Jean Fresnel, returning from the Napoleonic wars, became interested in the phenomena of light, and made some experiments concerning diffraction which seemed to him to controvert the accepted notions of the materiality of light, he was quite unaware that his experiments had been anticipated... He communicated his experiments and results to the French Institute, supposing them to be absolutely novel. That body referred them to a committee, of which... the dominating member was Dominique Francois Arago... [who] at once recognized the merit of Fresnel's work, and soon became a convert to the theory. He told Fresnel that Young had anticipated him as regards the general theory, but that much remained to be done, and he offered to associate himself with Fresnel in prosecuting the investigation. Fresnel was not a little dashed to learn that his original ideas had been worked out by another while he was a lad, but he... went ahead with unabated zeal. ... [A] bitter feud ensued, in which Arago was opposed by the "Jupiter Olympus of the Academy," Laplace, by the only less famous Poisson, and by the younger but hardly less able Biot. So bitterly raged the feud that a life-long friendship between Arago and Biot was ruptured forever. The opposition managed to delay the publication of Fresnel's papers, but Arago continued to fight with his customary enthusiasm and pertinacity, and at last, in 1823, the Academy yielded, and voted Fresnel into its ranks, thus implicitly admitting the value of his work."

"Anaxagoras holds that sense perception comes to pass by means of opposites, for the like is unaffected by the like. He then essays to review each separately. Accordingly he maintains that seeing is due to the reflection in the pupil, but that nothing is reflected in what is of like hue, but only in what is of a different hue. Now with most this contrast of hue occurs by day, but with some by night, and this is why the latter are keen of vision by night. But, in general, night the rather is of the eye's own hue. Furthermore, there is reflection by day, he holds, because the light is a contributing cause of reflection, and because the stronger of two colours is regularly reflected better in the weaker."

"Of those who ascribe perception to something other than similarity, Alcmaeon states... the difference between men and animals. For man, he says, differs from other creatures "inasmuch as he alone has the power to understand. Other creatures perceive by sense but do not understand"; since to think and to perceive by sense are different processes and not, as Empedocles held, identical. not Empedocles held He next speaks of the senses severally. ...Eyes see through the water round about. And the eye obviously has fire within, for when one is struck flashes out. Vision is due to the gleaming,—that is to say, the transparent character of that which [in the eye] reflects the object; and sight is the more perfect, the greater the purity of this substance."

"[I]t was Ibn al-Haytham's early embrace of empiricism and trust in mathematical proof that underlay the revolutionary project of his mature magnum opus, the Optics, the book that pointed the science of vision in the direction later pursued in seventeenth-century Europe. It was wholly composed of systematically arranged experiments and geometrical proofs, all expressed in clear, consistent vocabulary and orderly exposition. The Latin translation influenced medieval European scientists and philosophers such as Roger Bacon and Witelo. But the book came into its own later, when it attracted the attention of mathematicians like Kepler, Descartes, and Huygens, thanks in part to 's edition published in Basel in 1572."

"One of the most distinguished and prolific mathematicians in the medieval tradition of Arabic Islamic science, al-Hasan ibn al-Haytham (Latinized as Alhacen or Alhazen) became known in Europe in the thirteenth century as the author of the monumental book on optics—the mathematical theory of vision. In his Kitâb al-Manâ zir (De aspectibus), the eleventh-century scholar offered a new solution to the problem of vision, combining experimental investigations of the behavior of light with inventive geometrical proofs and constant forays into the psychology of visual perception — all systematically tied together to form a coherent alternative to the Euclidean and Ptolemaic theories of "visual rays" issuing from the eye."