The Book of Optics (Arabic: Kitāb al-Manāẓir (كتاب المناظر); Persian: Ketāb e Manzarehā (کتاب منظره ها); Latin: De Aspectibus or Opticae Thesaurus: Alhazeni Arabis; Italian: Deli Aspecti) was a seven-volume treatise on optics, physics, mathematics, anatomy and psychology written by the Iraqi Muslim scientist, Ibn al-Haytham (in Europe, Latinized as Alhacen or Alhazen), from 1011 to 1021, when he was under house arrest in Cairo, Egypt. It was originally written in Arabic and was later translated into Persian, Latin and Italian within the next several centuries.
The book had an important influence on the development of optics, as it laid the foundations for modern physical optics after drastically transforming the way in which light and vision had been understood, and on science in general with its introduction of the experimental scientific method. Ibn al-Haytham has been called the "father of modern optics", the "pioneer of the modern scientific method," and the founder of experimental physics, and for these reasons he has been described as the "first scientist."
The Book of Optics has been ranked alongside Isaac Newton's Philosophiae Naturalis Principia Mathematica as one of the most influential books in the history of physics, as it is widely considered to have initiated a revolution in the fields of optics and visual perception, also known as the 'Optical Revolution'. It established experimentation as the norm of proof in optics, and gave optics a physico-mathematical conception at a much earlier date than the other mathematical disciplines of astronomy and mechanics.
The Book of Optics also contains the earliest discussions and descriptions of the psychology of visual perception and optical illusions, as well as experimental psychology, and the first accurate descriptions of the camera obscura, a precursor to the modern camera. In medicine and ophthalmology, the book also made important advances in eye surgery, as it correctly explained the process of sight for the first time.
Optics and visionEdit
In classical antiquity, there were two major theories on vision. The first theory, the emission theory, was supported by such thinkers as Euclid and Ptolemy, who believed that sight worked by the eye emitting rays of light. The second theory, the intromission theory, supported by Aristotle and his followers, had physical forms entering the eye from an object. Alhacen argued on the basis of common observations (such as the eye being dazzled or even injured if we look at a very bright light) and logical arguments (such as how a ray could proceeding from the eyes reach the distant stars the instant after we open our eye) to maintain that we cannot see by rays being emitted from the eye nor through physical forms entering the eye. Alhacen instead developed a highly successful theory which explained the process of vision by rays of light proceeding to the eye from each point on an object, which he proved through the use of experimentation. His unification of geometrical optics with philosophical physics forms the basis of modern optics.
Ibn al-Haytham proved that rays of light travel in straight lines, and carried out a number of experiments with lenses, mirrors, refraction, and reflection. He was also the first to reduce reflected and refracted light rays into vertical and horizontal components, which was a fundamental development in geometric optics. He also discovered a result similar to Snell's law of sines, but did not quantify it and derive the law mathematically, unlike his contemporary Ibn Sahl who both discovered and formulated the law of sines in his On Burning Mirrors and Lenses (984).
Ibn al-Haytham is also credited with the invention of the camera obscura and pinhole camera. Alhacen also wrote on the refraction of light, especially on atmospheric refraction, for example, the cause of morning and evening twilight. He solved the problem of finding the point on a convex mirror at which a ray coming from one point is reflected to another point. He also experimented on the dispersion of light into its constituent colours, experimented on the finite speed of light, discovered that light is variable and moves slower in denser bodies, speculated on the rectilinear propagation and electromagnetic aspects of light, and argued that rays of light are streams of tiny energy particles travelling in straight lines. He also discovered spherical aberration.
Ibn al-Haytham made a thorough examination of the passage of light through various media and discovered the laws of refraction. He also carried out the first experiments on the dispersion of light into its constituent colours. His book Kitab al-Manazir (Book of Optics) was translated into Latin in the Middle Ages, as also was his book dealing with the colours of sunset. He dealt at length with the theory of various physical phenomena such as shadows, eclipses, and the rainbow, and speculated on the physical nature of light. He is the first to describe accurately the various parts of the eye and give a scientific explanation of the process of vision. He also attempted to explain binocular vision and the apparent increase in size of the Sun and the Moon when near the horizon. Through his extensive research on optics, he has been hailed as the "father of modern optics".
In his work on optics, Alhacen described sight as the inference of distinct properties of two similar and dissimilar objects. The eye perceives the size, shape, transparency (color and light), position, and motion from cognitive distinction which is entirely different from perceiving by mere sensation the characteristics of the object. The faculty of the mind, for Alhacen, includes perceiving through judgement and inference of distinct properties of similar objects outline and structure. Alhacen continues this body of work by concluding that the discrimination performed by the faculty of judgment and inference is in addition to sensing the objects visible form and not by pure sensation alone. We recognize visible objects that we frequently see. Recognition of an object is not pure sensation because we do not recognize everything we see. Ultimately, recognition does not take place without remembering. Recognition is due to the inference because of our mental capacity to conclude what objects are. Alhacen uses our ability to recognize species and likening their characteristics to that of similar individuals to support recognition associated and processed by inference. Alhacen further concludes that we are processing visual stimuli in very short intervals which allows us to recognize and associate objects through inference but we do not need syllogism to recognize it. These premises are stored infinitely in our souls.
- "He explained that sight results from the light penetrating the eye from the object, thus initiating a revolt against the ancient belief that visionary rays emanate from the eye."
- "He showed that the corneal region of the eye is curved and is close to the conjunctiva; but the cornea do not coalesce with the conjunctiva."
- "He suggested that the inner surface of the cornea at the point where it joins the foramen of the eye becomes concave in accordance with the curvature of its outer surface. The edges of the surfaces of the foramen and the middle part of the corneal regions become even but not one."
- "He endeavored by use of hyperbola and geometric optics to chart and formulate basic laws on reflection, and on atmospheric and light-ray refraction. He speculated on electromagnetic aspects of light, its velocity, and its rectilinear propagation. He recorded formation of an image in a camera obscura during an eclipse of the sun (the principle of the pinhole camera)."
- "He stated that the lens is that part of the eye where vision is felt first."
- "He theorized on how the image is transmitted through the optic nerve to the brain and made a distinction between luminous and nonluminous bodies."
The Book of Optics also provides the first correct definition of the twilight, discusses atmospheric refraction, shows that the twilight only begins when the Sun is 19 degrees below the horizon, and uses a complex geometric demonstration to measure the height of the Earth's atmosphere as 52,000 passuum (49 miles), which is very close to the modern measurement of 50 miles. However, one has to remember that such close agreement is just a coincidence as Boyle's Law and Charles' Law, laws of gravity were yet unknown to us. Moreover, the definition of the boundary of the atmosphere is somewhat arbitrary.
The Book of Optics is considered by some to mark the beginning of experimental psychology. Ibn al-Haytham made use of his experimental method in his pioneering work on the psychology of visual perception and optical illusions. His investigations and experiments on psychology and visual perception included sensation, variations in sensitivity, sensation of touch, perception of colours, perception of darkness, the psychological explanation of the moon illusion, and binocular vision.
Other apparatus Ibn al-Haytham described in the Book of Optics, besides the camera obscura, include "specially arranged dark chambers, specially designed apertures for the controlled admission of light," and "viewing tubes". The Book of Optics is also credited with providing the earliest "historical proof of a magnifying device, a convex lens forming a magnified image". Its translation into Latin in the 12th century was instrumental to the invention of eyeglasses in 13th century Italy.
The earliest evidence of "a magnifying device, a convex lens forming a magnified image," dates back to the Book of Optics published by Ibn al-Haytham (Alhazen) in 1021. The properties of a magnifying lens became known to Europeans after the book was translated into Latin in the 12th century. Ibn al-Haytham described his magnifying lens as follows:
"If an object is placed in a dense spherical medium of which the curved surface is turned towards the eye and is between the eye and the centre of the sphere, the object will appear magnified."
Roshdi Rashed notes that "by promoting the use of experiments in scientific research, al-Haytham played an important part in setting the scene for modern science." Rosanna Gorini wrote the following on the Book of Optic's introduction of the scientific method:
"According to the majority of the historians al-Haytham was the pioneer of the modern scientific method. With his book he changed the meaning of the term optics and established experiments as the norm of proof in the field. His investigations are based not on abstract theories, but on experimental evidences and his experiments were systematic and repeatable."
Ibn al-Haytham's scientific method was very similar to the modern scientific method and consisted of the following procedures:
- Statement of problem
- Formulation of hypothesis
- Testing of hypothesis using experimentation
- Analysis of experimental results
- Interpretation of data and formulation of conclusion
- Publication of findings
An aspect associated with Ibn al-Haytham's optical research is related to systemic and methodological reliance on experimentation (i'tibar) and controlled testing in his scientific inquiries. Moreover, his experimental directives rested on combining classical physics ('ilm tabi'i) with mathematics (ta'alim; geometry in particular) in terms of devising the rudiments of what may be designated as a hypothetico-deductive procedure in scientific research. This mathematical-physical approach to experimental science supported most of his propositions in Kitab al-Manazir (The Optics; De aspectibus or Perspectivae) and grounded his theories of vision, light and colour, as well as his research in catoptrics and dioptrics. His legacy was further advanced through the 'reforming' of his Optics by Kamal al-Din al-Farisi (d. ca. 1320) in the latter's Kitab Tanqih al-Manazir (The Revision of [Ibn al-Haytham's] Optics).
He describes his experimental approach in the introduction to the book as follows:
"We should distinguish the properties of particulars, and gather by induction what pertains to the eye when vision takes place and what is found in the manner of sensation to be uniform, unchanging, manifest, and not subject to doubt. After which we should ascend in our inquiry and reasonings, gradually and orderly, criticizing premises and exercising caution in regard to conclusions—our aim in all that we make subject to inspection and review being to employ justice, not to follow prejudice, and to take care in all that we judge and criticize that we seek the truth and not be swayed by opinion."
From Ibn al-Haytham to the present day, the emphasis of the scientific method has always been on seeking truth:
"Truth is sought for its own sake. And those who are engaged upon the quest for anything for its own sake are not interested in other things. Finding the truth is difficult, and the road to it is rough. ..."
"How does light travel through transparent bodies? Light travels through transparent bodies in straight lines only. ... We have explained this exhaustively in our Book of Optics. But let us now mention something to prove this convincingly: the fact that light travels in straight lines is clearly observed in the lights which enter into dark rooms through holes. ... the entering light will be clearly observable in the dust which fills the air."
The conjecture that "Light travels through transparent bodies in straight lines only", was corroborated by Alhacen only after years of effort. His demonstration of the conjecture was to place a straight stick or a taut thread next to the light beam, to prove that light travels in a straight line.
The Book of Optics was the first book to emphasize the role of experimentation as a form of proof in scientific inquiry. The term "experiment" itself may have origins in the Book of Optics. Ibn al-Haytham used the Arabic terms i'tabara, 'itibar and mu'tabir to refer to his experiments. During the Latin translation of the book, these terms were rendered into Latin as experimentare (or experiri), experimentum and experimentatar respecively.
Ibn al-Haytham also employed scientific skepticism and criticism, and emphasized the role of empiricism. He also explained the role of induction in syllogism, and criticized Aristotle for his lack of contribution to the method of induction, which Ibn al-Haytham regarded as superior to syllogism, and he considered induction to be the basic requirement for true scientific research.
The concept of Ockam's razor is also present in the Book of Optics. For example, after demonstrating that light is generated by luminous objects and emitted or reflected into the eyes, he states that therefore "the extramission of [visual] rays is superfluous and useless." He was also the first scientist to adopt a form of positivism in his approach, centuries before a term for positivism was coined. He wrote that "we do not go beyond experience, and we cannot be content to use pure concepts in investigating natural phenomena", and that the understanding of these cannot be acquired without mathematics. After assuming that light is a material substance, he does not discuss its nature any further but confines his investigations to the diffusion and propagation of light. The only properties of light he takes into account are that which can be treated by geometry and verified by experiment, noting that energy is the only quality of light that can be sensed.
Early European translationsEdit
Optics was translated into Latin by an unknown scholar at the end of the 12th century or the beginning of the 13th century. By the 14th century, Alhazen's Book of Optics was available in Italian translation, entitled Deli Aspecti. The Latin translation was later printed by Friedrich Risner in 1572, with the title Opticae thesaurus: Alhazeni Arabis libri septem, nuncprimum editi; Eiusdem liber De Crepusculis et nubium ascensionibus. Risner is also the author of the name variant "Alhazen", before him he was known in the west as Alhacen, which is a more correct transcription of the Arabic name.
This work enjoyed a great reputation during the Middle Ages. Works by Alhacen on geometrical subjects were discovered in the Bibliothèque nationale in Paris in 1834 by E. A. Sedillot. Other manuscripts are preserved in the Bodleian Library at Oxford and in the library of Leiden.
The Book of Optics initiated a scientific revolution in optics and visual perception, and laid the foundations for modern optics, the scientific method, experimental physics and experimental psychology, for which it has been ranked alongside Isaac Newton's Philosophiae Naturalis Principia Mathematica as one of the most influential books in the history of physics. The Latin translation of the Book of Optics influenced the works of many later European scientists, such as Robert Grosseteste, Roger Bacon, John Peckham, Witelo, William of Ockham, Leonardo da Vinci, Francis Bacon, René Descartes, Johannes Kepler, Galileo Galilei, Isaac Newton, and others. The Book of Optics also laid the foundations for a variety of later optical technologies, such as eyeglasses, the camera, the telescope and microscope, microscopy, retinal surgery, and robotic vision. Richard Powers expressed the opinion that Ibn al-Haytham's scientific method and scientific skepticism in his experiments on optics to be a candidate for the most important idea of the 2nd millennium.
Besides its influence on science and technology, the Book of Optics also influenced other aspects of Western culture. In religion, for example, John Wycliffe, the intellectual progenitor of the Protestant Reformation, referred to Alhazen in discussing the seven deadly sins in terms of the distortions in the seven types of mirrors analyzed in De aspectibus. In literature, Alhazen's Book of Optics is praised in Guillaume de Lorris' Roman de la Rose and Geoffrey Chaucer's The Canterbury Tales. In art in particular, the Book of Optics laid the foundations for the linear perspective technique and the use of optical aids in Renaissance art (see Hockney-Falco thesis). The Renaissance artist Lorenzo Ghiberti relied heavily upon Alhazen, quoting him "verbatim and at length" while framing his account of art and its aesthetic imperatives in the “Commentario terzo.” Alhazen’s work was thus "central to the development of Ghiberti’s thought about art and visual aesthetics" and "may well have have been central to the development of artificial perspective in early Renaissance Italian painting." The linear perspective technique was also employed in European geographical charts during the Age of Exploration, such as Paolo Toscanelli's chart which was used by Christopher Columbus when he went on a voyage to the New World.
Robert S. Elliot wrote the following on the Book of Optics:
"Alhazen was one of the ablest students of optics of all times and published a seven-volume treatise on this subject which had great celebrity throughout the medieval period and strongly influenced Western thought, notably that of Roger Bacon and Kepler. This treatise discussed concave and convex mirrors in both cylindrical and spherical geometries, anticipated Fermat's law of least time, and considered refraction and the magnifying power of lenses. It contained a remarkably lucid description of the optical system of the eye, which study led Alhazen to the belief that light consists of rays which originate in the object seen, and not in the eye, a view contrary to that of Euclid and Ptolemy."
"Ibn Haytham's writings reveal his fine development of the experimental faculty. His tables of corresponding angles of incidence and refraction of light passing from one medium to another show how closely he had approached discovering the law of constancy of ratio of sines, later attributed to Snell. He accounted correctly for twilight as due to atmospheric refraction, estimating the sun's depression to be 19 degrees below the horizon, at the commencement of the phenomenon in the mornings or at its termination in the evenings."
Matthias Schramm wrote in his Ibn al-Haythams Weg zur Physik:
“Through a closer examination of Ibn al-Haytham's conceptions of mathematical models and of the role they play in his theory of sense perception, it becomes evident that he was the true founder of physics in the modern sense of the word; in fact he anticipated by six centuries the fertile ideas that were to mark the beginning of this new branch of science.”
In Book I, Ibn al-Haytham begins by writing an introduction to the two conflicting doctrines of vision which previously dominated ancient thought on optics: the intromission theory of the the “natural philosophers” (Aristotle and his followers) where “vision is effected by a form which comes from the visible object to the eye”, and the emission theory of “mathematicians” (such as Euclid, Ptolemy and Al-Kindi) where “vision is effected by a ray which issues from the eye to the visible object.” He states:
“These two notions, appear to diverge and contradict one another if taken at face value. Now, for any two different doctrines, it is either the case that one of them is true and the other false; or they are both false, the truth being other than either of them; or they both lead to one thing which is the truth…That being the case…and because the manner of vision has not been ascertained, we have thought it appropriate that we direct our attention to this subject as much as we can, and seriously apply ourselves to it, and examine it, and diligently inquire into its nature.”
He states that his research and investigation of light will be based on experimental evidence rather than on abstract theory, and describes the systematic approach he will use to resolve the problem of vision in his investigations on optics:
“We should distinguish the properties of particulars, and gather by induction what pertains to the eye when vision takes place and what is found in the manner of sensation to be uniform, unchanging, manifest, and not subject to doubt. After which we should ascend in our inquiry and reasonings, gradually and orderly, criticizing premises and exercising caution in regard to conclusions—our aim in all that we make subject to inspection and review being to employ justice, not to follow prejudice, and to take care in all that we judge and criticize that we seek the truth and not be swayed by opinion.”
“Straight lines [exist between] the surface of the eye [and] each point on the seen surface of the object. An accurate experimental examination of this fact may be easily made with the help of rulers and tubes. [...] If…he covers any part of the opening, then there will be screened off only that portion…that lies on a straight line with the eye and the screening body—this straightness being secured by the ruler and the straightness of the tube, [...] It follows from this experiment, with a necessity that dispels doubt, that sight does not perceive any visible object existing with it in the same atmosphere, this perception being not by reflection, except through straight lines alone that can be imagined to extend between the surface of the object and the surface of the eye. Sight does not perceive any visible object unless there exists in the object some light, which the object possesses of itself or which radiates upon it from another object.”
Ibn al-Haytham then resolves the problem by explaining that it is light that travels from visible objects to the eye, rather than the physical “forms” mentioned by the physicists, and that the rays that create vision travel into the eye, rather than travel out of the eyes as believed by the mathematicians. Most of the volume is thus dedicated to experiments and investigations on light. He begins by dividing light into primary light, the light radiated by an illuminating body, and secondary light, the light reflected off another surface. Alongside a lamp, fire and the stars, he cites sunlight as a primary light, every other visible object (including birds, trees, stones and grass) which reflects the sunlight as secondary light. He realized that the atmosphere also reflects light, from his observations of the sky brightening even before the Sun rises. In support of his intromission theory, he describes a number of observations where the eyes feel pain when exposed to a bright light (primary light) and where the eyes see afterimages when staring at an illuminated object (secondary light) for a prolonged period of time. He also notes that light is always the same from every source, using sunlight, fire, and a mirror as examples. He then examines the anatomical structure of the eye, and proposes the first use of a camera obscura.
Book II of the treatise contains a discussion on visual perception. In Book III, he pioneered the psychology of visual perception and optical illusions, being the first scientist to argue that vision occurs in the brain, rather than the eyes. He pointed out that personal experience has an effect on what people see and how they see, and that vision and perception are subjective. He explained possible errors in vision in detail, and as an example, describes how a small child with less experience may have more difficulty interpreting what he/she sees. He also gives an example of an adult that can make mistakes in vision because of how one's experience suggests that he/she is seeing one thing, when he/she is really seeing something else.
Book IV deals with the theory of reflection mathematically, while Book V deals with catoptrics and the influential Alhazen's problem. Book VI examines errors in vision due to reflection, while the final volume, Book VII, examines refraction.
In order to demonstrate that straight lines of light exist between “the surface of the eye” and “each point on the seen surface of the object”, he states than an “accurate experimental examination of this fact may be easily made with the help of rulers and tubes.” He describes how an observer looking through a straight tube can only see parts of an object lying directly across from the opening of the tube, and states:
“If…he covers any part of the opening, then there will be screened off only that portion…that lies on a straight line with the eye and the screening body—this straightness being secured by the ruler and the straightness of the tube. It follows from this experiment, with a necessity that dispels doubt, that sight does not perceive any visible object existing with it in the same atmosphere, this perception being not by reflection, except through straight lines alone that can be imagined to extend between the surface of the object and the surface of the eye. Sight does not perceive any visible object unless there exists in the object some light, which the object possesses of itself or which radiates upon it from another object.”
Ibn al-Haytham states that the “light shining from a self-luminous body into the transparent air, radiates from every part of the luminous body facing that air,…and it issues from every point on the luminous body in every straight line that can be imagined to extend in the air from that point.” To prove this, he describes an experiment with a sheet of copper with a large circular hole in the center. He states that the experimenter should slide “a well-straightened cylindrical tube of regular circularity and convenient length” through the hole, while one end of the tube is open, and the other end is closed but punctured by an aperture that should “not exceed the thickness of a needle.” He then states that the experimenter should hold a candle up to the open end of the cylinder “in the darkness of night” and hold an opaque object up to the aperture at the other end. He explains that only a small amount of light from the flame passes through the aperture, while the rest of the light is blocked by the sheet of copper. He then states that “the experimenter should…gently move the flame so another part of it may face the hole, and then inspect the body opposite.” He explains that as the flame moves, the light projected onto the opaque object changes, like how the light on the object appears weak when the tip of the flame is opposite the aperture and the light on the object appears bright when the center of the flame is opposite the aperture. He concludes: “Therefore, it appears from this experiment that light radiates from each part of the fire.”
Ibn al-Haytham also constructed a tube which he used to prove that light is emitted equally from all parts of a wick and dispersed radially. "When the light was rotated around the aperture of the tube, the spot projected onto the screen remained unaltered. With the narrowing of the opening, the luminous spot, fainter and smaller, still continued to appear. In this way, he demonstrated that light is emitted equally from all parts of the wick and dispersed radially."
In his various experiments, Ibn al-Haytham used the term “al-Bayt al-Muthlim” (Arabic: البيت المظلم), translated in English as "dark room", to describe the camera obscura. While earlier philosophers such as Mozi, Aristotle, Theon of Alexandria and Al-Kindi (Alkindus) described the effects of a single light passing through a pinhole camera, none of them suggested that what is being projected onto the screen is an image of everything on the other side of the aperture. Ibn al-Haytham was the first to demonstrate this with his lamp experiment where several different light sources are arranged across a large area, and he was thus the first scientist to successfully project an image from outdoors onto a screen indoors with a camera obscura.
One of the most famous experiments described in the Book of Optics is the lamp experiment with the camera obscura, used to test the hypothesis that lights and colours cannot blend in the air. This experiment covers all the necessary steps in Ibn al-Haytham's scientific method of inquiry: stating the problem, gathering information through observation, the formulation of a hypothesis, an experiment to test the hypothesis, repeating the experiment to confirm the results, and then stating the conclusion. He describes it as follows:
"The proof that lights and colours do not blend in the air or in transparent bodies is [the following]. Let several lamps be positioned at various points in the same area, all being opposite a single aperture leading to a dark place; opposite the aperture let there be a wall in that dark place or let an opaque body be held facing the aperture: the lights of those lamps will appear separately on that wall or body and in the same number as the lamps, each light being opposite one of the lamps on the straight line passing through aperture. If one of the lamps is screened, only the light opposite that lamp in the dark will vanish. When the screen is moved away from the lamp, that light will return to its place. Whichever lamp is screened, only the light facing it in the [dark] place will disappear. When the screen is removed, the light will return to its place."
"Now this fact may be easily examined experimentally at any time [in the following way]. Let the experimenter employ a chamber with a two-panel door in a dark night, and let him bring several lamps which he should set up at different points in front of the door. The experimenter should enter the chamber, close the door but leave a small gap between the panels, and observe the wall opposite the door. On it he will find separate lights, in the same number as the lamps, which have entered through the opening at the door, each facing one of those lamps. If the experimenter then screens one of the lamps, the light facing it will vanish; and upon his lifting the screen, that light will return. If he covers the opening at the door, leaving only a small aperture facing the lamps, he will again find on the chamber’s wall the separate lights in the number of those lamps, all according to the magnitude of the aperture."
"Now all the lights that appear in the dark place have reached it through the aperture alone, and therefore the lights of all those lamps have come together at the aperture, then separated after passing through it. Thus, if lights blended in the atmosphere, the lights of the lamps meeting at the aperture would have mixed in the air at the aperture and in the air preceding it before they reached the aperture, and they would have come out so mingled together that they would not be subsequently distinguishable. We do not, however, find the matter to be so; rather the lights are found to come out separately, each being opposite the lamp from which it has arrived."
Ibn al-Haytham theorized on the rectilinear propagation and finite speed of light. He argued that light is a “substantial matter”, the propagation of which requires time “even if this is hidden to our senses”. He argued that its "forms" (or "species" in the Latin translation) were dimensional, and on this basis, he "demonstrated that the perception of light required time: light entering a darkened chamber would have to pass through a dimensional aperture, which could only be opened temporally." In an experiment he undertook with the camera obscura, in order to establish that light travels in time and with finite speed, he states:
“If the hole was covered with a curtain and the curtain was taken off, the light traveling from the hole to the opposite wall will consume time.”
He reiterated the same experience when he established that light travels in straight lines. The most revealing experiment which indeed introduced the camera obscura was in his studies of the half-moon shape of the sun’s image during eclipses which he observed on the wall opposite a small hole made in the window shutters. In his famous essay "On the form of the Eclipse" (Maqalah-fi-Surat-al-Kosuf) (Arabic: مقالة في صورةالكسوف) he commented on his observation:
“The image of the sun at the time of the eclipse, unless it is total, demonstrates that when its light passes through a narrow, round hole and is cast on a plane opposite to the hole it takes on the form of a moon-sickle.”
In his experiment of the sun light he extended his observation of the penetration of light through the pinhole camera to conclude that when the sun light reaches and penetrates the hole it makes a conic shape at the points meeting at the pinhole, forming later another conic shape reverse to the first one on the opposite wall in the dark room. This happens when sun light diverges from point “ﺍ” until it reaches an aperture “ﺏﺤ” and is projected through it onto a screen at the luminous spot “ﺩﻫ”. Since the distance between the aperture and the screen is insignificant in comparison to the distance between the aperture and the sun, the divergence of sunlight after going through the aperture should be insignificant. In other words, “ﺏﺤ” should be about equal to “ﺩﻫ”. However, it is observed to be much greater “ﻙﻁ” when the paths of the rays which form the extremities of “ﻙﻁ” are retraced in the reverse direction, it is found that they meet at a point outside the aperture and then diverge again toward the sun. This was indeed the first accurate description of the Camera Obscura phenomenon.
In camera terms, the light converges into the room through the hole transmitting with it the object(s) facing it. The object will appear in full colour but upside down on the projecting screen/wall opposite the hole inside the dark room. The explanation is that light travels in a straight line and when some of the rays reflected from a bright subject pass through the small hole in thin material they do not scatter but cross and reform as an upside down image on a flat white surface held parallel to the hole. Ibn al-Haitham established that the smaller the hole is, the clearer the picture is.
Ibn al-Haytham's Risala fi l-Daw’ (Treatise on Light) is a supplement to his Kitab al-Manazir (Book of Optics). The text contained further investigations on the properties of luminance and its radiant dispersion through various transparent and translucent media. He also carried out further observations, investigations and examinations on the anatomy of the eye, the camera obscura and pinhole camera, the illusions in visual perception, the meteorology of the rainbow and the density of the atmosphere, various celestial phenomena (including the eclipse, twilight, and moonlight), refraction, catoptrics, dioptrics, spherical and parabolic mirrors, and magnifying lenses.
According to Giambattista della Porta, Ibn al-Haytham was the first to give a correct explanation of the apparent increase in the size of the Moon and Sun when near Earth's horizon, known as the Sun and Moon illusion respectively. (Ptolemy made earlier attempts at explaining it, according to Roger Bacon.)
In another supplementary treatise, Ibn al-Haytham attempted to provide a scientific explanation for the rainbow phenomenon. In his Maqala fi al-Hala wa Qaws Quzah (On the Rainbow and Halo), he "explained the formation of rainbow as an image, which forms at a concave mirror. If the rays of light coming from a farther light source reflect to any point on axis of the concave mirror, they form concentric circles in that point. When it is supposed that the sun as a farther light source, the eye of viewer as a point on the axis of mirror and a cloud as a reflecting surface, then it can be observed the concentric circles are forming on the axis." He was not able to verify this because his theory that "light from the sun is reflected by a cloud before reaching the eye" did not allow for a possible experimental verification. This explanation was later repeated by Averroes, and, though incorrect, provided the groundwork for the correct explanations later given by Kamāl al-Dīn al-Fārisī and Theodoric of Freiberg.
Ibn al-Haytham's work on catoptrics in Book V of the Book of Optics contains the important mathematical problem known as Alhazen's problem. It comprises drawing lines from two points in the plane of a circle meeting at a point on the circumference and making equal angles with the normal at that point. This is equivalent to finding the point on the edge of a circular billiard table at which a cue ball at a given point must be aimed in order to canon off the edge of the table and hit another ball at a second given point. Thus, its main application in optics is to solve the problem, "Given a light source and a spherical mirror, find the point on the mirror were the light will be reflected to the eye of an observer." This leads to an equation of the fourth degree.
Ibn al-Haytham solved the problem using conic sections and a geometric proof, but Alhazen's problem remained influential in Europe, when later mathematicians such as Christiaan Huygens, James Gregory, Guillaume de l'Hôpital, Isaac Barrow, and many others, attempted to find an algebraic solution to the problem, using various methods, including analytic methods of geometry and derivation by complex numbers. An algebraic solution to the problem was finally found in 1997 by the Oxford mathematician Peter M. Neumann.
While investigating Alhazen's problem, Ibn al-Haytham derived the earliest formula for the sum of the fourth powers, and using an early proof by mathematical induction, he developed a method for determining the general formula for the sum of any integral powers. He used his result on sums of integral powers to perform an integration, in order to find the volume of a paraboloid. He was thus able to find the integrals for polynomials up to the fourth degree, and came close to finding a general formula for the integrals of any polynomials. This was fundamental to the development of infinitesimal and integral calculus.
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Over the centuries, Ibn al-Haytham's contributions showed up in the work of various mathematicians. According to mathematics historian Victor J. Katz: "Ibn al-Haytham's formula for the sum of fourth powers shows up in other places in the Islamic world over the next few centuries. It appears in the work of Abu-l-Hasan ibn Haydur (d. 1413), who lived in what is now Morocco, and in the work of Abu Abdallah ibn Ghazi (1437-1514), who also lived in Morocco. Furthermore, one also finds the formula in The Calculator's Key of Ghiyath al-Din Jamshid al-Kashi (d. 1429), a mathematician and astronomer whose most productive years were spent in Samarkand, now in Uzbekistan, in the court of Ulugh Beg." Ibn al-Haytham's equation also later showed up in Indian mathematics, specifically the Kerala school of astronomy and mathematics in the 16th century.
Chapters 15-16 of the Book of Optics dealt with astronomy. Ibn al-Haytham was the first to discover that the celestial spheres do not consist of solid matter, and he also discovered that the heavens are less dense than the air:
"The body of heaven differs ... from the air. [...] In fineness, the body of air being denser than the body of heaven, [which is] finer than the body of air. The entire heaven differs from the transparency of air. The body in which the fixed stars are, differs in transparency from the air. The body of heaven is finer than the body of air, that is, it is more transparent. In the heavens there is no clear body that is dense."
At a scientific conference in February 2007, Charles M. Falco argued that Ibn al-Haytham's work on optics may have influenced the use of optical aids by Renaissance artists. Falco said that his and David Hockney's examples of Renaissance art "demonstrate a continuum in the use of optics by artists from circa 1430, arguably initiated as a result of Ibn al-Haytham's influence, until today."
The Book of Optics describes several early experimental observations that Ibn al-Haytham made in mechanics and how he used his results to explain certain optical phenomena using mechanical analogies. He conducted experiments with projectiles, and concluded that "it was only the impact of perpendicular projectiles on surfaces which was forceful enough to enable them to penetrate whereas the oblique ones were deflected. For example, to explain refraction from a rare to a dense medium, he used the mechanical analogy of an iron ball thrown at a thin slate covering a wide hole in a metal sheet. A perpendicular throw would break the slate and pass through, whereas an oblique one with equal force and from an equal distance would not." He used this result to explain explained how intense direct light hurts the eye: "Applying mechanical analogies to the effect of light rays on the eye, lbn al-Haytham associated 'strong' lights with perpendicular rays and 'weak' lights with oblique ones. The obvious answer to the problem of multiple rays and the eye was in the choice of the perpendicular ray since there could only be one such ray from each point on the surface of the object which could penetrate the eye."
In philosophy, Ibn al-Haytham is considered a pioneer of phenomenology. He articulated a relationship between the physical and observable world and that of intuition, psychology and mental functions. His theories regarding knowledge and perception, linking the domains of science and religion, led to a philosophy of existence based on the direct observation of reality from the observer's point of view. Much of his thought on phenomenology was not further developed until the 20th century.
Ibn al-Haytham has been described as the father of ophthalmology. He discussed the topics of medicine, ophthalmology and eye surgery in the anatomical and physiological portions of the Book of Optics and in his commentaries on Galenic works. He made several improvements to eye surgery and accurately described the process of sight, the structure of the eye, image formation in the eye and the visual system. He also discovered the underlying principles of Hering's law of equal innervation, binocular vision, motion perception, vertical horopters, and binocular disparity.
He discussed ocular anatomy, and was the first author to deal with the "descriptive anatomy" and "functional anatomy" of the eye independently. Much of his decriptive anatomy was faithful to Galen's gross anatomy, but with significant differences in his approach. For example, the whole area of the eye behind the iris constitutes what Ibn al-Haytham uniquely called the uveal sphere, and his description of the eye was devoid of any teleological or humoural theories associated with Galenic anatomy. He also described the eye as being made up of two interesecting globes, which was essential to his functional anatomy of the eye.
After describing the construction of the eye, Ibn al-Haytham makes his most original anatomical contribution in describing the functional anatomy of the eye as an optical system, or optical instrument. His mulitple light-source experiment via a reduction slit with the camera obscura, also known as the lamp experiment, provided sufficient empirical grounds for him to develop his theory of corresponding point projection of light from the surface of an object to form an image on a screen. It was his comparison between the eye and the beam-chamber, or camera obscura, which brought about his synthesis of anatomy and optics, giving rise to a new field of optics now known as "physiological optics". As he conceptualized the essential principles of pinhole projection from his experiments with the pinhole camera, he considered image inversion to also occur in the eye, and viewed the pupil as being similar to an aperture. Regarding the process of image formation, however, he incorrectly agreed with Avicenna that the lens was the receptive organ of sight, but correctly hinted at the retina also being involved in the process.
In the Book of Optics, Ibn al-Haytham was the first scientist to argue that vision occurs in the brain, rather than the eyes. He pointed out that personal experience has an effect on what people see and how they see, and that vision and perception are subjective. He explained possible errors in vision in detail, and as an example described how a small child with less experience may have more difficulty interpreting what he or she sees. He also gave an example of how an adult can make mistakes in vision due to experience that suggests that one is seeing one thing, when one is really seeing something else.
In the Book of Optics, Ibn al-Haytham also developed the "concept of a sensory core that interprets visual stimuli" and which was "highly sophisticated, incorporating mathematical, anatomical and physiopsychological components."
Ibn al-Haytham also described what became known as Hering's law of equal innervation, vertical horopters, and binocular disparity, and improved on the theories of binocular vision, motion perception and horopters previously discussed by earlier scholars such as Aristotle, Euclid and Ptolemy.
Omar Khaleefa has argued that Ibn al-Haytham should be considered the founder of psychophysics, contrary to the orthodox opinion that Gustav Fechner founded this field in 1860 with the publication of his Elements of Psychophysics. There is, however, no evidence that Ibn al-Haytham employed any quantitative psychophysical techniques, so this remains a minority opinion. The psychophysicist Craig Aaen-Stockdale has written a rebuttal to Khaleefa's arguments, noting that the claim for Ibn al-Haytham being the ‘founder of psychophysics’ "rests upon unsupported assertions, a conflation of psychophysics with the wider discipline of psychology, and semantic arguments over what it is to ‘found’ a school of thought."
Ibn al-Haytham was also the first to study the cognitive process of reading, giving the first descriptions on the role of perception in the understanding of written language. For example, he wrote the following observation on the dual nature of word recognition:
"For when a literate person glances at the form abjad on a written paper, he would immediately perceive it to be abjad [a word denoting the Arabic alphabet] because of his recognition of the form. Thus from his perception that the 'a' and the 'd' last, or from his perception of the configuration of the total form, he perceives that it is abjad. Similarly, when he sees the written name of Allah, be He exalted, he perceives by recognition, at the moment of glancing at it, that it is Allah's name. And it is so with all well-known written words which have appeared many times before the eye: a literate person immediately perceives what the word is by recognition, without the need to inspect the letters in it one by one. The case is different when a literate person notices a strange word which he has not come upon beforehand or the like of which he has not already read. For he will perceive such a word only after inspecting its letters one by one and discerning their meanings; then he will perceive the meaning of the word."
Ibn al-Haytham's psychology may have also possibly been influenced by Buddhist philosophy, echoes of which can be in some of his views on pain and sensation. He writes that every sensation is a form of 'suffering' and that what people call pain is only an exaggerated perception; that there is no qualitative difference but only a quantitative difference between pain and ordinary sensation.
He also came up with a theory to explain the Moon illusion, which played an important role in the scientific tradition of medieval Europe and for which there is still no universally accepted explanation. It was an attempt to the solve the problem of the Moon appearing larger near the horizon than it does while higher up in the sky. Arguing against Ptolemy's refraction theory, he redefined the problem in terms of perceived, rather than real, enlargement. He said that judging the distance of an object depends on there being an uninterrupted sequence of intervening bodies in between the object and the observer. With the Moon however, there are no intervening objects. Therefore, since the size of an object depends on its observed distance, which is in this case inaccurate, the Moon appears larger on the horizon. Through works by Roger Bacon, John Pecham and Witelo based on Ibn al-Haytham's explanation, the Moon illusion gradually came to be accepted as a psychological phenomenon, with Ptolemy's theory being rejected in the 17th century.
Ibn al-Haytham attributed his experimental scientific method and scientific skepticism to his Islamic faith. He believed that human beings are inherently flawed and that only God is perfect. He reasoned that to discover the truth about nature, it is necessary to eliminate human opinion and error, and allow the universe to speak for itself.
Ibn al-Haytham described his search for truth and knowledge as a way of leading him closer to God:
- Sabra, A. I., ed. (1983), The Optics of Ibn al-Haytham, Books I-II-III: On Direct Vision. The Arabic text, edited and with Introduction, Arabic-Latin Glossaries and Concordance Tables, Kuwait: National Council for Culture, Arts and Letters
- Sabra, A. I., ed. (2002), The Optics of Ibn al-Haytham. Edition of the Arabic Text of Books IV-V: On Reflection and Images Seen by Reflection. 2 vols., Kuwait: The National Council for Culture, Arts and Letters
- Sabra, A. I., trans. (1989), The Optics of Ibn al-Haytham. Books I-II-III: On Direct Vision. English Translation and Commentary. 2 vols., Studies of the Warburg Institute, vol. 40, London: The Warburg Institute, University of London, ISBN 0-85481-072-2
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- ↑ 1.0 1.1 1.2 R. L. Verma (1969). Al-Hazen: father of modern optics.
- ↑ 2.0 2.1 2.2 2.3 Rosanna Gorini (2003). "Al-Haytham the Man of Experience. First Steps in the Science of Vision", International Society for the History of Islamic Medicine. Institute of Neurosciences, Laboratory of Psychobiology and Psychopharmacology, Rome, Italy.
- ↑ 3.0 3.1 Rüdiger Thiele (2005). "In Memoriam: Matthias Schramm", Arabic Sciences and Philosophy 15, p. 329–331. Cambridge University Press.
- ↑ Bradley Steffens (2006), Ibn al-Haytham: First Scientist, Morgan Reynolds Publishing, ISBN 1599350246 (cf. Reviews of Ibn al-Haytham: First Scientist, The Critics, Barnes & Noble)
- ↑ 5.0 5.1 H. Salih, M. Al-Amri, M. El Gomati (2005). "The Miracle of Light", A World of Science 3 (3). UNESCO.
- ↑ 6.0 6.1 Sabra, A. I.; Hogendijk, J. P. (2003), The Enterprise of Science in Islam: New Perspectives, MIT Press, pp. 85–118, ISBN 0262194821
- ↑ 7.0 7.1 Hatfield, Gary (1996), "Was the Scientific Revolution Really a Revolution in Science?", in Ragep, F. J.; Ragep, Sally P.; Livesey, Steven John, Tradition, Transmission, Transformation: Proceedings of Two Conferences on Pre-modern Science held at the University of Oklahoma, Brill Publishers, p. 500, ISBN 9004091262
- ↑ Simon, Gérard (2006), "The Gaze in Ibn al-Haytham", The Medieval History Journal 9 (1): 89–98, Error: Bad DOI specified
- ↑ Bellosta, Hélèna (2002), "Burning Instruments: From Diocles to Ibn Sahl", Arabic Sciences and Philosophy (Cambridge University Press) 12: 285–303, Error: Bad DOI specified
- ↑ Rashed, Roshdi (2 August 2002), "Portraits of Science: A Polymath in the 10th Century", Science 297 (5582): 773, Error: Bad DOI specified
- ↑ Lindberg, David C. (1967), "Alhazen's Theory of Vision and Its Reception in the West", Isis 58 (3): 321–341 , Error: Bad DOI specified
- ↑ Bala, Arun, The Dialogue of Civilizations in the Birth of Modern Science, Palgrave Macmillan
- ↑ Dijksterhuis, Fokko Jan (2004), Lenses and Waves: Christiaan Huygens and the Mathematical Science of Optics in the Seventeenth Century, Springer, pp. 113–5, ISBN 1402026978: "Through the influential work of Alhacen the onset of a physico-mathematical conception of optics was established at a much earlier time than would be the case in the other mathematical sciences."
- ↑ 14.00 14.01 14.02 14.03 14.04 14.05 14.06 14.07 14.08 14.09 14.10 14.11 14.12 Bradley Steffens (2006), Ibn al-Haytham: First Scientist, Chapter Five, Morgan Reynolds Publishing, ISBN 1599350246
- ↑ 15.0 15.1 15.2 15.3 15.4 Omar Khaleefa (Summer 1999). "Who Is the Founder of Psychophysics and Experimental Psychology?", American Journal of Islamic Social Sciences 16 (2).
- ↑ 16.0 16.1 16.2 Nicholas J. Wade, Stanley Finger (2001), "The eye as an optical instrument: from camera obscura to Helmholtz's perspective", Perception 30 (10), p. 1157-1177.
- ↑ Bashar Saad, Hassan Azaizeh, Omar Said (October 2005). "Tradition and Perspectives of Arab Herbal Medicine: A Review", Evidence-based Complementary and Alternative Medicine 2 (4), p. 475-479 . Oxford University Press.
- ↑ D. C. Lindberg, Theories of Vision from al-Kindi to Kepler, (Chicago, Univ. of Chicago Pr., 1976), pp. 60-7.
- ↑ Toomer, G. J. (December 1964), "Review: Ibn al-Haythams Weg zur Physik by Matthias Schramm", Isis 55 (4): 463–465, Error: Bad DOI specified
- ↑ 20.0 20.1 20.2 20.3 20.4 20.5 20.6 Dr. Mahmoud Al Deek. "Ibn Al-Haitham: Master of Optics, Mathematics, Physics and Medicine, Al Shindagah, November-December 2004.
- ↑ Albrecht Heeffer. Kepler’s near discovery of the sine law: A qualitative computational model, Ghent University, Belgium.
- ↑ A. I. Sabra (1981), Theories of Light from Descartes to Newton, Cambridge University Press. (cf. Pavlos Mihas, Use of History in Developing ideas of refraction, lenses and rainbow, p. 5, Demokritus University, Thrace, Greece.)
- ↑ K. B. Wolf, "Geometry and dynamics in refracting systems", European Journal of Physics 16, p. 14-20, 1995.
- ↑ R. Rashed, "A pioneer in anaclastics: Ibn Sahl on burning mirrors and lenses", Isis 81, p. 464–491, 1990.
- ↑ 25.0 25.1 25.2 25.3 O'Connor, John J.; Robertson, Edmund F., "Abu Ali al-Hasan ibn al-Haytham", MacTutor History of Mathematics archive, University of St Andrews, http://www-history.mcs.st-andrews.ac.uk/Biographies/Al-Haytham.html.
- ↑ MacKay, R. J.; Oldford, R. W. (August 2000), "Scientific Method, Statistical Method and the Speed of Light", Statistical Science 15 (3): 254–78
- ↑ 27.0 27.1 27.2 Sami Hamarneh (March 1972). Review of Hakim Mohammed Said, Ibn al-Haitham, Isis 63 (1), p. 119.
- ↑ 28.0 28.1 Rashed, Roshdi (2007), "The Celestial Kinematics of Ibn al-Haytham", Arabic Sciences and Philosophy (Cambridge University Press) 17: 7–55 , Error: Bad DOI specified: "In reforming optics he as it were adopted ‘‘positivism’’ (before the term was invented): we do not go beyond experience, and we cannot be content to use pure concepts in investigating natural phenomena. Understanding of these cannot be acquired without mathematics. Thus, once he has assumed light is a material substance, Ibn al-Haytham does not discuss its nature further, but confines himself to considering its propagation and diffusion. In his optics ‘‘the smallest parts of light’’, as he calls them, retain only properties that can be treated by geometry and verified by experiment; they lack all sensible qualities except energy."
- ↑ J. J. O'Connor and E. F. Robertson (2002). Light through the ages: Ancient Greece to Maxwell, MacTutor History of Mathematics archive.
- ↑ Hamid-Eddine Bouali, Mourad Zghal, Zohra Ben Lakhdar (2005). "Popularisation of Optical Phenomena: Establishing the First Ibn Al-Haytham Workshop on Photography" (PDF). The Education and Training in Optics and Photonics Conference. Retrieved on 2008-07-08.
- ↑ Frisinger, H. Howard (March 1973), "Aristotle's Legacy in Meteorology", Bulletin of the American Meteorological Society 3 (3): 198–204 
- ↑ Huff, Toby (2007), The Rise of Early Modern Science, Cambridge University Press, p. 216, ISBN 0521529948
- ↑ 33.0 33.1 33.2 Kriss, Timothy C.; Kriss, Vesna Martich (April 1998), "History of the Operating Microscope: From Magnifying Glass to Microneurosurgery", Neurosurgery 42 (4): 899–907, Error: Bad DOI specified
- ↑ King, Henry C. (2003), The History of the Telescope, Courier Dover Publications, p. 25, ISBN 0486432653
- ↑ (Rashed 2002, p. 773):
"His work on optics, which includes a theory of vision and a theory of light, is considered by many to be his most important contribution, setting the scene for developments well into the 17th century. His contributions to geometry and number theory go well beyond the archimedean tradition. And by promoting the use of experiments in scientific research, al-Haytham played an important part in setting the scene for modern science."
- ↑ 36.0 36.1 Bradley Steffens (2006), Ibn al-Haytham: First Scientist, Morgan Reynolds Publishing, ISBN 1599350246. (cf. Bradley Steffens, "Who Was the First Scientist?", Ezine Articles.)
- ↑ Nader El-Bizri, "A Philosophical Perspective on Alhazen’s Optics," Arabic Sciences and Philosophy, Vol. 15, Issue 2 (2005), pp. 189-218 (Cambridge University Press)
- ↑ Nader El-Bizri, "Ibn al-Haytham," in Medieval Science, Technology, and Medicine: An Encyclopedia, eds. Thomas F. Glick, Steven J. Livesey, and Faith Wallis (New York — London: Routledge, 2005), pp. 237-240.
- ↑ Alhazen (Ibn Al-Haytham) Critique of Ptolemy, translated by S. Pines, Actes X Congrès internationale d'histoire des sciences, Vol I Ithaca 1962, as referenced on p.139 of Shmuel Sambursky (ed. 1974) Physical Thought from the Presocratics to the Quantum Physicists ISBN 0-87663-712-8
- ↑ Alhazen, translated into English from German by M. Schwarz, from "Abhandlung über das Licht", J. Baarmann (ed. 1882) Zeitschrift der Deutschen Morgenländischen Gesellschaft Vol 36 as referenced on p.136 by Shmuel Sambursky (1974) Physical thought from the Presocratics to the Quantum Physicists ISBN 0-87663-712-8
- ↑ p.136, as quoted by Shmuel Sambursky (1974) Physical thought from the Presocratics to the Quantum Physicists ISBN 0-87663-712-8
- ↑ Rashed, Roshdi; Armstrong, Angela (1994), The Development of Arabic Mathematics, Springer, pp. 345–6, ISBN 0792325656
- ↑ Huff, Toby (2007), The Rise of Early Modern Science, Cambridge University Press, p. 91, ISBN 0521529948
- ↑ 44.0 44.1 Plott, C. (2000), Global History of Philosophy: The Period of Scholasticism, Motilal Banarsidass, p. 462, ISBN 8120805518
- ↑ 45.0 45.1 Alhazen; Smith, A. Mark (2001), Alhacen's Theory of Visual Perception: A Critical Edition, with English Translation and Commentary of the First Three Books of Alhacen's De Aspectibus, the Medieval Latin Version of Ibn al-Haytham's Kitab al-Manazir, DIANE Publishing, pp. 372 & 408, ISBN 0871699141
- ↑ A. C. Crombie, Robert Grosseteste and the Origins of Experimental Science, 1100 - 1700, (Oxford: Clarendon Press, 1971), p. 147, n. 2.
- ↑ 47.0 47.1 A. Mark Smith (2001), "The Latin Source of the Fourteenth-Century Italian Translation of Alhacen's De aspectibus (Vat. Lat. 4595)", Arabic Sciences and Philosophy: A Historical Journal (Cambridge University Press) 11: 27-43 
- ↑ Smith, A Mark (2001). Alhacen's theory of visual perception: a critical edition, with English translation and commentary, of the first three books of Alhacen's De aspectibus, the medieval Latin version of Ibn al-Haytham's Kitab al-Manazir. Vol 1. Philadelphia: American Philosophical Society, xxi. ISBN 9780871699145. .
- ↑ 49.0 49.1 Marshall, Peter (September 1981), "Nicole Oresme on the Nature, Reflection, and Speed of Light", Isis 72 (3): 357–374 [367–74], Error: Bad DOI specified
- ↑ 50.0 50.1 50.2 Richard Powers (University of Illinois), Best Idea; Eyes Wide Open, New York Times, April 18, 1999.
- ↑ Falco, Charles M. (12–15 February 2007), Ibn al-Haytham and the Origins of Modern Image Analysis, International Conference on Information Sciences, Signal Processing and its Applications
- ↑ R. S. Elliott (1966). Electromagnetics, Chapter 1. McGraw-Hill.
- ↑ Dr. A. Zahoor and Dr. Z. Haq (1997), Quotations from Famous Historians of Science
- ↑ Thiele, Rüdiger (August 2005), "In Memoriam: Matthias Schramm, 1928–2005", Historia Mathematica 32 (3): 271–274, Error: Bad DOI specified
- ↑ Alhazen; Smith, A. Mark (2001), Alhacen's Theory of Visual Perception: A Critical Edition, with English Translation and Commentary of the First Three Books of Alhacen's De Aspectibus, the Medieval Latin Version of Ibn al-Haytham's Kitab al-Manazir, DIANE Publishing, pp. 343–6, ISBN 0871699141
- ↑ G. A. Russell, "Emergence of Physiological Optics", pp. 686-7, in Morelon, Régis; Rashed, Roshdi (1996), Encyclopedia of the History of Arabic Science, 2, Routledge, ISBN 0415124107
- ↑ Bradley Steffens (2006), Ibn al-Haytham: First Scientist, Morgan Reynolds Publishing, ISBN 1599350246
- ↑ A. I. Sabra (1989), Ibn al-Haytham, The Optics of Ibn al-Haytham, London: The Warburg Institute, vol. I, pp. 90-91
- ↑ Lauginie, Pierre (July 2005). "Measuring: Why? How? What?" (PDF). Eighth International History, Philosophy, Sociology & Science Teaching Conference. Retrieved on 2008-07-18.
- ↑ Dr. Nader El-Bizri, "Ibn al-Haytham or Alhazen", in Josef W. Meri (2006), Medieval Islamic Civilization: An Encyclopaedia, Vol. II, p. 343-345, Routledge, New York, London.
- ↑ Vernon O. Georgia (2003). A History of the Muslim World to 1405: The Making of a Civilization, p. 200. Prentice Hall. ISBN 0-13-098389-6.
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- ↑ Topdemir, Hüseyin Gazi (2007), "Kamal Al-Din Al-Farisi’s Explanation of the Rainbow" (PDF), Humanity & Social Sciences Journal 2 (1): 75–85 , http://www.idosi.org/hssj/hssj2(1)07/10.pdf, retrieved 2008-09-16
- ↑ Weisstein, Eric. "Alhazen's Billiard Problem". Mathworld. Retrieved on 2008-09-24.
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- ↑ Falco, Charles M. "Ibn al-Haytham and the Origins of Modern Image Analysis", presented at a plenary session at the International Conference on Information Sciences, Signal Processing and its Applications, 12–15 February 2007. Sharjah, United Arab Emirates (U.A.E.). 
- ↑ Covington, Richard (May-June 2007), "Rediscovering Arabic Science", Saudi Aramco World: 2–16, http://www.saudiaramcoworld.com/issue/200703/rediscovering.arabic.science.htm, retrieved 2008-01-23
- ↑ Gul A. Russell, "Emergence of Physiological Optics", p. 695, in Morelon, Régis; Rashed, Roshdi (1996), Encyclopedia of the History of Arabic Science, 2, Routledge, ISBN 0415124107
- ↑ Dr Valérie Gonzalez, "Universality and Modernity", The Ismaili United Kingdom, December 2002, p. 50-53.
- ↑ André Authier (2013). "3: The Dual Nature of Light", Early Days of X-ray Crystallography. Oxford University Press, 23. ISBN 9780191635014. “Tables of angles of incidence and refraction were given by the famous Arab mathematician and physicist Alhazen, considered as the 'father of modern optics' and ophthalmology.”
- ↑ Steffens (cf. Review by Sulaiman Awan)
- ↑ Bashar Saad, Hassan Azaizeh, Omar Said (October 2005). "Tradition and Perspectives of Arab Herbal Medicine: A Review", Evidence-based Complementary and Alternative Medicine 2 (4), p. 475-479 . Oxford University Press
- ↑ 78.0 78.1 Ian P. Howard (1996). "Alhazen's neglected discoveries of visual phenomena". Perception 25 (10): 1203–1217. doi:10.1068/p251203.
- ↑ 79.0 79.1 Gul A. Russell, "Emergence of Physiological Optics", p. 689, in Morelon, Régis; Rashed, Roshdi (1996), Encyclopedia of the History of Arabic Science, 2, Routledge, ISBN 0415124107
- ↑ Gul A. Russell, "Emergence of Physiological Optics", pp. 689-90, in Morelon, Régis; Rashed, Roshdi (1996), Encyclopedia of the History of Arabic Science, 2, Routledge, ISBN 0415124107
- ↑ Gul A. Russell, "Emergence of Physiological Optics", p. 690, in Morelon, Régis; Rashed, Roshdi (1996), Encyclopedia of the History of Arabic Science, 2, Routledge, ISBN 0415124107
- ↑ Gul A. Russell, "Emergence of Physiological Optics", p. 692, in Morelon, Régis; Rashed, Roshdi (1996), Encyclopedia of the History of Arabic Science, 2, Routledge, ISBN 0415124107
- ↑ Gul A. Russell, "Emergence of Physiological Optics", p. 691, in Morelon, Régis; Rashed, Roshdi (1996), Encyclopedia of the History of Arabic Science, 2, Routledge, ISBN 0415124107
- ↑ Gul A. Russell, "Emergence of Physiological Optics", pp. 695-8, in Morelon, Régis; Rashed, Roshdi (1996), Encyclopedia of the History of Arabic Science, 2, Routledge, ISBN 0415124107
- ↑ 85.0 85.1 N. J. Wade (1998). A Natural History of Vision. Cambridge, MA: MIT Press.
- ↑ Lutz, Peter L. (2002), The Rise of Experimental Biology: An Illustrated History, Humana Press, p. 60, ISBN 0896038351
- ↑ Ian P. Howard & N. J. Wade (1996). "Ptolemy's contributions to the geometry of binocular vision". Perception 25 (10): 1189–201. doi:10.1068/p251189.
- ↑ Aaen-Stockdale, Craig (2008), "Ibn al-Haytham and psychophysics", Perception 37 (4): 636–638, Error: Bad DOI specified
- ↑ Kennedy, Alan; Radach, R.; Heller, D.; Pynte, J. (2000), Reading as a Perceptual Process, Elsevier, p. ii, ISBN 0080436420
- ↑ Hershenson, Maurice (1989), The Moon Illusion, Lawrence Erlbaum Associates, pp. 9–10, ISBN 0805801219, http://books.google.co.uk/books?id=x1qcL4CTwlIC, retrieved 2008-09-22
- ↑ C. Plott (2000), Global History of Philosophy: The Period of Scholasticism, Pt. II, p. 465. ISBN 8120805518, Motilal Banarsidass Publ.
- History of optics
- History of physics
- History of science
- History of scientific method
- Physics in medieval Islam
- Science in medieval Islam
- Scientific method