“Ibn al-Haytham”的意思、由来-开放百科全书

Ibn al-Haytham was the first to explain that vision occurs when light bounces on an object and then is directed to one's eyes.^[22] And he was the first to point out that vision occurs in the brain, rather than in the eyes.^[23] He was also an early proponent of the concept that a hypothesis must be proved by experiments based on confirmable procedures or mathematical evidence—hence understanding the scientific method five centuries before Renaissance scientists.^[24]^[25]^[26]^[27]^[28]^[29]

Born in Basra, he spent most of his productive period in the Fatimid capital of Cairo and earned his living authoring various treatises and tutoring members of the nobilities.^[30] Ibn al-Haytham is sometimes given the byname al-Baṣrī after his birthplace,^[31] or al-Miṣrī ("of Egypt").^[32]^[33] Ibn al-Haytham was nicknamed the "Second Ptolemy" by Abu'l-Hasan Bayhaqi^[34]^[35], and the "The Physicist" by John Peckham.^[36] Ibn al-Haytham paved the way for the modern science of physical optics.^[37]

Biography

Ibn al-Haytham (Alhazen) was born c. 965 to an Arab^[17]^[13] family in Basra, Iraq,

He held a position with the title vizier in his native Basra, and made a name for himself for his knowledge of applied mathematics.

As he claimed to be able to regulate the flooding of the Nile, he was invited to by Fatimid Caliph al-Hakim in order to realise a hydraulic project at Aswan. However, Ibn al-Haytham was forced to concede the impracticability of his project.^[38]

Upon his return to Cairo, he was given an administrative post. After he proved unable to fulfill this task as well, he contracted the ire of the caliph Al-Hakim bi-Amr Allah,^[39] and is said to have been forced into hiding until the caliph's death in 1021, after which his confiscated possessions were returned to him.^[40]

Legend has it that Alhazen feigned madness and was kept under house arrest during this period.^[41] During this time, he wrote his influential Book of Optics.

Alhazen continued to live in Cairo, in the neighborhood of the famous University of al-Azhar, and lived from the proceeds of his literary production^[42] until his death in c. 1040.^[38] (A copy of Apollonius' Conics, written in Ibn al-Haytham's own handwriting exists in Aya Sofya: (MS Aya Sofya 2762, 307 fob., dated Safar 415 a.h. [1024]).)^[35]{{rp|Note 2}}

Among his students were Sorkhab (Sohrab), a Persian from Semnan, and Abu al-Wafa Mubashir ibn Fatek, an Egyptian prince.^[43]

Book of Optics

Alhazen's most famous work is his seven-volume treatise on optics Kitab al-Manazir (Book of Optics), written from 1011 to 1021.^[44]

Theory of optics

Two major theories on vision prevailed in classical antiquity. 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. Previous Islamic writers (such as al-Kindi) had argued essentially on Euclidean, Galenist, or Aristotelian lines. The strongest influence on the Book of Optics was from Ptolemy's Optics, while the description of the anatomy and physiology of the eye was based on Galen's account.^[49] Alhazen's achievement was to come up with a theory that successfully combined parts of the mathematical ray arguments of Euclid, the medical tradition of Galen, and the intromission theories of Aristotle. Alhazen's intromission theory followed al-Kindi (and broke with Aristotle) in asserting that "from each point of every colored body, illuminated by any light, issue light and color along every straight line that can be drawn from that point".^[50] This however left him with the problem of explaining how a coherent image was formed from many independent sources of radiation; in particular, every point of an object would send rays to every point on the eye. What Alhazen needed was for each point on an object to correspond to one point only on the eye.^[50] He attempted to resolve this by asserting that the eye would only perceive perpendicular rays from the object—for any one point on the eye, only the ray that reached it directly, without being refracted by any other part of the eye, would be perceived. He argued, using a physical analogy, that perpendicular rays were stronger than oblique rays: in the same way that a ball thrown directly at a board might break the board, whereas a ball thrown obliquely at the board would glance off, perpendicular rays were stronger than refracted rays, and it was only perpendicular rays which were perceived by the eye. As there was only one perpendicular ray that would enter the eye at any one point, and all these rays would converge on the centre of the eye in a cone, this allowed him to resolve the problem of each point on an object sending many rays to the eye; if only the perpendicular ray mattered, then he had a one-to-one correspondence and the confusion could be resolved.^[51] He later asserted (in book seven of the Optics) that other rays would be refracted through the eye and perceived as if perpendicular.^[52]

His arguments regarding perpendicular rays do not clearly explain why only perpendicular rays were perceived; why would the weaker oblique rays not be perceived more weakly?^[53] His later argument that refracted rays would be perceived as if perpendicular does not seem persuasive.^[54] However, despite its weaknesses, no other theory of the time was so comprehensive, and it was enormously influential, particularly in Western Europe. Directly or indirectly, his De Aspectibus (Book of Optics) inspired much activity in optics between the 13th and 17th centuries.^[55] Kepler's later theory of the retinal image (which resolved the problem of the correspondence of points on an object and points in the eye) built directly on the conceptual framework of Alhazen.^[55]

Alhazen showed through experiment that light travels in straight lines, and carried out various experiments with lenses, mirrors, refraction, and reflection.^[56] His analyses of reflection and refraction considered the vertical and horizontal components of light rays separately.^[57]

The camera obscura was known to the ancient Chinese, and was described by the Han Chinese polymathic genius Shen Kuo in his scientific book Dream Pool Essays, published in the year 1088 C.E. Aristotle had discussed the basic principle behind it in his Problems, but Alhazen's work also contained the first clear description, outside of China, of camera obscura in the areas of the middle east, Europe, Africa and India.^[58] and early analysis^[59] of the device.

Alhazen utilized his species of camera obscura to observe the eclipse. In his essay "On the Form of the Eclipse" he writes that he observed the sickle-like shape of the sun at the time of an eclipse. The introduction to his essay reads as follows: 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 moonsickle. His findings solidified the importance in the history of the camera obscura.^[60]

Alhazen studied the process of sight, the structure of the eye, image formation in the eye, and the visual system. Ian P. Howard argued in a 1996 Perception article that Alhazen should be credited with many discoveries and theories previously attributed to Western Europeans writing centuries later. For example, he described what became in the 19th century Hering's law of equal innervation. He wrote a description of vertical horopters 600 years before Aguilonius that is actually closer to the modern definition than Aguilonius's—and his work on binocular disparity was repeated by Panum in 1858.^[61] Craig Aaen-Stockdale, while agreeing that Alhazen should be credited with many advances, has expressed some caution, especially when considering Alhazen in isolation from Ptolemy, with whom Alhazen was extremely familiar. Alhazen corrected a significant error of Ptolemy regarding binocular vision, but otherwise his account is very similar; Ptolemy also attempted to explain what is now called Hering's law.^[62] In general, Alhazen built on and expanded the optics of Ptolemy.^[63] In a more detailed account of Ibn al-Haytham's contribution to the study of binocular vision based on Lejeune^[64] and Sabra,^[65] Raynaud^[66] showed that the concepts of correspondence, homonymous and crossed diplopia were in place in Ibn al-Haytham's optics. But contrary to Howard, he explained why Ibn al-Haytham did not give the circular figure of the horopter and why, by reasoning experimentally, he was in fact closer to the discovery of Panum's fusional area than that of the Vieth-Müller circle. In this regard, Ibn al-Haytham's theory of binocular vision faced two main limits: the lack of recognition of the role of the retina, and obviously the lack of an experimental investigation of ocular tracts.

Alhazen's most original contribution was that, after describing how he thought the eye was anatomically constructed, he went on to consider how this anatomy would behave functionally as an optical system.^[67] His understanding of pinhole projection from his experiments appears to have influenced his consideration of image inversion in the eye,^[68] which he sought to avoid.^[69] He maintained that the rays that fell perpendicularly on the lens (or glacial humor as he called it) were further refracted outward as they left the glacial humor and the resulting image thus passed upright into the optic nerve at the back of the eye.^[70] He followed Galen in believing that the lens was the receptive organ of sight, although some of his work hints that he thought the retina was also involved.^[71]

Alhazen's synthesis of light and vision adhered to the Aristotelian scheme, exhaustively describing the process of vision in a logical, complete fashion.^[72]

Scientific method

An aspect associated with Alhazen's optical research is related to systemic and methodological reliance on experimentation (i'tibar)(Arabic: إعتبار) 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). This mathematical-physical approach to experimental science supported most of his propositions in Kitab al-Manazir (The Optics; De aspectibus or Perspectivae)^[73] and grounded his theories of vision, light and colour, as well as his research in catoptrics and dioptrics (the study of the reflection and refraction of light, respectively).^[74]

According to Matthias Schramm,^[75] Alhazen "was the first to make a systematic use of the method of varying the experimental conditions in a constant and uniform manner, in an experiment showing that the intensity of the light-spot formed by the projection of the moonlight through two small apertures onto a screen diminishes constantly as one of the apertures is gradually blocked up."^[76] G. J. Toomer expressed some skepticism regarding Schramm's view,^[77] arguing that caution is needed to avoid reading anachronistically particular passages in Alhazen's very large body of work, because at the time (1964), his Book of Optics had not yet been fully translated from Arabic. While acknowledging Alhazen's importance in developing experimental techniques, Toomer argued that Alhazen should not be considered in isolation from other Islamic and ancient thinkers.^[77] Toomer does concede that "Schramm sums up [Alhazen's] achievement in the development of scientific method."^[78] Toomer 1964 lists, as a precondition, what is needed for historians to investigate Schramm's claim (1963) that Ibn al-Haytham was the true founder of modern physics,^[75] is translations of Ibn al-Haytham.^[79]

Mark Smith recounts Alhazen's elaboration of Ptolemy's experiments in double vision, reflection, and refraction: Alhazen's Optics book influenced the Perspectivists in Europe, Roger Bacon, Witelo, and Peckham. The Optics was incorporated into Risner's 1572 printing of Opticae Thesaurus, through which Kepler^[80] finally resolved the contradictions inherent in Witelo's explanation of the imaging chain, from external object to the retina of the eye.^[81] {{see|scientific method}}

Alhazen's problem

His work on catoptrics in Book V of the Book of Optics contains a discussion of what is now known as Alhazen's problem, first formulated by Ptolemy in 150 AD. 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 player must aim a cue ball at a given point to make it bounce off the table edge 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 where the light will be reflected to the eye of an observer." This leads to an equation of the fourth degree.^[82] This eventually led Alhazen to derive a formula for the sum of fourth powers, where previously only the formulas for the sums of squares and cubes had been stated. His method can be readily generalized to find the formula for the sum of any integral powers, although he did not himself do this (perhaps because he only needed the fourth power to calculate the volume of the paraboloid he was interested in). He used his result on sums of integral powers to perform what would now be called an integration, where the formulas for the sums of integral squares and fourth powers allowed him to calculate the volume of a paraboloid.^[83] Alhazen eventually solved the problem using conic sections and a geometric proof. His solution was extremely long and complicated and may not have been understood by mathematicians reading him in Latin translation. Later mathematicians used Descartes' analytical methods to analyse the problem,^[84] with a new solution being found in 1997 by the Oxford mathematician Peter M. Neumann.^[85] Recently, Mitsubishi Electric Research Laboratories (MERL) researchers Amit Agrawal, Yuichi Taguchi and Srikumar Ramalingam solved the extension of Alhazen's problem to general rotationally symmetric quadric mirrors including hyperbolic, parabolic and elliptical mirrors.^[86] They showed that the mirror reflection point can be computed by solving an eighth degree equation in the most general case. If the camera (eye) is placed on the axis of the mirror, the degree of the equation reduces to six.^[87] Alhazen's problem can also be extended to multiple refractions from a spherical ball. Given a light source and a spherical ball of certain refractive index, the closest point on the spherical ball where the light is refracted to the eye of the observer can be obtained by solving a tenth degree equation.^[87]

Other contributions

Sudanese psychologist Omar Khaleefa has argued that Alhazen should be considered the founder of experimental psychology, for his pioneering work on the psychology of visual perception and optical illusions.^[90] Khaleefa has also argued that Alhazen should also be considered the "founder of psychophysics", a sub-discipline and precursor to modern psychology.^[90] Although Alhazen made many subjective reports regarding vision, there is no evidence that he used quantitative psychophysical techniques and the claim has been rebuffed.^[91]

Alhazen offered an explanation of the Moon illusion, an illusion that played an important role in the scientific tradition of medieval Europe.^[92] Many authors repeated explanations that attempted to solve the problem of the Moon appearing larger near the horizon than it does when higher up in the sky. Alhazen argued against Ptolemy's refraction theory, and defined 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 between the object and the observer. When the Moon is high in the sky there are no intervening objects, so the Moon appears close. The perceived size of an object of constant angular size varies with its perceived distance. Therefore, the Moon appears closer and smaller high in the sky, and further and larger on the horizon. Through works by Roger Bacon, John Pecham and Witelo based on Alhazen's explanation, the Moon illusion gradually came to be accepted as a psychological phenomenon, with the refraction theory being rejected in the 17th century.^[93] Although Alhazen is often credited with the perceived distance explanation, he was not the first author to offer it. Cleomedes ({{circa}} 2nd century) gave this account (in addition to refraction), and he credited it to Posidonius ({{circa}} 135–50 BC).^[94] Ptolemy may also have offered this explanation in his Optics, but the text is obscure.^[95] Alhazen's writings were more widely available in the Middle Ages than those of these earlier authors, and that probably explains why Alhazen received the credit.

Other works on physics

Optical treatises

Besides the Book of Optics, Alhazen wrote several other treatises on the same subject, including his Risala fi l-Daw’ (Treatise on Light). He investigated the properties of luminance, the rainbow, eclipses, twilight, and moonlight. Experiments with mirrors and the refractive interfaces between air, water, and glass cubes, hemispheres, and quarter-spheres provided the foundation for his theories on catoptrics.^[96]

Celestial physics

Alhazen discussed the physics of the celestial region in his Epitome of Astronomy, arguing that Ptolemaic models must be understood in terms of physical objects rather than abstract hypotheses—in other words that it should be possible to create physical models where (for example) none of the celestial bodies would collide with each other. The suggestion of mechanical models for the Earth centred Ptolemaic model "greatly contributed to the eventual triumph of the Ptolemaic system among the Christians of the West". Alhazen's determination to root astronomy in the realm of physical objects was important, however, because it meant astronomical hypotheses "were accountable to the laws of physics", and could be criticised and improved upon in those terms.^[97]

Mechanics

In his work, Alhazen discussed theories on the motion of a body.^[96] In his Treatise on Place, Alhazen disagreed with Aristotle's view that nature abhors a void, and he used geometry in an attempt to demonstrate that place (al-makan) is the imagined three-dimensional void between the inner surfaces of a containing body.^[98]

Astronomical works

On the Configuration of the World

In his On the Configuration of the World Alhazen presented a detailed description of the physical structure of the earth:{{quote|The earth as a whole is a round sphere whose center is the center of the world. It is stationary in its [the world's] middle, fixed in it and not moving in any direction nor moving with any of the varieties of motion, but always at rest.^[99]}}

The book is a non-technical explanation of Ptolemy's Almagest, which was eventually translated into Hebrew and Latin in the 13th and 14th centuries and subsequently had an influence on astronomers such as Georg von Peuerbach^[100] during the European Middle Ages and Renaissance.^[101]

Doubts Concerning Ptolemy

In his Al-Shukūk ‛alā Batlamyūs, variously translated as Doubts Concerning Ptolemy or Aporias against Ptolemy, published at some time between 1025 and 1028, Alhazen criticized Ptolemy's Almagest, Planetary Hypotheses, and Optics, pointing out various contradictions he found in these works, particularly in astronomy. Ptolemy's Almagest concerned mathematical theories regarding the motion of the planets, whereas the Hypotheses concerned what Ptolemy thought was the actual configuration of the planets. Ptolemy himself acknowledged that his theories and configurations did not always agree with each other, arguing that this was not a problem provided it did not result in noticeable error, but Alhazen was particularly scathing in his criticism of the inherent contradictions in Ptolemy's works.^[102] He considered that some of the mathematical devices Ptolemy introduced into astronomy, especially the equant, failed to satisfy the physical requirement of uniform circular motion, and noted the absurdity of relating actual physical motions to imaginary mathematical points, lines and circles:^[103]

Having pointed out the problems, Alhazen appears to have intended to resolve the contradictions he pointed out in Ptolemy in a later work. Alhazen believed there was a "true configuration" of the planets that Ptolemy had failed to grasp. He intended to complete and repair Ptolemy's system, not to replace it completely.^[102] In the Doubts Concerning Ptolemy Alhazen set out his views on the difficulty of attaining scientific knowledge and the need to question existing authorities and theories:

He held that the criticism of existing theories—which dominated this book—holds a special place in the growth of scientific knowledge.

Model of the Motions of Each of the Seven Planets

Alhazen's The Model of the Motions of Each of the Seven Planets was written {{circa}} 1038. Only one damaged manuscript has been found, with only the introduction and the first section, on the theory of planetary motion, surviving. (There was also a second section on astronomical calculation, and a third section, on astronomical instruments.) Following on from his Doubts on Ptolemy, Alhazen described a new, geometry-based planetary model, describing the motions of the planets in terms of spherical geometry, infinitesimal geometry and trigonometry. He kept a geocentric universe and assumed that celestial motions are uniformly circular, which required the inclusion of epicycles to explain observed motion, but he managed to eliminate Ptolemy's equant. In general, his model didn't try to provide a causal explanation of the motions, but concentrated on providing a complete, geometric description that could explain observed motions without the contradictions inherent in Ptolemy's model.^[105]

Other astronomical works

Alhazen wrote a total of twenty-five astronomical works, some concerning technical issues such as Exact Determination of the Meridian, a second group concerning accurate astronomical observation, a third group concerning various astronomical problems and questions such as the location of the Milky Way; Alhazen argued for a distant location, based on the fact that it does not move in relation to the fixed stars.^[106] The fourth group consists of ten works on astronomical theory, including the Doubts and Model of the Motions discussed above.^[107]

Mathematical works

In mathematics, Alhazen built on the mathematical works of Euclid and Thabit ibn Qurra and worked on "the beginnings of the link between algebra and geometry".^[108]

He developed a formula for summing the first 100 natural numbers, using a geometric proof to prove the formula.^[109]

Geometry

Alhazen explored what is now known as the Euclidean parallel postulate, the fifth postulate in Euclid's Elements, using a proof by contradiction,^[110] and in effect introducing the concept of motion into geometry.^[111] He formulated the Lambert quadrilateral, which Boris Abramovich Rozenfeld names the "Ibn al-Haytham–Lambert quadrilateral".^[112]

In elementary geometry, Alhazen attempted to solve the problem of squaring the circle using the area of lunes (crescent shapes), but later gave up on the impossible task.^[113] The two lunes formed from a right triangle by erecting a semicircle on each of the triangle's sides, inward for the hypotenuse and outward for the other two sides, are known as the lunes of Alhazen; they have the same total area as the triangle itself.^[114]

Number theory

Alhazen's contributions to number theory include his work on perfect numbers. In his Analysis and Synthesis, he may have been the first to state that every even perfect number is of the form 2ⁿ⁻¹(2ⁿ − 1) where 2ⁿ − 1 is prime, but he was not able to prove this result; Euler later proved it in the 18th century.^[113]

Alhazen solved problems involving congruences using what is now called Wilson's theorem. In his Opuscula, Alhazen considers the solution of a system of congruences, and gives two general methods of solution. His first method, the canonical method, involved Wilson's theorem, while his second method involved a version of the Chinese remainder theorem.^[113]

Calculus

Alhazen discovered the sum formula for the fourth power, using a method that could be generally used to determine the sum for any integral power. He used this to find the volume of a paraboloid. He could find the integral formula for any polynomial without having developed a general formula.^[115]

Other works

Influence of Melodies on the Souls of Animals

Alhazen also wrote a Treatise on the Influence of Melodies on the Souls of Animals, although no copies have survived. It appears to have been concerned with the question of whether animals could react to music, for example whether a camel would increase or decrease its pace.

Engineering

In engineering, one account of his career as a civil engineer has him summoned to Egypt by the Fatimid Caliph, Al-Hakim bi-Amr Allah, to regulate the flooding of the Nile River. He carried out a detailed scientific study of the annual inundation of the Nile River, and he drew plans for building a dam, at the site of the modern-day Aswan Dam. His field work, however, later made him aware of the impracticality of this scheme, and he soon feigned madness so he could avoid punishment from the Caliph.^[116]

Philosophy

In his Treatise on Place, Alhazen disagreed with Aristotle's view that nature abhors a void, and he used geometry in an attempt to demonstrate that place (al-makan) is the imagined three-dimensional void between the inner surfaces of a containing body.^[98] Abd-el-latif, a supporter of Aristotle's philosophical view of place, later criticized the work in Fi al-Radd ‘ala Ibn al-Haytham fi al-makan (A refutation of Ibn al-Haytham’s place) for its geometrization of place.^[98]

Alhazen also discussed space perception and its epistemological implications in his Book of Optics. In "tying the visual perception of space to prior bodily experience, Alhazen unequivocally rejected the intuitiveness of spatial perception and, therefore, the autonomy of vision. Without tangible notions of distance and size for

Theology

Alhazen was a Muslim; it is not certain to which school of Islam he belonged. As a Sunni, he may have been either a follower of the Ash'ari school,^[118] or a follower of the Mu'tazili school.^[119]

Sabra (1978) even suggested he might have been an adherent of Shia Islam.^[120]{{Request quotation|date=June 2009}}

Alhazen wrote a work on Islamic theology in which he discussed prophethood and developed a system of philosophical criteria to discern its false claimants in his time.^[121]

He also wrote a treatise entitled Finding the Direction of Qibla by Calculation in which he discussed finding the Qibla, where prayers (salat) are directed towards, mathematically.^[122]

There are occasional references to theology or religious sentiment in his technical works, e.g.

Legacy

Alhazen made significant contributions to optics, number theory, geometry, astronomy and natural philosophy. Alhazen's work on optics is credited with contributing a new emphasis on experiment.

His main work, Kitab al-Manazir (Book of Optics), was known in the Muslim world mainly, but not exclusively, through the thirteenth-century commentary by Kamāl al-Dīn al-Fārisī, the Tanqīḥ al-Manāẓir li-dhawī l-abṣār wa l-baṣā'ir.^[126] In al-Andalus, it was used by the eleventh-century prince of the Banu Hud dynasty of Zaragossa and author of an important mathematical text, al-Mu'taman ibn Hūd. A Latin translation of the Kitab al-Manazir was made probably in the late twelfth or early thirteenth century.^[127] This translation was read by and greatly influenced a number of scholars in Christian Europe including: Roger Bacon,^[128] Robert Grosseteste,^[129] Witelo, Giambattista della Porta,^[130] Leonardo Da Vinci,^[131] Galileo Galilei,^[132] Christiaan Huygens,^[133] René Descartes,^[134] and Johannes Kepler.^[135] His research in catoptrics (the study of optical systems using mirrors) centred on spherical and parabolic mirrors and spherical aberration. He made the observation that the ratio between the angle of incidence and refraction does not remain constant, and investigated the magnifying power of a lens. His work on catoptrics also contains the problem known as "Alhazen's problem".^[56] Meanwhile in the Islamic world, Alhazen's work influenced Averroes' writings on optics,^[136] and his legacy was further advanced through the 'reforming' of his Optics by Persian scientist Kamal al-Din al-Farisi (died c. 1320) in the latter's Kitab Tanqih al-Manazir (The Revision of [Ibn al-Haytham's] Optics).^[74] Alhazen wrote as many as 200 books, although only 55 have survived. Some of his treatises on optics survived only through Latin translation. During the Middle Ages his books on cosmology were translated into Latin, Hebrew and other languages.

The impact crater Alhazen on the Moon is named in his honour,^[137] as was the asteroid 59239 Alhazen.^[138] In honour of Alhazen, the Aga Khan University (Pakistan) named its Ophthalmology endowed chair as "The Ibn-e-Haitham Associate Professor and Chief of Ophthalmology".^[139] Alhazen, by the name Ibn al-Haytham, is featured on the obverse of the Iraqi 10,000-dinar banknote issued in 2003,^[140] and on 10-dinar notes from 1982.

The 2015 International Year of Light celebrated the 1000th anniversary of the works on optics by Ibn Al-Haytham.^[141]

Commemorations

In 2014, the "Hiding in the Light" episode of A Spacetime Odyssey, presented by Neil deGrasse Tyson, focused on the accomplishments of Ibn al-Haytham. He was voiced by Alfred Molina in the episode.

Over forty years previously, Jacob Bronowski presented Alhazen's work in a similar television documentary (and the corresponding book), The Ascent of Man. In episode 5 (The Music of the Spheres), Bronowski remarked that in his view, Alhazen was "the one really original scientific mind that Arab culture produced", whose theory of optics was not improved on till the time of Newton and Leibniz.

H. J. J. Winter, a British historian of science, summing up the importance of Ibn al-Haytham in the history of physics wrote:

UNESCO declared 2015 the International Year of Light and its Director-General Irina Bokova dubbed Ibn al-Haytham 'the father of optics'.^[143] Amongst others, this was to celebrate Ibn Al-Haytham's achievements in optics, mathematics and astronomy. An international campaign, created by the 1001 Inventions organisation, titled 1001 Inventions and the World of Ibn Al-Haytham featuring a series of interactive exhibits, workshops and live shows about his work, partnering with science centers, science festivals, museums, and educational institutions, as well as digital and social media platforms.^[144] The campaign also produced and released the short educational film 1001 Inventions and the World of Ibn Al-Haytham.

Criticism

Refraction

List of works

According to medieval biographers, Alhazen wrote more than 200 works on a wide range of subjects, of which at least 96 of his scientific works are known. Most of his works are now lost, but more than 50 of them have survived to some extent. Nearly half of his surviving works are on mathematics, 23 of them are on astronomy, and 14 of them are on optics, with a few on other subjects.^[146] Not all his surviving works have yet been studied, but some of the ones that have are given below.^[147]

Lost works

See also

Notes

1. ^{{Harvnb|Falco|2007}}.
2. ^{{Harvnb|Rosenthal|1960–1961}}.
3. ^{{harv|Smith|2001|p=xvi}}
4. ^Euclid's Optics
5. ^[https://www.jstor.org/stable/233604?seq=1#page_scan_tab_contents Smith, A. Mark (1988) "Ptolemy, Optics" Isis Vol. 79, No. 2 (Jun., 1988), pp. 188-207, via JSTOR]*[https://www.jstor.org/stable/3231951 Smith, A. Mark (1996) Ptolemy's Theory of Visual Perception: An English Translation of the "Optics" with Introduction and Commentary Transactions of the American Philosophical Society 86(2) (1996) via JSTOR]*[https://www.jstor.org/stable/3185879 Smith, A. Mark (1999) Ptolemy and the Foundations of Ancient Mathematical Optics: A Source Based Guided Study Transactions of the American Philosophical Society New Series, 89(3) (1999) via JSTOR]
6. ^{{Cite book|url=https://books.google.co.in/books?id=mhLVHR5QAQkC&printsec=frontcover#v=onepage&q&f=false|title=Ptolemy's Theory of Visual Perception: An English Translation of the Optics|last=A. Mark Smith|publisher=American Philosophical Society|year=1996|isbn=|location=|pages=58}}
7. ^{{Harvnb|O'Connor|Robertson|1999}}.
8. ^{{Harvnb|El-Bizri|2010|p=11}}: "Ibn al-Haytham's groundbreaking studies in optics, including his research in catoptrics and dioptrics (respectively the sciences investigating the principles and instruments pertaining to the reflection and refraction of light), were principally gathered in his monumental opus: Kitåb al-manåóir (The Optics; De Aspectibus or Perspectivae; composed between 1028 CE and 1038 CE)."
9. ^{{Harvnb|Rooney|2012|p=39}}: "As a rigorous experimental physicist, he is sometimes credited with inventing the scientific method."
10. ^{{Harvnb|Baker|2012|p=449}}: "As shown earlier, Ibn al-Haytham was among the first scholars to experiment with animal psychology.
11. ^Also Alhacen, Avennathan, Avenetan (etc.); the identity of "Alhazen" with Ibn al-Haytham al-Basri "was identified towards the end of the 19th century". ({{harvnb|Vernet|1996|p=788}})
12. ^{{cite web|last1=J.|first1=Vernet,|title=Ibn al-Hayt̲h̲am|url=http://referenceworks.brillonline.com/entries/encyclopaedia-of-islam-2/ibn-al-haytham-SIM_3195|website=Encyclopaedia of Islam|language=en}}"Abu ʿAlī al-Ḥasan b. al-Ḥasan b. al-Hayt̲h̲am al-Baṣrī al-Miṣrī , was identified towards the end of the 19th century with the Alhazen , Avennathan and Avenetan of mediaeval Latin texts. He is one of the principal Arab mathematicians and, without any doubt, the best physicist."
13. ^¹{{harvnb|Simon|2006}}
14. ^{{cite web|title=OPTICS – Encyclopaedia Iranica|url=http://www.iranicaonline.org/articles/optics|website=www.iranicaonline.org|language=en}}
15. ^{{cite web|title=Ibn al-Haytham {{!}} Arab astronomer and mathematician|url=https://www.britannica.com/biography/Ibn-al-Haytham|website=Encyclopedia Britannica|language=en}}
16. ^{{cite book|last1=Esposito|first1=John L.|title=The Oxford History of Islam|date=2000|publisher=Oxford University Press|page=192}}: "Ibn al-Haytham (d. 1039), known in the West as Alhazan, was a leading Arab mathematician, astronomer, and physicist. His optical compendium, Kitab al-Manazir, is the greatest medieval work on optics."
17. ^¹For the description of his main fields, see e.g. {{harvnb|Vernet|1996|p=788}} ("He is one of the principal Arab mathematicians and, without any doubt, the best physicist.") {{Harvnb|Sabra|2008}}, {{Harvnb|Kalin|Ayduz|Dagli|2009|p=}} ("Ibn al-Ḥaytam was an eminent eleventh-century Arab optician, geometer, arithmetician, algebraist, astronomer, and engineer."), {{Harvnb|Dallal|1999|p=}} ("Ibn al-Haytham (d. 1039), known in the West as Alhazan, was a leading Arab mathematician, astronomer, and physicist. His optical compendium, Kitab al-Manazir, is the greatest medieval work on optics.")
18. ^{{Cite web|url=https://en.unesco.org/news/international-year-light-ibn-al-haytham-pioneer-modern-optics-celebrated-unesco|title=International Year of Light: Ibn al Haytham, pioneer of modern optics celebrated at UNESCO|website=UNESCO|language=en|access-date=2 June 2018}}
19. ^{{Cite news|url=http://news.bbc.co.uk/2/hi/7810846.stm|title=The 'first true scientist'|date=2009|access-date=2 June 2018|language=en-GB}}
20. ^{{Harvnb|Selin|2008|p=}}: "The three most recognizable Islamic contributors to meteorology were: the Alexandrian mathematician/ astronomer Ibn al-Haytham (Alhazen 965-1039), the Arab-speaking Persian physician Ibn Sina (Avicenna 980-1037), and the Spanish Moorish physician/jurist Ibn Rushd (Averroes; 1126-1198)." He has been dubbed the "father of modern optics" by the UNESCO. {{Cite journal|last=|first=|date=1976|title=Impact of Science on Society|url=https://books.google.co.uk/books?id=4YE3AAAAMAAJ&q=%22Father+of+Modern+Optics%22&dq=%22Father+of+Modern+Optics%22&hl=en&sa=X&ei=RuhgVJCUIcHksATBo4CoDA|journal=UNESCO|volume= 26–27|pages=140|via=}}.{{Cite web|url=http://www.light2015.org/Home/ScienceStories/1000-Years-of-Arabic-Optics.html|title=International Year of Light - Ibn Al-Haytham and the Legacy of Arabic Optics|website=www.light2015.org|language=en|access-date=9 October 2017}}.{{Cite web|url=http://en.unesco.org/news/international-year-light-ibn-al-haytham-pioneer-modern-optics-celebrated-unesco|title=International Year of Light: Ibn al Haytham, pioneer of modern optics celebrated at UNESCO|website=UNESCO|language=en|access-date=9 October 2017}}. Specifically, he was the first to explain that vision occurs when light bounces on an object and then enters an eye. {{cite book|ref=harv|last=Adamson|first=Peter|title=Philosophy in the Islamic World: A History of Philosophy Without Any Gaps|url=https://books.google.com/books?id=KEpRDAAAQBAJ|date=7 July 2016|publisher=Oxford University Press|isbn=978-0-19-957749-1|p=77}}
21. ^Roshdi Rashed, Ibn al-Haytham's Geometrical Methods and the Philosophy of Mathematics: A History of Arabic Sciences and Mathematics, Volume 5, Routledge (2017), p. 635
22. ^{{cite book|ref=harv|last=Adamson|first=Peter|title=Philosophy in the Islamic World: A History of Philosophy Without Any Gaps|url=https://books.google.com/books?id=KEpRDAAAQBAJ|date=7 July 2016|publisher=Oxford University Press|isbn=978-0-19-957749-1|p=77}}
23. ^Baker, David B. (2012). The Oxford Handbook of the History of Psychology: Global Perspectives. Oxford University Press, USA, p. 445
24. ^{{Harvnb|Ackerman|1991}}.
25. ^Haq, Syed (2009). "Science in Islam". Oxford Dictionary of the Middle Ages. {{ISSN|1703-7603}}. Retrieved 22 October 2014.
26. ^G. J. Toomer. [https://www.jstor.org/stable/228328?pg=464 Review on JSTOR, Toomer's 1964 review of Matthias Schramm (1963) Ibn Al-Haythams Weg Zur Physik] Toomer p.464: "Schramm sums up [Ibn Al-Haytham's] achievement in the development of scientific method."
27. ^{{cite web|url=http://www.light2015.org/Home/ScienceStories/1000-Years-of-Arabic-Optics.html|title=International Year of Light - Ibn Al-Haytham and the Legacy of Arabic Optics|publisher=}}
28. ^{{Cite news|url=http://news.bbc.co.uk/2/hi/science/nature/7810846.stm|work=BBC News|title=The 'first true scientist'|author=Al-Khalili, Jim|date=4 January 2009|accessdate=24 September 2013}}
29. ^{{Cite journal|last=Gorini|first=Rosanna|title=Al-Haytham the man of experience. First steps in the science of vision|url=http://www.ishim.net/ishimj/4/10.pdf|journal=Journal of the International Society for the History of Islamic Medicine|volume=2|issue=4|pages=53–55|date=October 2003|format=PDF|accessdate=25 September 2008|ref=harv}}
30. ^According to Al-Qifti. {{Harvnb|O'Connor|Robertson|1999}}.
31. ^{{harvnb|O'Connor|Robertson|1999}}
32. ^{{harvnb|O'Connor|Robertson|1999|p=}}
33. ^Disputed: {{harvnb|Corbin|1993|p=149}}.
34. ^Noted by Abu'l-Hasan Bayhaqi (ca. 1097 – 1169), and by *[https://books.google.com/books?id=AsnaAAAAMAAJ&dq=%22Second+Ptolemy%22+A.+I.+Sabra&focus=searchwithinvolume&q=%22Second+Ptolemy%22 Sabra 1994] p.197 *[https://books.google.com/books?id=NazQAAAAMAAJ&dq=%22Second+Ptolemy%22+The+Rainbow&focus=searchwithinvolume&q=%22Second+Ptolemy%22 Carl Boyer 1959 p.80]
35. ^¹[https://www.encyclopedia.com/science/dictionaries-thesauruses-pictures-and-press-releases/ibn-al-haytham-abu A. I. Sabra encyclopedia.com Ibn Al-Haytham, Abū ]
36. ^{{harvnb|Lindberg|1967|p=331}}:"Peckham continually bows to the authority of Alhazen, whom he cites as "the Author" or "the Physicist"."
37. ^{{Cite book|url=https://books.google.co.in/books?id=mhLVHR5QAQkC&printsec=frontcover#v=onepage&q&f=false|title=Ptolemy's Theory of Visual Perception: An English Translation of the Optics|last=A. Mark Smith|publisher=American Philosophical Society|year=1996|isbn=|location=|pages=57}}
38. ^¹{{Harvnb|Corbin|1993|p=149}}.
39. ^The Prisoner of Al-Hakim. Clifton, NJ: Blue Dome Press, 2017. {{ISBN|1682060160}}
40. ^Carl Brockelmann, Geschichte der arabischen Litteratur, vol. 1 (1898), [https://archive.org/stream/geschichtederar00brocgoog#page/n522/mode/2up p. 469].
41. ^{{cite web|url=http://www.cgie.org.ir/shavad.asp?id=123&avaid=1917 |title=the Great Islamic Encyclopedia |publisher=Cgie.org.ir |accessdate=27 May 2012 |deadurl=yes |archiveurl=https://web.archive.org/web/20110930153427/http://www.cgie.org.ir/shavad.asp?id=123&avaid=1917 |archivedate=30 September 2011 }}{{verify source|date=February 2016}}
42. ^For Ibn al-Haytham's life and works, {{harv|Smith|2001|p=cxix}} recommends {{harv|Sabra|1989|pp=vol.2, xix-lxxiii}}
43. ^Sajjadi, Sadegh, "Alhazen", Great Islamic Encyclopedia, Volume 1, Article No. 1917;{{verify source|date=February 2016}}
44. ^{{Harvnb|Al-Khalili|2015}}.
45. ^{{harvnb|Crombie|1971|p=147, n. 2}}.
46. ^{{Citation|url=http://www.mala.bc.ca/~mcneil/cit/citlcalhazen1.htm |title=Alhazen (965–1040): Library of Congress Citations | publisher=Malaspina Great Books |accessdate=23 January 2008 |deadurl=yes |archiveurl=https://web.archive.org/web/20070927190009/http://www.mala.bc.ca/~mcneil/cit/citlcalhazen1.htm |archivedate=27 September 2007 }}{{verify source|date=February 2016}}
47. ^{{harvnb|Smith|2001|p=xxi}}.
48. ^{{harvnb|Smith|2001|p=xxii}}.
49. ^{{harvnb|Smith|2001|p=lxxix}}.
50. ^¹{{harvnb|Lindberg|1976|p=73}}.
51. ^{{harv|Lindberg|1976|p=74}}
52. ^{{harv|Lindberg|1976|p=76}}
53. ^{{harvnb|Lindberg|1976|p=75}}
54. ^{{harvnb|Lindberg|1976|pages=76–78}}
55. ^¹{{harvnb|Lindberg|1976|p=86}}.
56. ^¹{{harvnb|Al Deek|2004}}.
57. ^{{harvnb|Heeffer|2003}}.
58. ^{{harvnb|Kelley|Milone|Aveni|2005|p=83}}: "The first clear description of the device appears in the Book of Optics of Alhazen."
59. ^{{harvtxt|Wade|Finger|2001}}: "The principles of the camera obscura first began to be correctly analysed in the eleventh century, when they were outlined by Ibn al-Haytham."
60. ^{{Cite book|title=History of Photography|last=Eder|first=Josef|publisher=Columbia University Press|year=1945|isbn=|location=New York|pages=37}}
61. ^{{harvnb|Howard|1996}}.
62. ^{{harvnb|Aaen-Stockdale|2008}}
63. ^{{harvnb|Wade|1998|pages=240,316,334,367}}; {{harvnb|Howard|Wade|1996|pages=1195,1197,1200}}.
64. ^{{harvnb|Lejeune|1958}}.
65. ^¹²{{harvnb|Sabra|1989}}.
66. ^{{harvnb|Raynaud|2003}}.
67. ^{{harvnb|Russell|1996|p=691}}.
68. ^{{harvnb|Russell|1996|p=689}}.
69. ^{{harvnb|Lindberg|1976|pages= 80–85}}
70. ^{{harvnb|Smith|2004|pages=186, 192}}.
71. ^{{harvnb|Wade|1998|p=14}}
72. ^{{harvnb|Smith|2001|p=437}} [https://www.jstor.org/stable/3657357?seq=104&Search=yes&resultItemClick=true&searchText=child&searchText=does&searchUri=%2Faction%2FdoBasicSearch%3FQuery%3Dchild%2Bdoes%26amp%3Bfilter%3Diid%253A10.2307%252Fi370516#page_scan_tab_contents De Aspectibus Book Two, 3.39 p.437, via JSTOR]
73. ^See, for example,De aspectibus Book 7, for his experiments in refraction
74. ^¹{{harvs|nb|last=El-Bizri|year=2005a|year2=2005b}}.
75. ^¹[https://core.ac.uk/download/pdf/82356023.pdf see Schramm's Habilitationsschrift, Ibn al-Haythams Weg zur Physik (Steiner, Wiesbaden, 1963) as cited by Rüdiger Thiele (2005) Historia Mathematica 32, 271–274. "In Memoriam: Matthias Schramm, 1928–2005"]
76. ^{{harvnb|Toomer|1964|pp=463–4}}
77. ^¹{{harvnb|Toomer|1964|p=465}}
78. ^{{harvnb|Toomer|1964|p=464}}
79. ^G. J. Toomer. [https://www.jstor.org/stable/228328?pg=464 Review on JSTOR, Toomer's 1964 review of Matthias Schramm (1963) Ibn Al-Haythams Weg Zur Physik] Toomer p. 464: "Schramm sums up [Ibn Al-Haytham's] achievement in the development of scientific method.", p. 465: "Schramm has demonstrated .. beyond any dispute that Ibn al-Haytham is a major figure in the Islamic scientific tradition, particularly in the creation of experimental techniques." p.465: "Only when the influence of ibn al-Haytam and others on the mainstream of later medieval physical writings has been seriously investigated can Schramm's claim that ibn al-Haytam was the true founder of modern physics be evaluated."
80. ^{{harvnb|Smith|2015|p=329}}
81. ^{{harvnb|Smith|2004|p=192}}
82. ^{{harvnb|O'Connor|Robertson|1999}}, {{harvnb|Weisstein|2008}}.
83. ^{{harvnb|Katz|1995|pp=165–9 & 173–4}}.
84. ^{{harvnb|Smith|1992}}.
85. ^{{harvnb|Highfield|1997}}.
86. ^{{harvnb|Agrawal|Taguchi|Ramalingam|2011}}.
87. ^¹{{harvnb|Agrawal|Taguchi|Ramalingam|2010}}.
88. ^{{harvnb|Russell|1996|p=695}}.
89. ^{{harvnb|Russell|1996|p=}}.
90. ^¹{{harvnb|Khaleefa|1999}}
91. ^{{harvnb|Aaen-Stockdale|2008}}.
92. ^{{harvnb|Ross|Plug|2002}}.
93. ^{{harvnb|Hershenson|1989|pp=9–10}}.
94. ^{{harvnb|Ross|2000}}.
95. ^{{harvnb|Ross|Ross|1976}}.
96. ^¹{{harvnb|El-Bizri|2006}}.
97. ^{{harvnb|Duhem|1969|p=28}}.
98. ^¹²{{harvnb|El-Bizri|2007}}.
99. ^{{harvnb|Langermann|1990}}, chap. 2, sect. 22, p. 61
100. ^{{harvnb|Lorch|2008}}.
101. ^{{harvnb|Langermann|1990|pp=34–41}}; {{harvnb|Gondhalekar|2001|p=21}}.
102. ^¹{{harvnb|Sabra|1998}}.
103. ^{{harvnb|Langermann|1990|pp=8–10}}
104. ^{{harvnb|Sabra|1978b|p=121, n. 13}}
105. ^{{harvnb|Rashed|2007}}.
106. ^{{harvnb|Mohamed|2000|pp=49–50}}
107. ^{{harvnb|Rashed|2007|pp=8–9}}.
108. ^{{harvnb|Faruqi|2006|pp=395–6}}:{{quote|In seventeenth century Europe the problems formulated by Ibn al-Haytham (965–1041) became known as 'Alhazen's problem'. ... Al-Haytham's contributions to geometry and number theory went well beyond the Archimedean tradition. Al-Haytham also worked on analytical geometry and the beginnings of the link between algebra and geometry. Subsequently, this work led in pure mathematics to the harmonious fusion of algebra and geometry that was epitomised by Descartes in geometric analysis and by Newton in the calculus. Al-Haytham was a scientist who made major contributions to the fields of mathematics, physics and astronomy during the latter half of the tenth century.}}
109. ^{{harvnb|Rottman|2000}}, Chapter 1.
110. ^{{harvnb|Eder|2000}}.
111. ^{{harvnb|Katz|1998|p=269}}: "In effect, this method characterised parallel lines as lines always equidistant from one another and also introduced the concept of motion into geometry."
112. ^{{harvnb|Rozenfeld|1988|p=65}}.
113. ^¹²{{harvnb|O'Connor|Robertson|1999}}.
114. ^{{Harvnb|Alsina|Nelsen|2010}}.
115. ^{{cite journal |doi=10.2307/2691411 |author=Katz, Victor J. |title=Ideas of Calculus in Islam and India |jstor=2691411 |journal=Mathematics Magazine |volume=68 |issue=3 |pages=163–174 |year=1995 }} [165–9, 173–4]
116. ^{{harvnb|Plott|2000}}, Pt. II, p. 459.
117. ^{{harvnb|Smith|2005|pp=219–40}}.
118. ^{{harvnb|Sardar|1998}}, {{harvnb|Bettany|1995|p=251}}.
119. ^{{harvnb|Hodgson|2006|p=53}}.
120. ^{{harv|Sabra|1978a|p=54}}
121. ^{{harvnb|Plott|2000}}, Pt. II, p. 464
122. ^{{harvnb|Topdemir|2007b|pp=8–9}}.
123. ^Translated by S. Pines, as quoted in {{harvnb|Sambursky|1974|p=139}}.
124. ^{{harvnb|Rashed|2007|p=11}}.
125. ^{{harvnb|Plott|2000}}, Pt. II, p. 465
126. ^{{harvnb|Sabra|2007}}.
127. ^{{harvnb|Sabra|2007|pages=122, 128–129}}. {{harvtxt|Grant|1974|p=[{{google books|fAPN_3w4hAUC|plainurl=yes|page=392}} 392]}} notes the Book of Optics has also been denoted as Opticae Thesaurus Alhazen Arabis, as De Aspectibus, and also as Perspectiva
128. ^{{harvnb|Lindberg|1996|p=11}}, passim.
129. ^{{Harvnb|Authier|2013|p=23}}: "Alhazen's works in turn inspired many scientists of the Middle Ages, such as the English bishop, Robert Grosseteste (ca 1175–1253), and the English Franciscan, Roger Bacon (ca 1214–1294), Erazmus Ciolek Witelo, or Witelon (ca 1230* 1280), a Silesian-born Polish friar, philosopher and scholar, published in ca 1270 a treatise on optics, Perspectiva, largely based on Alhazen's works."
130. ^{{Harvnb|Magill|Aves|1998|p=66}}: "Roger Bacon, John Peckham, and Giambattista della Porta are only some of the many thinkers who were influenced by Alhazen's work."
131. ^{{Harvnb|Zewail|Thomas|2010|p=5}}: "The Latin translation of Alhazen's work influenced scientists and philosophers such as (Roger) Bacon and da Vinci, and formed the foundation for the work by mathematicians like Kepler, Descartes and Huygens..."
132. ^{{Harvnb|El-Bizri|2010|p=12}}: "This [Latin] version of Ibn al-Haytham's Optics, which became available in print, was read and consulted by scientists and philosophers of the caliber of Kepler, Galileo, Descartes, and Huygens as discussed by Nader El-Bizri."
133. ^{{Harvnb|Magill|Aves|1998|p=66}}: "Sabra discusses in detail the impact of Alhazen's ideas on the optical discoveries of such men as Descartes and Christiaan Huygens; see also {{harvnb|El-Bizri|2005a}}."
134. ^{{Harvnb|El-Bizri|2010|p=12}}.
135. ^{{Harvnb|Magill|Aves|1998|p=66}}: "Even Kepler, however, used some of Alhazen's ideas, for example, the one-to-one correspondence between points on the object and points in the eye. It would not be going too far to say that Alhazen's optical theories defined the scope and goals of the field from his day to ours."
136. ^{{harvnb|Topdemir|2007a|p=77}}.
137. ^{{Harvnb|Chong|Lim|Ang|2002}} Appendix 3, [{{google books|id=vIcFxgAs-C8C|plainurl=yes|page=129}} p. 129].
138. ^{{Harvnb|NASA|2006}}.
139. ^AKU Research Publications 1995-98 {{webarchive |url=https://web.archive.org/web/20150104215931/http://www.aku.edu/res-office/pdfs/AKU_Research_Publications_1995 |date=4 January 2015 }}
140. ^{{harvnb|Murphy|2003}}.
141. ^{{cite web |title=Ibn Al-Haytham and the Legacy of Arabic Optics|publisher=2015 INTERNATIONAL YEAR OF LIGHT|url=http://www.light2015.org/Home/ScienceStories/1000-Years-of-Arabic-Optics.html|date=2015}}
142. ^{{cite journal |last1=Winter |first1=H. J. J. |title=THE OPTICAL RESEARCHES OF IBN AL-HAITHAM |journal=Centaurus |date=September 1953 |volume=3 |issue=1 |pages=190–210 |doi=10.1111/j.1600-0498.1953.tb00529.x |url=https://onlinelibrary.wiley.com/doi/abs/10.1111/j.1600-0498.1953.tb00529.x |language=en |issn=0008-8994}}
143. ^2015, International Year of Light
144. ^{{cite web| url=http://www.unesco.org/new/en/media-services/single-view/news/1000_years_of_arabic_optics_to_be_a_focus_of_the_international_year_of_light_in_2015 |title=1000 Years of Arabic Optics to be a Focus of the International Year of Light in 2015 |publisher=United Nations |accessdate=27 November 2014}}
145. ^{{harvnb|Smith| 2010}} para.[3.33], p.259, footnote67. Note 67 is on p.361. [3.33] is the summary of how to measure the sizes of the angle of refraction for air to water, air to glass, glass to air, glass to water, for plane, concave, and convex surfaces
146. ^{{harvnb|Rashed|2002a|p=773}}.
147. ^{{harvnb|Rashed|2007|pp=8–9}}; {{harvnb|Topdemir|2007b}}
148. ^From Ibn Abi Usaibia's catalog, as cited in {{harvnb|Smith|2001}} 91(vol.1), p.xv.