Abū ʿAlī al-Ḥasan ibn al-Ḥasan ibn al-Haytham (Arabic: أبو علي، الحسن بن الحسن بن الهيثم, Persian: ابن هیثم, Latinized: Alhacen or (deprecated) Alhazen) (965 in Basra – c. 1040 in Cairo) was a Muslim, scientist and polymath described in various sources as either Arabic or Persian. He is frequently referred to as Ibn al-Haytham, and sometimes as al-Basri (Arabic: البصري), after his birthplace in the city of Basra. Alhazen made significant contributions to the principles of optics, as well as to physics, astronomy, mathematics, ophthalmology, philosophy, visual perception, and to the scientific method. He was also nicknamed Ptolemaeus Secundus ("Ptolemy the Second") or simply "The Physicist" in medieval Europe. Alhazen wrote insightful commentaries on works by Aristotle, Ptolemy, and the Greek mathematician Euclid.

Born circa 965, in Basra, present day Iraq, he lived mainly in Cairo, Egypt, dying there at age 76. Over - confident about practical application of his mathematical knowledge, he assumed that he could regulate the floods of the Nile. After being ordered by Al-Hakim bi-Amr Allah, the sixth ruler of the Fatimid caliphate, to carry out this operation, he quickly perceived the impossibility of what he was attempting to do, and retired from engineering. Fearing for his life, he feigned madness and was placed under house arrest, during and after which he devoted himself to his scientific work until his death.

Alhazen was born in Basra, in the Iraq province of the Buyid Empire. Many historians have different opinions about his ethnicity whether he was Arab or Persian. He probably died in Cairo, Egypt. During the Islamic Golden Age, Basra was a "key beginning of learning", and he was educated there and in Baghdad, the capital of the Abbasid Caliphate, and the focus of the "high point of Islamic civilization". During his time in Buyid Iran, he worked as a civil servant and read many theological and scientific books.

One account of his career has him called to Egypt by Al-Hakim bi-Amr Allah, ruler of the Fatimid Caliphate, to regulate the flooding of the Nile, a task requiring an early attempt at building a dam at the present site of the Aswan Dam. After his field work made him aware of the impracticality of this scheme, and fearing the caliph's anger, he feigned madness. He was kept under house arrest from 1011 until al-Hakim's death in 1021. During this time, he wrote his influential Book of Optics. After his house arrest ended, he wrote scores of other treatises on physics, astronomy and mathematics. He later traveled to Islamic Spain. During this period, he had ample time for his scientific pursuits, which included optics, mathematics, physics, medicine, and the development of the modern experimental scientific method.

Some biographers have claimed that Alhazen fled to Syria, ventured into Baghdad later in his life, or was in Basra when he pretended to be insane. In any case, he was in Egypt by 1038. During his time in Cairo, he became associated with Al-Azhar University, as well the city's "House of Wisdom", known as Dar al-`Ilm (House of Knowledge), which was a library "first in importance" to Baghdad's House of Wisdom.

Among his students were Sorkhab (Sohrab), a Persian student who was one of the greatest people of Iran's Semnan and was his student for over 3 years, and Abu al-Wafa Mubashir ibn Fatek, an Egyptian scientist who learned mathematics from Alhazan.

Alhazen made significant improvements in optics, physical science, and the scientific method. Alhazen's work on optics is credited with contributing a new emphasis on experiment. His influence on physical sciences in general, and on optics in particular, has been held in high esteem and, in fact, ushered in a new era in optical research, both in theory and practice.

The Latin translation of his main work, Kitab al-Manazir (Book of Optics), exerted a great influence on Western science: for example, on the work of Roger Bacon, who cites him by name, and on Johannes Kepler. His research in catoptrics (the study of optical systems using mirrors) centered 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". Meanwhile in the Islamic world, Alhazen's work influenced Averroes' writings on optics, and his legacy was further advanced through the 'reforming' of his Optics by Persian scientist Kamal al-Din al-Farisi (d. ca. 1320) in the latter's Kitab Tanqih al-Manazir (The Revision of [Ibn al-Haytham's] Optics). The correct explanations of the rainbow phenomenon given by al-Fārisī and Theodoric of Freiberg in the 14th century depended on Alhazen's Book of Optics. The work of Alhazen and al-Fārisī was also further advanced in the Ottoman Empire by polymath Taqi al-Din in his Book of the Light of the Pupil of Vision and the Light of the Truth of the Sights (1574). He wrote as many as 200 books, although only 55 have survived, and many of those have not yet been translated from Arabic. Even 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 crater Alhazen on the Moon is named in his honor, as was the asteroid 59239 Alhazen. In honor of Alhazen, the Aga Khan University (Pakistan) named its Ophthalmology endowed chair as "The Ibn-e-Haitham Associate Professor and Chief of Ophthalmology".

Alhazen (by the name Ibn al-Haytham) is featured on the obverse of the Iraqi 10,000 dinars banknote issued in 2003, and on 10 dinar notes from 1982. A research facility that UN weapons inspectors suspected of conducting chemical and biological weapons research in Saddam Hussein's Iraq was also named after him.

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

Optics was translated into Latin by an unknown scholar at the end of the 12th century or the beginning of the 13th century. It was 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 Risner he was known in the west as Alhacen, which is the correct transcription of the Arabic name. This work enjoyed a great reputation during the Middle Ages. Works by Alhazen on geometric 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.

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. Alhazen argued that the process of vision occurs neither by rays emitted from the eye, nor through physical forms entering it. He reasoned that a ray could not proceed from the eyes and reach the distant stars the instant after we open our eyes. He also appealed to common observations such as the eye being dazzled or even injured if we look at a very bright light. He instead developed a highly successful theory which explained the process of vision as 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 physical optics.

Alhazen proved that rays of light travel in straight lines, and carried out various 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 proposed a causal model for the refraction of light that could have been extended to yield a result similar to Snell's law of sines, however Alhazen did not develop his model sufficiently to attain that result.

Alhazen also gave the first clear description and correct analysis of the camera obscura and pinhole camera. While Aristotle, Theon of Alexandria, Al-Kindi (Alkindus) and Chinese philosopher Mozi had earlier described the effects of a single light passing through a pinhole, none of them suggested that what is being projected onto the screen is an image of everything on the other side of the aperture. Alhazen was the first to demonstrate this with his lamp experiment where several different light sources are arranged across a large area. He was thus the first to successfully project an entire image from outdoors onto a screen indoors with the camera obscura.

In addition to physical optics, The Book of Optics also gave rise to the field of "physiological optics". Alhazen discussed the topics of medicine, ophthalmology, anatomy and physiology, which included commentaries on Galenic works. He described the process of sight, the structure of the eye, image formation in the eye, and the visual system. He 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 Aristotle, Euclid and Ptolemy.

His most original anatomical contribution was his description of the functional anatomy of the eye as an optical system, or optical instrument. His experiments with the camera obscura 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 camera obscura which brought about his synthesis of anatomy and optics, which forms the basis of 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, he incorrectly agreed with Avicenna that the lens was the receptive organ of sight, but correctly hinted at the retina being involved in the process.

Neuroscientist Rosanna Gorini notes that "according to the majority of the historians al-Haytham was the pioneer of the modern scientific method." From this point of view, Alhazen developed rigorous experimental methods of controlled scientific testing to verify theoretical hypotheses and substantiate inductive conjectures. Other historians of science place his experiments in the tradition of Ptolemy and see in such interpretations a "tendency to 'modernize' Alhazen ... [which] serves to wrench him slightly out of proper historical focus."

An aspect associated with Alhazen'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 color, as well as his research in catoptrics and dioptrics (the study of the refraction of light). 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).

The concept of Occam'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."

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 cue ball at a given point must be aimed in order to carom 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 where the light will be reflected to the eye of an observer." This leads to an equation of the fourth degree. This eventually led Alhazen to derive the earliest formula for the sum of fourth powers; by using an early proof by mathematical induction, he developed a method that can be readily generalized to find the formula for the sum of any integral powers. He applied his result of sums on integral powers to find the volume of a paraboloid through integration. He was thus able to find the integrals for polynomials up to the fourth degree. Alhazen eventually solved the problem using conic sections and a geometric proof, though many after him attempted to find an algebraic solution to the problem, which was finally found in 1997 by the Oxford mathematician Peter M. Neumann. Recently, Mitsubishi Electric Research Labs (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. 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. 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.

The Book of Optics describes several early experimental observations that Alhazen 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." This result explained how intense direct light hurts the eye: "Applying mechanical analogies to the effect of light rays on the eye, Alhazen 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."

Chapters 15 – 16 of the Book of Optics covered astronomy. Alhazen was the first to discover that the celestial spheres do not consist of solid matter. He also discovered that the heavens are less dense than the air. These views were later repeated by Witelo and had a significant influence on the Copernican and Tychonic systems of astronomy.

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. In the Book of Optics, Alhazen 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. Khaleefa has also argued that Alhazen should also be considered the "founder of psychophysics", a subdiscipline and precursor to modern psychology. Although Alhazen made many subjective reports regarding vision, there is no evidence that he used quantitative psychophysical techniques and the claim has been rebuffed.

Alhazen offered an explanation of the Moon illusion, an illusion that played an important role in the scientific tradition of medieval Europe. 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, a debate that is still unresolved. 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. Although Alhazen is often credited with the perceived distance explanation, he was not the first author to offer it. Cleomedes (c. 2nd century) gave this account (in addition to refraction), and he credited it to Posidonius (c. 135 - 50 BC) Ptolemy may also have offered this explanation in his Optics, but the text is obscure. 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.

Some have suggested that Alhazen's views on pain and sensation may have been influenced by Buddhist philosophy. 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.

Besides the Book of Optics, Alhazen wrote several other treatises on optics. His 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 examinations into anatomy of the eye and illusions in visual perception. He built the first camera obscura and pinhole camera, and investigated the meteorology of the rainbow and the density of the atmosphere. Various celestial phenomena (including the eclipse, twilight, and moonlight) were also examined by him. He also made investigations into refraction, catoptrics, dioptrics, spherical mirrors, and magnifying lenses.

In his treatise, Mizan al-Hikmah (Balance of Wisdom), Alhazen discussed the density of the atmosphere and related it to altitude. He also studied atmospheric refraction. He discovered that the twilight only ceases or begins when the Sun is 19° below the horizon and attempted to measure the height of the atmosphere on that basis.

In astrophysics and the celestial mechanics field of physics, Alhazen, in his Epitome of Astronomy, discovered that the heavenly bodies "were accountable to the laws of physics". Alhazen's Mizan al-Hikmah (Balance of Wisdom) covered statics, astrophysics, and celestial mechanics. He discussed the theory of attraction between masses, and it seems that he was also aware of the magnitude of acceleration due to gravity at a distance. His Maqala fi'l-qarastun is a treatise on centers of gravity. Little is known about the work, except for what is known through the later works of al-Khazini in the 12th century. In this treatise, Alhazen formulated the theory that the heaviness of bodies varies with their distance from the center of the Earth.

Another treatise, Maqala fi daw al-qamar (On the Light of the Moon), which he wrote some time before his famous Book of Optics, was the first successful attempt at combining mathematical astronomy with physics, and the earliest attempt at applying the experimental method to astronomy and astrophysics. He disproved the universally held opinion that the Moon reflects sunlight like a mirror and correctly concluded that it "emits light from those portions of its surface which the sun's light strikes." To prove that "light is emitted from every point of the Moon's illuminated surface", he built an "ingenious experimental device." According to Matthias Schramm, Alhazen had

formulated a clear conception of the relationship between an ideal mathematical model and the complex of observable phenomena; in particular, he 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.

In the dynamics and kinematics fields of mechanics, Alhazen's Risala fi’l-makan (Treatise on Place) discussed theories on the motion of a body. He maintained that a body moves perpetually unless an external force stops it or changes its direction of motion. Alhazen's concept of inertia was not verified by experimentation, however. Galileo Galilei repeated Alhazen's principle, centuries later, but introduced the concept of frictional force and provided experimental results.

In his Treatise on Place, Alhazen disagreed with Aristotle's view that nature abhors a void, and he thus used geometry to demonstrate that place (al-makan) is the imagined three - dimensional void between the inner surfaces of a containing body.

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 many of Ptolemy's works, including the Almagest, Planetary Hypotheses, and Optics, pointing out various contradictions he found in these works. 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 wrote a scathing critique of the physical reality of Ptolemy's astronomical system, noting the absurdity of relating actual physical motions to imaginary mathematical points, lines and circles:

Ptolemy assumed an arrangement (hay'a) that cannot exist, and the fact that this arrangement produces in his imagination the motions that belong to the planets does not free him from the error he committed in his assumed arrangement, for the existing motions of the planets cannot be the result of an arrangement that is impossible to exist... [F]or a man to imagine a circle in the heavens, and to imagine the planet moving in it does not bring about the planet's motion.

Alhazen further criticized Ptolemy's model on other empirical, observational and experimental grounds, such as Ptolemy's use of conjectural undemonstrated theories in order to "save appearances" of certain phenomena, which Alhazen did not approve of due to his insistence on scientific demonstration. Unlike some later astronomers who criticized the Ptolemaic model on the grounds of being incompatible with Aristotelian natural philosophy, Alhazen was mainly concerned with empirical observation and the internal contradictions in Ptolemy's works.

In his Aporias against Ptolemy, Alhazen commented on the difficulty of attaining scientific knowledge:

Truth is sought for itself [but] the truths, [he warns] are immersed in uncertainties [and the scientific authorities (such as Ptolemy, whom he greatly respected) are] not immune from error...

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

Therefore, the seeker after the truth is not one who studies the writings of the ancients and, following his natural disposition, puts his trust in them, but rather the one who suspects his faith in them and questions what he gathers from them, the one who submits to argument and demonstration, and not to the sayings of a human being whose nature is fraught with all kinds of imperfection and deficiency. Thus the duty of the man who investigates the writings of scientists, if learning the truth is his goal, is to make himself an enemy of all that he reads, and, applying his mind to the core and margins of its content, attack it from every side. He should also suspect himself as he performs his critical examination of it, so that he may avoid falling into either prejudice or leniency.