*This article is about the physicist. For the physician, see Ali ibn Sahl Rabban al-Tabari*Abu al-Hasan Ali ibn Sahl Rabban al-Tabari also given as 810-855 and 783-858 was a Persian Muslim hakim, Islamic scholar, physician and psychologist of Zoroastrian descent, who produced one of the first encyclopedia of medicine. He was a pioneer of pediatrics and the field of child development...

. For the poet, see Ibn Sahl of SevillaIbn Sahl of Seville is considered one of the greatest Moorish poets of Andalusia of the 13th century. He was a Jewish convert to Islam....

.
**Ibn Sahl** (

**Abu Saʿd al-ʿAlaʾ ibn Sahl **) (c. 940-1000) was a

MuslimA Muslim, also spelled Moslem, is an adherent of Islam, a monotheistic, Abrahamic religion based on the Quran, which Muslims consider the verbatim word of God as revealed to prophet Muhammad. "Muslim" is the Arabic term for "submitter" .Muslims believe that God is one and incomparable...

Persian

mathematicianIn the history of mathematics, mathematics in medieval Islam, often termed Islamic mathematics or Arabic mathematics, covers the body of mathematics preserved and developed under the Islamic civilization between circa 622 and 1600...

,

physicistPhysics in medieval Islam is the development of physics in the medieval Islamic world in the history of physics. In the course of the expansion of the Islamic world, Muslim scholars encountered the science, mathematics, and medicine of antiquity through the works of Aristotle, Archimedes, Galen,...

and

opticsOptics is the branch of physics which involves the behavior and properties of light, including its interactions with matter and the construction of instruments that use or detect it. Optics usually describes the behavior of visible, ultraviolet, and infrared light...

engineerA number of inventions were developed in the medieval Islamic world, a geopolitical region that has at various times extended from Spain and Africa in the west to the Indian subcontinent in the east. The inventions listed here were developed during the medieval Islamic world, which covers the...

of the

Islamic Golden AgeDuring the Islamic Golden Age philosophers, scientists and engineers of the Islamic world contributed enormously to technology and culture, both by preserving earlier traditions and by adding their own inventions and innovations...

associated with the

AbbasidThe Abbasid Caliphate or, more simply, the Abbasids , was the third of the Islamic caliphates. It was ruled by the Abbasid dynasty of caliphs, who built their capital in Baghdad after overthrowing the Umayyad caliphate from all but the al-Andalus region....

court of

BaghdadBaghdad is the capital of Iraq, as well as the coterminous Baghdad Governorate. The population of Baghdad in 2011 is approximately 7,216,040...

. Ibn Sahl's 984 treatise

*On Burning Mirrors and Lenses* sets out his understanding of how

curved mirrorA curved mirror is a mirror with a curved reflective surface, which may be either convex or concave . Most curved mirrors have surfaces that are shaped like part of a sphere, but other shapes are sometimes used in optical devices...

s and

lensesA lens is an optical device with perfect or approximate axial symmetry which transmits and refracts light, converging or diverging the beam. A simple lens consists of a single optical element...

bend and focus light. Ibn Sahl is credited with first discovering the law of

refractionRefraction is the change in direction of a wave due to a change in its speed. It is essentially a surface phenomenon . The phenomenon is mainly in governance to the law of conservation of energy. The proper explanation would be that due to change of medium, the phase velocity of the wave is changed...

, usually called

Snell's lawIn optics and physics, Snell's law is a formula used to describe the relationship between the angles of incidence and refraction, when referring to light or other waves passing through a boundary between two different isotropic media, such as water and glass...

. He used the law of refraction to derive lens shapes that focus light with no geometric aberrations, known as anaclastic lenses.

In the reproduction of the figure from Ibn Sahl's manuscript, the critical part is the right-angled

triangleA triangle is one of the basic shapes of geometry: a polygon with three corners or vertices and three sides or edges which are line segments. A triangle with vertices A, B, and C is denoted ....

. The inner

hypotenuseIn geometry, a hypotenuse is the longest side of a right-angled triangle, the side opposite the right angle. The length of the hypotenuse of a right triangle can be found using the Pythagorean theorem, which states that the square of the length of the hypotenuse equals the sum of the squares of the...

shows the path of an incident ray and the outer hypotenuse shows an extension of the path of the refracted ray if the incident ray met a

crystalA crystal or crystalline solid is a solid material whose constituent atoms, molecules, or ions are arranged in an orderly repeating pattern extending in all three spatial dimensions. The scientific study of crystals and crystal formation is known as crystallography...

whose face is vertical at the point where the two hypotenuses intersect. According to Rashed, the ratio of the length of the smaller hypotenuse to the larger is the

reciprocalIn mathematics, a multiplicative inverse or reciprocal for a number x, denoted by 1/x or x−1, is a number which when multiplied by x yields the multiplicative identity, 1. The multiplicative inverse of a fraction a/b is b/a. For the multiplicative inverse of a real number, divide 1 by the...

of the

refractive indexIn optics the refractive index or index of refraction of a substance or medium is a measure of the speed of light in that medium. It is expressed as a ratio of the speed of light in vacuum relative to that in the considered medium....

of the crystal.

The lower part of the figure shows a representation of a plano-convex lens (at the right) and its

principal axisAn optical axis is a line along which there is some degree of rotational symmetry in an optical system such as a camera lens or microscope.The optical axis is an imaginary line that defines the path along which light propagates through the system...

(the intersecting horizontal line). The curvature of the convex part of the lens brings all rays parallel to the horizontal axis (and approaching the lens from the right) to a

focal pointIn geometrical optics, a focus, also called an image point, is the point where light rays originating from a point on the object converge. Although the focus is conceptually a point, physically the focus has a spatial extent, called the blur circle. This non-ideal focusing may be caused by...

on the axis at the left.

In the remaining parts of the treatise, Ibn Sahl dealt with parabolic mirrors, ellipsoidal mirrors, biconvex lenses, and techniques for drawing hyperbolic arcs.

Ibn Sahl's treatise was used by

Ibn al-Haitham' was a Muslim, scientist and polymath described in various sources as either Arabic or Persian...

(965–1039), one of the greatest Arab scholars of optics. In modern times, Rashed found the text to have been dispersed in manuscripts in two different libraries, one in Teheran, and the other in Damascus. He reassembled the surviving portions, translated and published them.

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