Ibn Sahl (full name: Abū Saʿd al-ʿAlāʾ ibn Sahl أبو سعد العلاء ابن سهل; c. 940–1000) was a Persian mathematician and physicist of the Islamic Golden Age, associated with the Buyid court of Baghdad. Nothing in his name allows us to glimpse his country of origin. He is known to have written an optical treatise around 984. The text of this treatise was reconstructed by Roshdi Rashed from two manuscripts (edited 1993).: Damascus, al-Ẓāhirīya MS 4871, 3 fols., and Tehran, Millī MS 867, 51 fols. The Tehran manuscript is much longer, but it is badly damaged, and the Damascus manuscript contains a section missing entirely from the Tehran manuscript. The Damascus manuscript has the title Fī al-'āla al-muḥriqa "On the burning instruments", the Tehran manuscript has a title added in a later hand Kitāb al-harrāqāt "The book of burners". Ibn Sahl is the first Muslim scholar known to have studied Ptolemy's Optics, and as such an important precursor to the Book of Optics by Ibn Al-Haytham (Alhazen), written some thirty years later. Ibn Sahl dealt with the optical properties of curved mirrors and lenses and has been described as the discoverer of the law of refraction (Snell's law). Ibn Sahl uses this law to derive lens shapes that focus light with no geometric aberrations, known as anaclastic lenses. 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 designed convex lenses that focus light rays that are parallel, which can cause an object to burn at a specific distance.

[Interpretation of Ibn Sahl's construction. If the ratio of lengths L_1/L_2 is kept equal to n_1/n_2 then the rays satisfy the law of sines, or Snell's law.

The inner hypotenuse of the right-angled triangle 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 change of medium whose face is vertical at the point where the two hypotenuses intersect. The ratio of the length of the smaller hypotenuse to the larger is the ratio of the refractive indices of the media. | upload.wikimedia.org/wikipedia/commons/3/38/Ibn///Sahl.svg]

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