A Pioneer in Anaclastics: Ibn Sahl on Burning Mirrors and Lenses

Abstract

THE GEOMETRICAL STUDY OF LENSES was essential for the development of optics in the late sixteenth and early seventeenth centuries.' This study, which historians have seen as a turning point in the history of optics, was designated as either anaclastics or dioptrics. In writing the history of this chapter, it is common practice to give prominence to Kepler, some of Mersenne's circle, Willebrord Snellius, and Descartes. Furthermore, the perceived modernity of the optics of this period is frequently explained, partially at least, by external reasons: a very modest technical advance in the construction of optical instruments.A reading of the eleventh-century Book of Optics (Kitab al-Mancdir) by Ibn al-Haytham, however, whether in Arabic or in Latin translation, should have suggested to historians that research on anaclastics started well before the late sixteenth century. In Book 7 there is a study of the spherical diopter and the spherical lens.2 Furthermore, Ibn al-Haytham devoted an entire memoir to the burning sphere, whose scientific and historical importance is unanimously recognized. This work contains an examination of double refraction in the sphere and of related problems. Three centuries later, Kamal al-Din al-Farisi wrote a commentary on the work and used it for the first correct explanation of the rainbow.3 Until now, however, historians have not constructed a clear picture of Ibn al-Haytham's research on lenses and of anaclastics in general. For example,

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“…This statement together with (6) is enough to uniquely specify the transmitted ray. This law has been known for over a millennium [40]. We shall write the incident unit direction vector as → i , similarly for the reflected ray direction we use → r and for the transmitted ray direction we shall write → t .…”

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“…Abu Sad Al Alla Ibn Sahl (940-1000), auteur d'un traité sur les instruments ardents vers 984, mathématicien associé à la cour de Bagdad, explique comment les lentilles et les instruments coniques dévient et focalisent la lumière [1,4]. On lui doit deux manuscrits découverts par Roshdi Rashed à Damas (Syrie) et à Téhéran (Iran).…”

“…Mustafa Nazif [8] était l'un des pionniers à se focaliser sur les travaux d'Ibn al Haytham. Roshdi Rashed a également très largement contribué à la mise en valeur et à la diffusion de ses travaux [1][2][3][4]. Abdelhamid I. Sabra a réalisé une première édition critique des 3 premiers livres d'Ibn al Haytham, ainsi que la traduction de ces livres en anglais [9].…”