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Reproduction of a page of Ibn Sahl's manuscript showing his discovery of the law of refraction (from Rashed, 1990).

Interpretation of Ibn Sahl's construction. If the ratio of lengths L₁ / L₂ is kept equal to n₁ / n₂ then the rays satisfy the law of sines, or Snell's law.

For the poet, see Ibn Sahl of Sevilla.

Ibn Sahl (Abu Sa`d al-`Ala' ibn Sahl, born ca. 940, died ca. 1000) was an Arabian mathematician and optics engineer associated with the court of Baghdad. In 984 he wrote a treatise On Burning Mirrors and Lenses in which he set out his understanding of how curved mirrors and lenses bend and focus light. Rashed^[1] credited Ibn Sahl with discovering the law of refraction, usually called Snell's law.

In the reproduction of the figure from Ibn Sahl's manuscript, the critical part is the right-angled triangle. The inner hypotenuse 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 crystal whose face is vertical at the point where the two hypotenuses intersect.^[2] According to Rashed,^[1] the ratio of the length of the smaller hypotenuse to the larger is the reciprocal of the refractive index of the crystal.

The lower part of the figure shows a representation of a plano-convex lens (at the right) and its principal axis (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 point 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 (965–1039), one of the greatest Arabic scholars of optics. In modern times, Rashed found the manuscript to have been dispersed over two libraries. He reassembled it, translated it, and published it.^[3]

• List of Arab scientists and scholars

1. ^ ^{a b} Rashed, R., "A pioneer in anaclastics: Ibn Sahl on burning mirrors and lenses," Isis, 81, pp. 464–491, 1990.
2. ^ Kurt Bernardo Wolf, Geometric Optics on Phase Space, p. 9, Springer, 2004, ISBN 3540220399 online
3. ^ Rashed, R., Géométrie et dioptrique au Xe siècle: Ibn Sahl, al-Quhi et Ibn al-Haytham. Paris: Les Belles Lettres, 1993.