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 Buwayhid 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 ms.
contains a section missing entirely from the Tehran ms. The Damascus ms. has
the title Fī al-'āla al-muḥriqa "On the burning
instruments", the Tehran ms. 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.
Interpretation of Ibn
Sahl's construction. If the ratio of lengths is kept equal to 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 crystal 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 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.
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