ABSTRACT
In Books IV and V of Book of Optics, Ibn al-Haytham [1] studied systematically and exhaustively the reflection of light on various mirrors. In the fifth book, he raises the issue that bears his Latin name: ‘The problem of Ibn al-Haytham’. He begins, in the simplest case, with that of the plane mirror. If two points A and B and a plane mirror DE are given, how to determine the point of reflection of a light ray emitted from A, reflected to B. One must then find a point C on the mirror so that the straight lines AC and BC represent the incident and the reflected rays. Later, Ibn al-Haytham provides a mechanical model of the mechanism of light reflection. Given a circular pool, find all paths from a ball A hitting a ball B after a single reflection on the pool table. This model is the general case encountered by Ibn al-Haytham immediately after the simple case, that is to say when the mirror is spherical, cylindrical or conical either concave or convex. The successors of Ibn al-Haytham resumed this issue, from the Arabic text by Kamãl al-Din al-Fãrisĩ [2] and Ibn H d ud [3], or from the Latin translation of his Optics, published by Risner [4]. Still, this Latin translation is poor and contains some inaccuracies that have been unfairly charged to Ibn al-Haytham. However, Galileo, Huygens, Sluse, Barrow and many others worked from this translation. The situation remained the same until 1942. It was in effect on that date that the physicist and historian of Optics M Nazif [7] wrote a study of optics of Ibn al-Haytham starting from the Arabic manuscripts. Recently, A Sabra [13,14] gave the edition of books IV and V of the Treaty. To pose and solve the problem that bears his name, Ibn al-Haytham outlines and demonstrates six lemmas. We will discuss here the first two.
