ALHACEN’S APPROACH TO ‘‘ALHAZEN’S PROBLEM’’

Abstract

In the fifth book of his De aspectibus, the medieval Latin version of Ibn al-Haytham’s Kitāb al-Manāẓir, Alhacen undertakes to determine precisely where a given ray of light will reflect to a given center of sight from a variety of convex and concave mirrors based on circular sections. As applied specifically to convex and concave spherical mirrors, this problem exercised several seventeenth-century thinkers, Christiaan Huygens foremost among them, and in that context it soon became known as ‘‘Alhazen’s Problem.’’ By current standards, Alhacen’s solution (or solutions) of this problem is deficient in comparison to that of Huygens and later mathematicians. It is my purpose in this paper to show by reconstruction that in fact, far from deficient in any absolute sense, Alhacen’s approach to this problem was remarkably ingenious and elegant in its conceptual simplicity.