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Alhazen's problem - mklabgr - 06-22-2026
Alhazen's problem
Alhazen’s Problem is a famous challenge in geometrical optics that asks: given two points and a circular (or spherical) mirror, where on the mirror must a light ray strike so that it reflects from one point to the other according to the law of reflection? Named after the 11th-century mathematician and physicist Ibn al-Haytham, who gave the first general solution in his Book of Optics, the problem can also be viewed as a billiards problem or as finding an ellipse tangent to a circle with the given points as foci.
While special cases were known earlier, the general problem proved remarkably difficult, leading mathematicians such as Christiaan Huygens to develop geometric solutions involving conic sections. In the 20th century it was shown that the problem reduces to solving a quartic (fourth-degree) equation and cannot, in general, be solved using only a straightedge and compass. The problem remains historically important because it connects geometry, optics, algebra, and the mathematics of reflection.
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