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Images in Christmas Balls

Eef van Beveren·Frieder Kleefeld·George Rupp
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Abstract

We describe light-reflection properties of spherically curved mirrors, like balls in the Christmas tree. In particular, we study the position of the image which is formed somewhere beyond the surface of a spherical mirror, when an eye observes the image of a pointlike light source. The considered problem, originally posed by Abu Ali Hasan Ibn al-Haitham -- alias Alhazen -- more than a millennium ago, turned out to have the now well known analytic solution of a biquadratic equation, being still of great relevance, e.g. for the aberration-free construction of telescopes. We do not attempt to perform an exhaustive survey of the rich historical and engineering literature on the subject, but develop a simple pedagogical approach to the issue, which we believe to be of continuing interest in view of its maltreating in many high-school textbooks.

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Eef van Beveren, Frieder Kleefeld, George Rupp. 2005-12-19. Images in Christmas Balls. https://doi.org/10.1088/0143-0807%2F27%2F2%2F016

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