Images in Christmas Balls

Details Images in Christmas Balls Images in Christmas Balls

2005-03-09

arxiv.org/abs/physics/0503069v3

Eur. J. Phys. 27 (2006) 337-346

Physics

Physics Education

13 pages, 7 figures plain LaTeX; Also see http://cft.fis.uc.pt/eef/mirrors.htm, revised version has simplified formulas, mor

Scientific paper

10.1088/0143-0807/27/2/016

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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