Images in Christmas Balls

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 pr...

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Bibliographic Details
Published in:arXiv.org 2005-12
Main Authors: Eef van Beveren, Kleefeld, Frieder, Rupp, George
Format: Article
Language:English
Subjects:
Exact solutions
Light reflection
Telescopes
Textbooks
Online Access:Get full text
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Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.0503069