dorsal/arxiv
View SchemaImages in Christmas Balls
| Authors | Eef van Beveren, Frieder Kleefeld, George Rupp |
|---|---|
| Categories | |
| ArXiv ID | physics/0503069 |
| URL | https://arxiv.org/abs/physics/0503069 |
| DOI | 10.1088/0143-0807/27/2/016 |
| Journal | Eur. J. Phys. 27 (2006) 337-346 |
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.
{
"annotation_id": "35e716ca-837e-4282-964d-60d803e5c968",
"date_created": "2026-03-02T18:00:56.227000Z",
"date_modified": "2026-03-02T18:00:56.227000Z",
"file_hash": "511ae9f28d6fd0541ee5e4c6a2e5bda19f45dc2d3bf9a3e63a59fa13cffb780f",
"private": false,
"record": {
"abstract": "We describe light-reflection properties of spherically curved mirrors, like\nballs in the Christmas tree. In particular, we study the position of the image\nwhich is formed somewhere beyond the surface of a spherical mirror, when an eye\nobserves the image of a pointlike light source. The considered problem,\noriginally posed by Abu Ali Hasan Ibn al-Haitham -- alias Alhazen -- more than\na millennium ago, turned out to have the now well known analytic solution of a\nbiquadratic equation, being still of great relevance, e.g. for the\naberration-free construction of telescopes. We do not attempt to perform an\nexhaustive survey of the rich historical and engineering literature on the\nsubject, but develop a simple pedagogical approach to the issue, which we\nbelieve to be of continuing interest in view of its maltreating in many\nhigh-school textbooks.",
"arxiv_id": "physics/0503069",
"authors": [
"Eef van Beveren",
"Frieder Kleefeld",
"George Rupp"
],
"categories": [
"physics.ed-ph",
"physics.optics"
],
"doi": "10.1088/0143-0807/27/2/016",
"journal_ref": "Eur. J. Phys. 27 (2006) 337-346",
"title": "Images in Christmas Balls",
"url": "https://arxiv.org/abs/physics/0503069"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "ec091458-2698-42d1-a23e-396903143d02",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}