{
  "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
}