The cat’s-eye phenomenon: a mathematical approach
This paper provides a mathematical basis for the well-known cat’s-eye effect appearing on chatoyant gemstones. After reminding the reader of the physical origin of this effect and the conditions for observing it, we introduce all required parameters and some reasonable assumptions in order to simpli...
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| Format: | Article |
| Language: | English |
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Académie des sciences
2025-02-01
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| Series: | Comptes Rendus. Physique |
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| Online Access: | https://comptes-rendus.academie-sciences.fr/physique/articles/10.5802/crphys.231/ |
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| author | Gauthier, Jean-Pierre Bui, Thanh Nhan Fereire, Jacques |
| author_facet | Gauthier, Jean-Pierre Bui, Thanh Nhan Fereire, Jacques |
| author_sort | Gauthier, Jean-Pierre |
| collection | DOAJ |
| description | This paper provides a mathematical basis for the well-known cat’s-eye effect appearing on chatoyant gemstones. After reminding the reader of the physical origin of this effect and the conditions for observing it, we introduce all required parameters and some reasonable assumptions in order to simplify the calculations. In fact, we describe the motion of a point located at the apex of the cat’s-eye line in the “main” plane, defined by the directions of the source and the observer and perpendicular to the set of acicular inclusions responsible for the optical phenomenon. These calculations confirm the qualitative cat’s-eye behavior commonly observed in various situations, when the source or the observer moves around the cabochon or when the stone rotates under them. |
| format | Article |
| id | doaj-art-d81ff8a3307245b3b58a2a0e3808f473 |
| institution | Kabale University |
| issn | 1878-1535 |
| language | English |
| publishDate | 2025-02-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Physique |
| spelling | doaj-art-d81ff8a3307245b3b58a2a0e3808f4732025-02-07T13:54:45ZengAcadémie des sciencesComptes Rendus. Physique1878-15352025-02-0126G118119810.5802/crphys.23110.5802/crphys.231The cat’s-eye phenomenon: a mathematical approachGauthier, Jean-Pierre0Bui, Thanh Nhan1Fereire, Jacques2Centre de Recherches Gemmologiques, 2 rue de la Houssinière, 44322 Nantes, FranceRue du Compas 47/4, 1070 Bruxelles, BelgiumCentre de Recherches Gemmologiques, 2 rue de la Houssinière, 44322 Nantes, FranceThis paper provides a mathematical basis for the well-known cat’s-eye effect appearing on chatoyant gemstones. After reminding the reader of the physical origin of this effect and the conditions for observing it, we introduce all required parameters and some reasonable assumptions in order to simplify the calculations. In fact, we describe the motion of a point located at the apex of the cat’s-eye line in the “main” plane, defined by the directions of the source and the observer and perpendicular to the set of acicular inclusions responsible for the optical phenomenon. These calculations confirm the qualitative cat’s-eye behavior commonly observed in various situations, when the source or the observer moves around the cabochon or when the stone rotates under them.https://comptes-rendus.academie-sciences.fr/physique/articles/10.5802/crphys.231/ChatoyancyCat’s-eyeAsterismOptical phenomenonMathematical approach |
| spellingShingle | Gauthier, Jean-Pierre Bui, Thanh Nhan Fereire, Jacques The cat’s-eye phenomenon: a mathematical approach Comptes Rendus. Physique Chatoyancy Cat’s-eye Asterism Optical phenomenon Mathematical approach |
| title | The cat’s-eye phenomenon: a mathematical approach |
| title_full | The cat’s-eye phenomenon: a mathematical approach |
| title_fullStr | The cat’s-eye phenomenon: a mathematical approach |
| title_full_unstemmed | The cat’s-eye phenomenon: a mathematical approach |
| title_short | The cat’s-eye phenomenon: a mathematical approach |
| title_sort | cat s eye phenomenon a mathematical approach |
| topic | Chatoyancy Cat’s-eye Asterism Optical phenomenon Mathematical approach |
| url | https://comptes-rendus.academie-sciences.fr/physique/articles/10.5802/crphys.231/ |
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