München 2019 – scientific programme

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GP: Fachverband Geschichte der Physik

GP 11: The tools of physical theory

GP 11.1: Talk

Wednesday, March 20, 2019, 14:00–14:30, HS 9

The Fresnel wave surface in the 1820s and 1830s: physical tool or object of mathematical study? — •Marta Jordi Taltavull — Johannes Gutenberg Universität Mainz

In 1821 Augustin Fresnel proposed that the propagation of light through biaxial crystals could be described by a special kind of surface, which is nowadays called the Fresnel wave surface. Biaxial crystals had posed a very challenging problem for optics ever since the 17th century, for light passing through them did not follow the ordinary laws of light propagation. The Fresnel surface became a tool to describe and understand better this anomalous behavior.

Yet Fresnel wave surface did not just remain a tool. Mathematicians and natural philosophers, in particular James MacCullagh, William R. Hamilton and Julius Plücker, turned their attention to the Fresnel surface as an object of mathematical study in the 1830s. They embedded it into more general mathematical theories, such as inversive geometry, and analyzed its properties as a mathematical surface. Relying on such properties, Hamilton even predicted a new optical phenomenon, conical refraction. Later, the Fresnel surface became just one instantiation of a special class of a more general kind of mathematical surfaces called quartics.

Thus the Fresnel wave surface had acquired a life on its own beyond biaxial crystals, having changed from tool in physics to object of study in mathematics, while mediating between both physical and mathematical cultures.