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Mathematics at TCD 1592-1992

400
years of
MATHEMATICS
by T. D. Spearman

CONICAL
REFRACTION

Hamilton's work in geometrical optics led him naturally to study the equation of the wave-surface, which had recently been derived by Fresnel. Hamilton showed that this wave-surface, which had a rather complicated mathematical form, could have certain singular points called cusps. He deduced that under specific circumstances a wholly new and hitherto un-observed observed phenomenon, which was named conical refraction, should occur.

This was in 1832, and Hamilton proposed to Humphrey Lloyd, who had just been appointed to the chair of natural and experimental philosophy, that he should perform the experiment to find out if this new phenomenon was in fact there to be seen. It was not an easy experiment. The crystals---in which the refraction took place---that were initially available to Lloyd were not of high quality, and the effect was easily obscured. At first Lloyd almost despaired but then on 14 December, using a fine new crystal specimen which he had just received from London, he observed conical refraction, just two months after Hamilton had proposed the experiment to him.

This prediction, on the basis of rather sophisticated mathematical analysis, of a new an completely unanticipated phenomenon, and its subsequent observation, was a remarkable achievement. It was, and remains, a classic vindication of the scientific method. Honour and recognition came swiftly: Llowd was invited to give the main review lecture on optics to the British Association in 1834 and shortly afterwards was elected to the Royal Society; Hamilton, now a famous man, was knighted by the lord lieutenant in 1837.

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