Page:A history of the theories of aether and electricity. Whittacker E.T. (1910).pdf/156

so that total reflexion takes place, this ratio may be written in the form

$e^{\theta {\sqrt {-1}}}$,

where θ denotes a real quantity defined by the equation

$\tan {{\frac {1}{2}}\theta }={\frac {(\mu _{1}^{2}\sin ^{2}i-\mu _{2}^{2})^{\frac {1}{2}}}{\mu _{1}\cos {i}}}$.

Fresnel interpreted this expression to mean that the amplitude of the reflected light is equal to that of the incident, but that the two waves differ in phase by an amount θ. The case of light polarized at right angles to the plane of reflexion may be treated in the same way, and the resulting formulae are completely confirmed by experiment.

A few months after the memoir on reflexion had been presented, Fresnel was elected to a seat in the Academy, and during the rest of his short life honours came to him both from France and abroad. In 1827 the Royal Society awarded him the Rumford medal; but Arago, to whom Young had confided the mission of conveying the medal, found him dying; and eight days afterwards he breathed his last.

By the genius of Young and Fresnel the wave-theory of light was established in a position which has since remained unquestioned, and it seemed almost a work of supererogation when, in 1850, Foucault^[1] and Fizeau,^[2] carrying out a plan long before imagined by Arago, directly measured the velocity of light in air and in water, and found that on the question so long debated between the rival schools the adherents of the undulatory theory had been in the right.

1. Comptes Rendus, xxx (1850), p. 551.
2. Ibid., p. 362