136 The Luminiferous Medium. 



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

 the form 



where 6 denotes a real quantity defined by the equation 



tan 



cos ^ 



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 0. 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* and Fizeau,f 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. 



* Comptes Rendus, xxx (1850), p. 551. t Ibid., p. 562. 



