The fact that other philosophers, notably Etienne Louis Malus and Augustin Fresnel, were pursuing the same investigations contemporaneously in France does not invalidate Brewster's claim to independent discovery, even though in one or two cases the priority must be assigned to others.
It is true that the dioptric apparatus was perfected independently by Fresnel, who had also the satisfaction of being the first to put it into operation.
Thanks to Fresnel and his followers, this department of optics is now precisely the one in which the theory has gained its greatest triumphs.
For the aggregate effect of the secondary waves is the half of that of the first Fresnel zone, and it is the central element only of that zone for which the distance to be travelled is equal to r.
When the primary wave is plane, the area of the first Fresnel zone is 7rXr, and, since the secondary waves vary as r 1, the intensity is independent of r, as of course it should be.