Page:Optics.djvu/104

 (Fig. 103.) be two incident rays inclined to each other at an infinitely small angle,, , the refracted rays. Let, be perpendicular to ,. Then, ; therefore ,. Now it was proved in the former proposition that, and , are evidently integrals of these differentials beginning together from nothing.

To return then to our problem,

and therefore the ray is refracted to.

106. These caustics are exactly analogous to those before treated of, being formed by the successive intersections of refracted rays, as those were by reflected ones.

. Required the caustic to a plane refracting surface.

Let (Fig. 104.) represent an incident ray,  the refracted one;,  are the rectangular co-ordinates of a point  on that line;  is parallel to.