and the Evolutions of Reflected Wave-Fronts. 



149 



rays issuing from a point, is very beautifully shown, the 

 spherical wave diverging from one focus being transformed 

 by reflexion into a converging sphere which shrinks to a 

 point at the other focus. 



The transformation of a spherical into a plane wave by a 

 parabolic mirror is also well shown (fig. 1). 



Fier. 1. 



The effect of spherical aberration of circular mirrors is 

 beautifully exhibited in several cases. 



When a plane wave enters a hemispherical mirror the 

 reflected wave-front is cusped, and the cusp will be seen to 

 lie always on the caustic surface. The form of the complete 

 wave in this case is not unlike a volcanic cone with a bowl- 

 shaped crater, the bowl eventually collapsing to a point, at 



R* 2. 



the focus of the mirror, the sides of the cone running in 

 under it and crossing. From now on the wave diverges, and 

 goes out of the mirror in a form somewhat resembling the 

 bell of a medusa, the caustic form by twice reflected rays 

 being traced by a second cusp (fig. 2). 



