REFRACTION OF RAYS THROUGH CURVED SURFACES. 415 
529. When the surface which separates the two media is 
not flat, hut is either convex or concave (bulging or hollowed- 
out), a very important alteration is produced in the direction 
e h 
of the rays that fall upon it. Thus we shall suppose that 
three diverging rays, issuing from a point, a (fig. 206), and 
traversing the air, strike upon a convex surface of glass, bb\ 
The central ray a c falls upon the glass in a direction perpen¬ 
dicular to its surface at that point, and passes-on unchanged 
in its course. But the ray a d falls upon the surface very 
obliquely; and consequently in entering the glass it will be 
bent towards the line e , which is perpendicular to the surface 
at the point where it enters, and will pass onwards in the 
direction/ In the same manner, the ray a g will be refracted 
into the direction i. Hence these rays, now converging , would 
be found, if prolonged, to meet each other again; and the 
point at which they meet is termed the focus. To this point 
all the other rays which fall upon the convex surface, at a 
moderate distance from the central ray, will also be conducted. 
530. On the other hand, if the surface of the glass, instead 
of being convex, is concave ', the diverging rays which fail upon 
it will be made to diverge still more. Thus in fig. 207, let a 
be the point whence the rays issue, and b b the surface of the 
lens; the central ray a c will pass-on unchanged as before; 
but the ray a d will be bent towards the perpendicular e , so 
as to pass-on in the direction/; and the ray a j will be bent 
towards the perpendicular k, into the direction i. It is easy 
to understand that the change of direction will be greater, as 
