REFRACTION OP RAYS THROUGH CURVED SURFACES. 415 



529. When the surface which separates the two media is 

 not flat, but is either convex or concave (bulging or hollowed- 

 out), a very important alteration is produced in the direction 



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 fall 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 h, into the direction i. It is easy 

 to understand that the change of direction will be greater, as 



