Chap, xxiv.] REAL AND VIRTUAL Foci. 305 



meet in the principal focus. Similarly, the more f 

 approaches the mirror the smaller angle do its rays 

 make with the normal, the smaller, therefore, grows 

 the angle of reflection, and the more does F' approach 

 to c. When f is at c, its rays are normal to the sur- 

 face ; they are reflected in the same line, and the 

 source of light and the focus coincide. 



Real and virtual . foci. In all the cases that 

 have been considered the source of light is not nearer 

 the mirror than the principal focus, and the principal 

 and conjugate foci liave all been on the same side of the 

 mirror as the source of light. They are, therefore, 

 called real foci. When, however, the source of light 

 is nearer the mirror than the principal focus, the 

 angle of incidence is so great that the reflected rays 

 become divergent from the axis. Thus, in Fig. 181, 

 AB is again the mirror, and the other letters are also 

 the same as before, f is the 

 source of light, /A /B are the in- 

 cident, and AM BN the reflected 

 rays. Being divergent, the re- 

 flected rays cannot meet on the 

 same side of the mirror as this 

 source of light, but if prolonged 

 backwards they meet in a point Fig . 131 ._ VirtualFocus 



F , which IS a Virtual foCUS, because of Concave Mirror. 



it is not on the same side of the 

 mirror as the source of light. 



In convex mirrors the foci are always virtual. 

 The principal focus (virtual) is formed by letting 

 parallel rays fall upon the mirror. The reflected rays 

 diverge, but if prolonged backwards meet in a point 

 on the prolongation of the principal axis. That point 

 is the principal virtual focus, and gives the principal 

 focal distance, equal to half the radius of curvature. 

 As in concave mirrors, if the rays falling on the 

 mirror be divergent, they form a conjugate focus, 

 u 7 



