Chap. XXV.] 



CONCAVE LENSES. 



approaches nearer to F, till, if f be at an infinite dis- 

 tance, when rays from it may be considered to be 

 parallel, f will approach to F till it coincides with it, 

 In all these cases the foci are real. Suppose now 

 that the luminous point is nearer to the lens than the 

 focal distance, the emergent 

 rays will be divergent. They 

 will not meet, and no real 

 focus will be formed. This 

 is shown in Fio;. 142, where 



.LI i IT j. i Fig. 142. Virtual Focus of a 



F is at the local distance, and Convex Lens. 



the luminous point is f. 



These divergent rays, however, if prolonged back- 

 wards, as represented by the dotted lines, will meet in 

 a point at /' on the same side of the lens as the luminous 

 point. This point is a virtual focus; convex lenses, 

 then, have both real and virtual foci. 



Concave lenses. In Fig. 143, LL' represents a 

 concave lens, with parallel rays falling upon it, n and 



Fig. 143. Principal Focus 

 (Virtual) of a Concave 

 Lens. 



Fig. 144. Conjugate Foci 

 of a Concave Lens. 



n being the normals. After refraction the rays 

 diverge, but their prolongations backwards meet in F ; 

 F is called the principal focus, but it is virtual. 



Should the rays diverge towards the concave lens, 

 their conjugate foci will be obtained, as in the convex 

 lens ; but both will be on the same side of the lens. 

 The conjugate foci are also virtual. Thus, in Fig. 144, 

 if the luminous point be at F, outside of the principal 



