THE FORMATION OF A 'REAL IMAGE' 23 



principal foci and distances are known, can be found from the formula 

 - + ,= 7- by assigning for the value of p the distance of the prin- 

 cipal focus of the first lens from the second, and so on. 



Example. Parallel rays fall on an equiconvex lens of four inches 

 focus. Two inches from this lens is another equiconvex lens of 

 three inches focus. Find the distance of the focal point from this 

 last lens, to which the rays will be brought. It is evident that the 

 rays would be brought by the first lens to a focus two inches behind 

 the second if it were not there. This point, which is negative with 

 regard to the second lens, must be taken as the value of p in the 

 formula. We have, therefore : 



-2 



3 



6 



Hitherto our attention has been confined, in studying the action 

 of lenses, to the manner in which they act upon a bundle of parallel 

 rays, or upon a pencil of rays issuing from a radiant point. More- 

 over, we have considered this point as situated in the line of axis. 

 But the surface of every luminous body may be regarded as compre- 

 hending an infinite number of such points, from every one of which 

 a pencil of rays proceeds, to be refracted in its passage through the 

 lens according to the laws enunciated. In this way a complete 

 image, i.e. picture of the object, will be formed upon a suitable 

 surface placed in the position of the focus. 



There are two kinds of image formed by lenses, a real image and 

 a virtual image. 



1. The formation of a real image means the production of a 



K 



FIG. 26. The formation of a real image. 



picture by a lens, or a combination of lenses, which can be thrown 

 upon a screen ; such are the images of a projection lantern and the 

 image produced by the camera upon the focussing glass. The manner 

 in which this takes place will be understood by reference to fig. 26, 

 where A B is an object placed beyond P, the principal focus of the 

 aplanatic combination. From every point of A B are rays radiating 

 at every possible angle. Let AF and AH be two such rays 

 radiating from the point A. Now if the refraction of these rays be 



