308 



THE SPECIAL SENSES. 



points within the limits specified will have their corresponding 

 conjugate foci, at which their images will be formed by the lens. 

 Lastly, if a luminous point is placed at v, Fig. 124, nearer to the 

 lens than the principal focal distance, the cone of strongly di- 

 vergent rays that falls upon the lens, although refracted, is still 

 divergent after leaving the lens on the other side and consequently 

 is not focused and forms no real image of the point. For every lens 

 there is a point known as the optical center, and for biconvex lenses 

 this point lies within the lens, o. The line joining this center and 

 the principal focus is the principal axis of the lens (o-F, Fig. 124) . 

 All other straight lines passing through the optical center are known 

 as secondary axes. Rays of light that are coincident with any of these 

 secondary axes suffer no angular deviation in passing through the 

 lens; they emerge parallel to their line of entrance and practically 

 unchanged in direction. Moreover, any luminous point not on the 



Fig. 125._ Diagrams to illustrate the formation of an image by a biconvex lens: a, For* 

 mation of the image of a point ; 6, formation of the images of a series of points. 



principal axis will have its image (conjugate focus) formed some- 

 where upon the secondary axis drawn from this point through the 

 optical center. The exact position of the image of such a point 

 can be determined by the following construction (Fig. 125) : Let A 

 represent the luminous point in question. It will throw a cone of 

 rays upon the lens, the limiting rays of which may be represented by 

 A-b and A-c. One of these rays, A-p, will be parallel to the prin- 

 cipal axis, and will therefore pass through the principal focus, F. 

 If this distance is determined and is indicated properly in the 

 construction, the line A-p may be drawn, as indicated, so as to 

 pass through F after leaving the lens. The point at wnich the 

 prolongation of this line cuts the secondary axis, A-o, marks the 



