470 REFRACTION THROUGH LENSES. 



If the luminous point is nearer to the lens than the 

 focus, as for example the point A in fig. 269,/ being 



the focus, the rays from A will diverge still more, and 

 the lens can no longer render them convergent nor 

 make them parallel after emergence; the rays will 

 still diverge after having passed through the lens, 

 but their divergence will be less than it was before 

 reaching the lens ; and the rays from A will, after 

 having passed through the lens, appear to proceed from 

 a point a, farther from the lens than A. 



Refraction through lenses, like reflection from mirrors, 

 gives rise to the production of optical images, and the 

 same distinction must be made between real and virtual 

 images; a in fig. 269 is a virtual image of A. 



In order to determine the position and magnitude of 

 images produced by lenses, it is not only necessary to 

 know that rays of light which proceed from a point 

 near the axis are refracted so as to converge to a point 

 near the axis, or so as to appear to diverge from that 

 point, and also that rays which are parallel to the 

 axis converge in the focus, while, conversely, rays which 

 diverge from the focus are refracted in parallel directions ; 

 but it is also important to consider that those rays which 



