IMAGES BY LENSES. 
If a radiant point be placed at A, fig. 23, at the principal focus 
of a lens, the rays diverging from it after passing through the 
lens will be rendered parallel, as may be shown experimentally by 
receiving them upon a screen as indicated in the figure. An 
Fi?. 23. 
illuminated disc will be produced upon the screen equal in size 
to the lens. 
34. Having explained the change of position which the image 
undergoes by removing the object indefinitely from the lens, let 
us now consider how its position will be affected if the object be 
moved indefinitely towards the lens. 
It is evident, from what has been already explained, that when 
a very distant object approaches the lens, no change whatever in 
the position of its image is at first produced, the image remaining 
always at the principal focus, but the magnitude of the image will 
be sensibly augmented, its linear dimensions increasing in exactly 
the same proportion as the distance of the object from the lens 
decreases. 
When, however, the object has approached within a certain 
limit of distance, the image will begin, at first very slowly, and 
afterwards more rapidly, to recede from the lens. It will thus 
continue to recede, and at the same time to increase in its dimen¬ 
sions, until the object is brought to a distance from the lens equal 
to its focal length. The image having then augmented indefinitely 
in magnitude and distance, will altogether disappear. 
This is, therefore, an exceptional position of the object, in which 
no optical image is produced by the lens. 
If we suppose the object to be brought still nearer to the lens 
than its focal distance, no actual optical image will be produced, 
but the rays of light which, having issued from the various points 
of the object, pass through the lens, will be refracted by it into 
directions such as they would have had if they had issued from a 
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