IMAGINARY IMAGES. 



convex lenses, subject, nevertheless, to some qualifications which 

 will be explained hereafter. 



36. The optical effect of a concave is, as might be expected, 

 the reverse of that of a convex lens. In no position can a con- 

 cave lens produce a real optical image. 



Let A c, fig. 25, be such a lens, and LM an object placed any- 



Fig. 25. 



L 



where before it. The rays which diverge from the various points 

 of L M will, after passing through the lens, diverge as if they had 

 issued from the corresponding points of a similar object I in, 

 nearer to the lens ; and an eye placed behind the lens will see the 

 object, not as it is at L M, but as it would be if placed at / w, and 

 reduced to a lesser magnitude. 



This explains a fact which must be familiar to every one who 

 may have looked through concave glasses, such for example as the 

 spectacles of short-sighted persons. All objects seen through 

 them appear to be diminished. 



37. The focal length of a lens depends on the degree of refraction 

 which it is capable of producing on the rays which pass through 

 it. The greater this refraction is the more the convergence of the 

 rays will be increased, and the less will be the focal length. 



The refracting power of a lens depends partly on its form, and 

 partly on the material of which it is made. With a given 

 material the refracting power will increase with the convexity. 

 The more convex the surfaces are the greater will be the refract- 

 ing power, and the less the focal length and the nearer to the lens 

 will the image of an object at a given distance be produced, the 

 lens being supposed to be convex. 



38. But the refracting power, and therefore the focal length, also 

 depends on the material of the lens. Two lenses having the same 

 convexity will have different refracting powers, and therefore 

 different focal lengths, if they are made of different transparent 

 bodies, or even of different sorts of the same substance. A lens 

 of water will have a longer focus than a similar one of glass; 

 and the latter will have a longer focus than a similar one 

 made from a diamond, because water has a less refracting power 

 than glass, and glass less than diamond. In the same way, a 



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