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. 
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 lm, 
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 lm, 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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