MAGNIFYING GLASSES. 



12. In all cases in which magnifying lenses are used, except 

 where the lens is large, and the magnifying power low, the eye of 

 the observer should be placed as close as possible to the lens, the 

 pupil being as nearly as possible concentric with the lens ; for 

 since the pencils of rays, which proceed from the extreme points 

 of the object, intersect at an angle equal to that formed by lines 

 drawn from the extremities of the object to the centre of the lens, 

 they will diverge after passing through the lens, at the same 

 angle ; and the farther the eye is removed from the lens, the more 

 rays it will lose, and beyond a certain limit of distance, a part 

 only of the object will be visible. 



13. Since eyes of average sight are adapted to the reception 

 of parallel rays, an object seen through a lens by them will be 

 distinctly visible, only on the condition that its distance from the 

 lens shall be equal to the focal length ; for, in that case, the rays 

 which diverge from each point of the object, will emerge from the 

 lens parallel, and therefore suitable to the power of the eye. 



It is for this reason that the magnifying powers of lenses are 

 estimated, by comparing their focal lengths with the distance of 

 distinct vision. For since the focal length is always the distance 

 of the object from the lens for average eyes, the distance of 

 distinct vision, divided by it, will, according to what has 

 been explained, be the magnifying power of the lens for such 

 eyes. 



14. The focal length of a lens will be less in proportion as its 

 refracting power upon the light transmitted through it is greater ; 

 but the refracting power of the lens depends partly on its con- 

 vexity and partly on its material. 



With the same material the refracting power will be greater 

 and the focal length less, as the convexity is increased ; and, on 

 the other hand, with a given convexity, the refracting power will 

 be greater, and the focal length less, as the refracting power of 

 the material, of which the lens is made, is greater. Thus, for 

 example, if two lenses be composed of the same sort of glass, that 

 which has the greater convexity will have the less focal length ; 

 and if, on the other hand, two lenses, one composed of glass and 

 the other of diamond, have equal convexities, the latter will have 

 a less focal length than the former ; because diamond has a 

 greater refracting power than glass. 



15. It will be evident, from what has been explained, that if 

 two lenses be formed of materials having different refracting 

 powers, such for example as glass and diamond, so as to have 

 equal focal length, that which has greater refracting power will 

 have the less convexity. 



If two lenses therefore be formed, having the same magnifying 

 104 



