8 THE OPTICAL DEFECTS OF THE EYE. 



and as a 2 inch lens is just half the strength, it is simply expresed 

 I", and as a 3 inch lens has just one-third the strength of a 1 inch, it 

 is written f ; a 4 inch is ^ &c. We "will find that this nomenclature 

 is not only very convenient, but scientifically correct. 



!For example, suppose we have two lenses of 4 inch focus each, and 

 we wish to know their combined "power " when used as one lens ; 

 we simply add their reciprocals thus i4-5=-|=|-. The two lenses 

 have, therefore, the magnifying power of |-, which is the reciprocal of 

 2, and are consequently, together, equal to a 2 inch lens, which can 

 be proved by actual measurement. Again, suppose we have a 6 inch 

 lens, and a 12 inch lens, and we wish to know their combined strength,, 

 ^+-iV=Ta"=T "Pf^ich represents the power of a 4 inch lens ; the 6 

 and the 12 inch lenses taken together being equal to one lens having 

 a focus of 4 inches. 



To save repetition, I may here state that when a concave lens- 

 enters into combination with a convex lens, it has a neutralizing effect, 

 upon the convex lens. If we have a convex 6 and a concave 6 

 the one would neutralize the other, — thus i— i=:0. But if the 

 convex lens has the higher power, the concave lens simply weakens 

 it — that is, lengthens its focus — thus, if we have a convex 6 and 

 a concave 9 the result will be i — i = -3^ — -i^ = Ts, which repre- 

 sents the strength of one lens having a focus of 18 inches. If, how- 

 ever, the concave lens has the higher "power" it will simply be 

 weakened by the concave lens, — the combination will be equal to 

 a concave lens having a lower " power," or a longer focus than the 

 concave lens taken, — thus reversing the last example, suppose we 

 have a concave 6 and a convex 9, we will then have — g-+-g- or simply 

 1^— g-=-i^— ^= — rs, which represents the strength of a concave lens 

 having a focus of 18 inches. 



This fractional nomenclature (taking 1 for numerator and the 

 focal length of the lens for denominator) will assist us also in under- 

 standing the principle of the formation of images at different distances 

 behind a convex lens, according to the distance of objects in front of it. 



Let me remind you that when an object, for instance the flame of 

 a candle, is placed in the focus of a convex lens, the diverging rays 

 of light from the object are rendered parallel by the lens. Thus, a 

 lens having a focus of 20 inches will render parallel pencils of light 

 diverging from an object 20 inches from the lens. Bearing this in 

 mind let us again try the solution .of the following question, pro- 



