THE OPTICAL DEFECTS OF THE EYE. 9 



pounded not long since, viz. : — When an object is 60 inches in front of 

 a 10 inch convex lens, how far behind the lens will be the inverted image 

 of the object? Or, to express it differently, when a divergent pencil of 

 light emanates from a point 60 inches from a 10 inch convex lens, at 

 what distance behind the lens will the pencil be converged to a focus ? 



Now, we know that a lens of 60 inches focus, placed in the position 

 of the 10 inch lens, would render the rays parallel that fall upon it 

 from the object 60 inches distant. Were it possible, therefore, 

 to divide the 10 inch lens into two lenses, one having a focus of 

 60 inches to render the rays parallel, the remaining portion 

 would bring these parallel rays to a focus at its principle focus. 

 Deducting then ^-^ from -^ will give the strength of the remaining 

 portion of the lens -^—-J^=-^=-^ ; the two parts then -^^ and -^ 

 are equal to the one lens ■^. And, as the -^ will render the rays 

 parallel Irom the object 60 inches distant, and these parallel rays 

 falling upon the other part -j^, they will be brought to a focus at the 

 principle focus of this part, viz : at 12 inches from the lens. Let us 

 illustrate this with another example. Suppose that an object is 30 

 inches in front of a convex lens of 10 inch focus, and we wish to 

 know how far behind the lens will be the focus of a pencil of rays 

 diverging from a point in the object. We will have ■^— ^0=-^= ^-^ ; 

 this -j^ represents the power of a 15 inch lens, which we know will 

 bring the parallel rays to a focus at 15 inches behind the lens. 



Eig. 4 illustrates this ; O represents an object 30 inches from a 

 ten inch convex lens, the lens supposed to be divided into two parts, 

 one having a focus of 30 inches, and the other a focus of 15 inches. 

 The 30 inch lens refracts the rays of the divergent pencil d, d, d, d, 

 so as to render them parallel, as shown at P, P, P, P, P. These 

 parallel rays, meeting the 15 inch lens, are again refracted and 

 are converged to a focus at F, which is the principle focus of the 

 lens, viz., at 15 inches. 



