THE FOCUS-APERTURE RATIO. 



289 



their optical aberrations beautifully corrected, also that opticians 

 are unable to keep up these conditions as the powers increase. 

 If then the corrections of the higher powers are to be maintained 

 at the same excellence as the lower ones, down must come the 

 optical index. The conditions with photographic lenses are the 

 same ; lenses of //1 6 giving sharp images are common and cheap, 

 but when they rise to //6-5 they are scarce and expensive; 



Fig. 2. 



beyond that opticians introduce " atmosphere," only another 

 word for imperfect correction. 



In plotting the curves, each of the squares represents 1 inch. 

 The first is that of Prof. Abbe (fig. 1). Here we see, at once, that 

 the line is at a high angle with the base, also that the curve is not 

 smooth. From to 12 is one curve, from 12 to 30 is another, and 

 from thence to 80 is a straight line. The chief fault of this curve 

 is its high angle with the base ; it therefore represents a class of 

 objectives endowed with much " empty magnification." 



The next is the R.M.S. curve (fig. 2). You will notice, at once, 

 that it is anything but a smooth curve ; its trend is much more 

 towards the horizontal than Prof. Abbe's. It starts with three 



