THE FOCUS-APERTURE RATIO. 



291 



of the curve is nearly a straight line, making an angle of 26° 36' 

 with the base. There is no lens in the whole curve that will 

 cause a manufacturing optician a moment's anxiety. A 4/lOth 

 in. of N.A. 0-5 cannot be said to have an excessive aperture, 

 and such a lens is of the greatest possible value in biological and 

 other work. After the 4/lOth the optical index is reduced and 

 the curve becomes steeper. The curve has been drawn to an 

 objective l/8th, of N.A. 0-9 ; but of the utility of an achromatic 

 dry lens of that aperture I have grave doubts. Prof. Abbe stated 



60 



-I -2 -3 -4 -5 -6 -7 -8 "9 10 



Fig. 3. 



that an angle of 110° was the limit for perfection in a dry lens (say 

 1/6 in. of N.A. 0-82 (optical index 13-7), and I agree with him. 



Anyone who will take the trouble to compare the image given 

 by an oil immersion 1/7 in. of N.A. 0-9 (introduced not long before 

 the war) with that from a dry 1/7 or 1/8 of even greater N.A. will 

 probably be convinced that high-power dry lenses with large 

 apertures are a mistake. My curve was drawn to the top, so that 

 it might be compared with the others, otherwise it would have 

 been stopped at N.A. 0-85 (optical index 13-5). There is nothing 

 else to be said, or explained, as the curve speaks for itself, which 

 no list of objectives and apertures could do nearly as well. It 



