S34 SUMMARY OF CURRENT RESEARCHES RELATING TO 



of bis contention that an immersion objective cannot bave a larger 

 aperture than a dry one, bave, as is known, been frequently drawn 

 before and their fallacy as often exposed, though, as the diagrams 

 bave been ultimately withdrawn by their authors, the exposition has 

 not hitherto appeared in print. We now, however, give it. 



Mr. Shadbolt's assumptions were as follows : — 



He supposed a Jiomogeneous-immersion objective with a front an 

 exact hemisphere as suggested by Professor Stokes (see Fig. 75) 

 which admits from Q a pencil of 113° balsam-angle and transmits 

 it to the back combination as a pencil from q of 66°. 



Fig. 75. 



Fig. 76. 



With this he compared a dry objective with a front lens of the 

 same curvature as the immersion front, but of less thichiess (as in 

 Fig. 76). The position of the front in regard to the radiant was 

 so arranged that a pencil from q of 66° is transmitted to the back 

 combination as before. This pencil, however, emanates from a 

 radiant z in air, and is of larger angle than the 113° which was the 

 limit of the Stokes objective, so that it was supposed and contended 

 that the latter had been changed into a dry objective of larger 

 aperture ! * 



The application of one of the simplest and most elementary optical 

 considerations shows at a glance that the demonstration is an entire 

 mistake, and it well illustrates how deceptive geometrical diagrams 

 of aperture may in reality be if they are drawn without a clear 

 appreciation of the optical principles applicable to the subject. 



There are two methods of demonstrating the fallacy, the one the 

 strict and the other the simple method. We deal with the former first. 



(a) Tlie Strict Method. 



With the same set of posterior lenses (of any given composition) 

 the Stokes front would give an immersion objective of 112° 20' 

 crown-glass angle, and the Shadbolt front a dry objective of 125° 40' 

 air-angle under the conditions laid down in his paper, viz. that the 

 emergent pencil with the virtual focus q is in both cases 66°. 



Compare now the performance of these systems as to the ampli- 



* The Shadbolt lens as it stands is not, of course, a practical construction, 

 though the Stokes lens is. It could, however, be utilized by adding a duplex 

 front to correct the spherical aberration. We have not done this, as it seemed 

 that it might give rise to the supposition (though it would not be really the case) 

 that we had altered the conditions laid down. We therefore simply note the 

 fact. 



