810 SUMMARY OF CUREENT RESEARCHES RELATING TO 



eflfect was lieiglitened by racking up the condenser mucli witliin its 

 focus. 



It is not difficult to calculate to what focus light, radiating from the 

 principal focus of the lens, will be brought by reflection from its 

 posterior siu'face. 



Let us examine a particular case, say a hemispherical lens of 1/10 in. 

 radius, of crown glass, ref. index 1 • 5. Then by ordinary formula — 



/ = 1/5. 



Now we have to find the apparent curvature of the concave surface as 

 seen through the plane. 



By formula— E = _ * 



where E is radius of curvature, F principal focus, and / the apparent 

 radius of reflecting surface seen through the plane — 



1/10= V^^ 



1/5-/ 



/ = 1/15. 



The next point we have to determine is the focus of a concave mirror 

 of 1/15 radius for rays coming from a radiant 1/5 in. in front of it. By 

 formula for a concave mirror — 



112 



- + - = - 



112 



+ 



p ' 1/5 1/15 

 2) = 1/25. 



Therefore we see the reason why the illumination by reflection from 

 the posterior surface of the lens should be feeble ; because it is brought 

 to a focus within the lens, and by the time the rays come to the object 

 they are greatly dispersed. 



"When the condenser is racked up, the radiant is placed nearer the 

 concave surface, and its conjugate focus brought nearer to the object, and 

 consequently the illumination of it is strengthened. Therefore we can 

 see that the single experiment put forward in support of the dioptric 

 theory fails. 



6th and last point. It is an established fact that the most critical of 

 all images are those on a dark ground. Here an objective is put on its 

 mettle, and its resolving power strained to the utmost, It is a great 

 pity that certain technical difficulties come in the way of this kind 

 of illumination with wide-angled lenses. Here we have no dioptric 

 beam, nothing but spectra, and we get a " true " image — i. e. one that 



* Formula by C. V. Boys, F.E.S., in " Measurement of Curvature and Eefractive 

 Index," ' Philosophical Magazine,' July 1882. 



