8 



NUMERICAL APERTURE. 



It is necessary for a clear understanding of this subject to 

 approach it ah initio, laying aside all_ preconceived notions, and 

 bringing in the abstruser laws of optics. 



For this purpose we must first realise what is meant by 

 aperture : — 



The word aperture means " an opening," and in optical 

 instruments ought to be measured by the greatest amount of 

 licrht from the same area, which can traverse the system, the 

 intensity of the illumination remaining constant. In the case 

 of the microscope, with which we are at present dealing, 

 this is evidently dependent on the objective. 



Now, if in Fig. I., A is a luminous point, placed at 



Fig I 



the focus of the lenses B or C, 

 acting independently of each other, 

 and giving out rays of light, Aa', 

 Aa", in every direction, — the lens C, 

 though of less diameter, has evi- 

 dently a larger aperture, that is, 

 admits more light than B. On the 

 other hand, C is of shorter focus 

 than B. This shows that focal a 



lens^th is an element in the true calculation of aperture. 



In a compound system, however constructed, as in Fig. II., 



where two lenses are repre- 

 sented in combination, viz., 

 BF and C, the amount of light 

 which passes through the sys- 

 tem from the point A at its 

 focus, is represented by the 

 amount of light included be- 

 r • , Tr tween BD and FE, the limit- 

 ' b -^ ing rays emerging from the 

 back lens ; as this back lens 

 cannot transmit more light 

 than it receives, for which it 



is dependent on the front 



lens C, it follows that in any 

 system of lenses, the system ought to be treated as a whole, 

 and the aperture measured by the emerging beam. Any method 

 v/hich does not do this is liable to error ; and in the following 

 arguments the objectiye is treated as if it were a single lens. 



On the undulatory theory, a wave of light passing from a 

 rarer to a denser medium is retarded, owing to the free vibrations 

 of the luminous ether being, so to say, " clogged," thus causing 

 the phenomenon of refraction. For example, if in Fig. III., 



