314 Microscopy and some of its Uses. [Sess. 



numerical aperture, which is so seriously important in an 

 objective, can be measured and stated by the product of the 

 index of refraction into the sine of half the aforesaid angle. 



Thus if we suppose the sides of this whole angle spread out 

 until they coincide with the slide, we shall have a semicircle, 

 or 180°: half of this is 90°, and the sine of 90° is 1 ; and 

 taking 1 as the refractive index of the air in which the 

 objective works, the product of these two ones is 1, and we 

 get 1 as a maximum, and as a staudard of comparison. Look- 

 ing now at a descriptive table of objectives, we see at once 

 that fractions such as "70, - 80, -90, are near the maximum, 

 and are high apertures, that - 50 is half the maximum, and 

 that "20 is only a fifth of it, and is a small aperture. Since 

 the performance of an objective depends both upon its angle 

 and the refractive index of the medium between it and the 

 object, this coupling of these two factors gives effect to a 

 natural relationship, and explains why when the index is 

 increased, as in immersion, the numerical aperture can be 

 raised to values above 1. 



The second contribution of Abbe, called his theory of 

 diffraction, is more complicated, but, probably, still more 

 important. It gives the scientific reason why objectives in 

 virtue of high aperture come to have the marvellous quality 

 of resolving very minute structures and details and making 

 them visible. It can only be learned by private and repeated 

 study, assisted by some previous knowledge of physical optics. 

 As a simple illustration, suppose we place under the micro- 

 scope a circular diatom, having an actual diameter of one- 

 hundredth of an inch, and which, from previous observation 

 with a wide-angled objective, we know has very fine lines or 

 markings all round its centre. Look at it with an inch 

 objective of low angle and magnifying, say, fifty diameters. 

 The object has now the apparent size of half an inch ; we see 

 it perfectly in outline, but the central part is somewhat hazy, 

 and there are no signs of the fine lines we know to be there. 

 How is this ? Is it not sufficiently magnified ? Well, with 

 a higher eyepiece magnify it a hundred times : it is now an 

 inch in diameter, and still the fine lines do not appear. We 

 must go back to the beginning and get the explanation from 

 Abbe's theory. 



