164 



PROGRESS IN MICROSCOPY 



the object considered to be either a point or a Hne. Granting that 

 such coincidence can be brought about, under normal conditions, 

 with an accuracy attaining one hundredth of the diffraction disk 

 diameter: the matter could be reasoned taking as basis the diffraction 

 disk lying in the image plane A. and then reverting to the space-object. 



Fig. 5.1. Lateral setting. 



dividing it by the objective's magnification. A prompter method is 

 to consider direct the phenomena taking place in the plane of the 

 object A. 



Let us'mu be the objective's numerical aperture (N.A.) and A 

 the wave-length. The dilTraction-disk diameter in the object plane is 

 1-22 A//7 sin w. Therefore, A can be located by a transverse setting with 

 an accuracy Iv equating: 



1 -22 / 

 Jv >-—-.— . (5.1) 



lOOwsmw ^ 



i.e. accuracy within 002/^ for / =0-6/< and a N.A. =0-30. 



N.B. The foregoing implies, of course, a mechanically excellent and 

 vibrationfree microscope. 



If the object is the edge of an area, accuracy is much impaired 

 and will in no way be provided by the foregoing formula. 



Axial setting accuracy (Fig. 5.2) 



The problem involved is the following: the object being properly 

 focused at A, to what length t- can it be shifted or — what amounts to 

 the same thing — can the microscope be shifted, A remaining motion- 

 less, without the eye noting any change in sharpness? Now, if the 

 object-point A can be shifted to A(, for a distance e without changing 

 sharpness of the image, it can be shifted for the same amount and 

 with the same result to the right at A^^. Under such conditions, the 

 eye perceives no change in image sharpness, irrespective of the object's 

 position within the interspace /f,,^] ^ 2f. Such interspace determines 



