70 NOTES ON THE RESOLVING POWER OF 



curve A is the resultant wlieu the separate illuminations are inde- 

 pendent, while B is the resultant when they are taken to be in 

 the same phase. From A it might be inferred that the object was 

 double from the presence of the two maxima in the resultant curve ; 

 in B the two maxima have merged into one and the resolution has 

 vanished. 



Examining, then, the case of two bright lines as the standard, 

 it is seen that for a dry objective they must not be closer than half 

 a wave-length for resolution under the best conditions of illumina- 

 tion. For the middle of the visible spectrum this means e = 

 .000025 cms. For an immersion objective with immersion medium: 

 of refractive index n this should be divided by n. For light of 

 shorter wave-lengths, e is proportionately less. Since this value 

 is calculated (for simplicity) from the assumption that the lens 

 aperture is rectangular, instead of circular, it differs very little 

 from the limit given by the modified definition given by me and 

 quoted near the beginning of this paper. 



Magnification . 



When an image is resolved it does not follow that it will be 

 seen to be resolved. The division marks on a scale may be perfectly 

 separate lines (much more so, in fact, than most optical images) ;. 

 yet they will not be seen separate if placed too far from the eye. 

 It was stated by Helmholtz that they must subtend an angle between 

 one and two minutes of arc in order to be seen as separate lines. In 

 my own case and in those of about ten others recently tested the 

 separation begins at about two minutes, i.e., at shortest distance of 



V 



clear vision, V, the lines must be separated about . This 



' ' ^ 1800 ^ 



statement, of course, assumes that the eye can focus the lines in 

 the position at which they are placed either without artificial aid 

 or with the appropriate spectacles. It is also assumed that the 

 illumination is good reading light. If the two lines in the image- 

 just resolved by a microscope objective subtend less angle than this, 

 they will not be seen resolved. We can calculate, therefore, the 

 limiting magnification necessary. An approximate calculation is 

 sufficient. 



With a total magnification of MiMj the size of the image^ 

 formed by the eye-piece is 



\ 



It is this that must be 



