LIMITS OF OPTICAL CAPACIir OF THE MICROSCOPE. 435 



itself out T7ith notable strength to the same width as would the 

 light from a slit in the card bounded by two other slits. 



ThEOHY of DIFFBACTIOX IX THE MiCRO SCOPE. 



In conclusion I shall here shew a method by which the diffraction 

 of rays passing through the microscope may be theoretically 

 calculated. Instead of the simple lengths of rectilinear rays, as 

 taken into consideration by the theory of diffraction of light which 

 passes through one medium only, the optical lengths of the rays 

 must be taken, that is to say, the lengths obtained by adding to- 

 gether the product of each portion of a ray multiplied by the index 

 of refraction of the medium through which it passes. 



The ivave phases of two rays that have started from the same 

 luminous point, and have equal optical lengths, are also equal at 

 the other terminal point, because the wave lengths in different 

 media are inversely proportional to the refractive indices. Further, 

 it is known*' that the optical length of all rays between two con- 

 jugate foci of the same pencil in which a perfect re-union of these 

 rays is accomplished is equally great. 



In order to calculate the diffraction through the (relatively) 

 narrowest aperture of the microscope, each point {c) in the plane of 

 this aperture must be treated as a ray centre whose phase is 

 determined by the optical length of the normally refracted ray, 

 which, starting from the luminous point [a), has arrived at c. 

 This length I designate with ac. On the other hand, the 

 difference of phase between c and the point h in the surface of the 

 image whose brightness is to be determined depends on the optical 

 length ch found for the normally refracted ray travelling from c 

 to I. The phase of movement continued from a, through c as a 

 new centre of the ray, to 5, will, therefore, depend on the sum of 

 the optical lengths ac •\- cb. The share which this ray has in 



* The proof of the law here adduced is to be found in my Handbook of 

 Physiological Optics, and elsewhere. 



