230 



THEORY OF MICROSCOPIC OBSERVATION. 



When the wave-length X = '5 mic., calculation gives the following 

 as the relative values of a and d : 



e c 



If d = X, a will, under all circumstances, = 90. Hence we find 

 that no objectives can, with direct (axial) illumination, take up even 

 the first image-forming diffraction pencil, if the distances of the 

 openings are less than 1 wave-length = *5 mic. 



The relations are different when 

 the incident rays are oblique to the 

 axis (Fig. 127). Besides the dif- 

 ference of phase b n of the deflected 

 rays, we have also that of the in- 

 cident rays m b. If, then, a is the 

 angle of inclination of the deflected 

 and 8 that of the incident rays, 

 the difference of phase in the 

 sin a + sin 8 



section a n is equal to 



a b 



FIG. 127. 



The resulting effects can easily be 

 deduced from this. We will confine 

 ourselves to the case where a = , 

 therefore sin a + sin B = 2 sin a, and will consider the first 

 diffraction pencil only. The condition above established for the 

 bright lines with any number of openings, according to which 

 3X 2 \ 3X 



sin a 



-T- , -T , &c. ; becomes 2 sin a = - , T , ' , 



a d it a A 



from which sin a for the first bright line = -- (instead of as 



' ' ^ 



above ^j. By suitable oblique illumination it is possible, by 

 means of the corresponding diffraction pencils, to bring still further 

 lines into view, whose distance is only half that which is the limit 



