OM INTERFERENCE IN THE MICROSCOPE. I^ 



of phase of the incident pencil {m h) . Thus, if a be the angle of 

 inflection of the diffracted pencil, and B the angle of inclination of 

 incident pencil, then the difference of phase at a n is equal to 



sine a •\- sine Z 



-7 — , from which the resulting effects can be deduced. 



We limit our calculation, however, to the case where a=^, and 



consequently sine a -^ sine ^=2 sine a 5 and we shall consider only 



the first diffraction pencil. The condition before determined for 



bright lines with any number of openings according to which 



\ 2X 3\ , , 



sme ^^^^ >'~J~' >~~j~> &c., stands now thus: 2 sme a= 



^ *'~T~ y~~j~> ^^' J L^ence, sine a for the first bright line, 



=~^ instead of as before, -v-. By suitable oblique illumination, 



therefore, bright diffraction images can be brought into view 

 by means of corresponding diffraction pencils when their 

 distance from each other amounts to half only of that 

 of the diffraction images which can be seen with central 

 illumination. For the cases of extreme limit, when a and 



I are both equal 90*^, and, therefore -7^=1, the minimum visible 



interspace d proves to be half a wave length. 



For further discussion of diffraction effects it will be 

 convenient to express the results thus far obtained in a 

 somewhat different form. In the foregoing remarks the 

 incident light has been treated as constituted of parallel rays. 

 Holding strictly to this condition, we reduce the dimensions 

 of the source of light as much as possible by means of a diaphragm. 

 The direct rays, then, produce in the focus of the objective a dioptric 

 image of the source of flight, {i.e., of the small bright opening in 

 the diaphragm) which can be seen by removing the ocular and 

 looking down the tube of the instrument. But the diffracted rays 

 which form an angle (a) with the optical axis also produce, 

 at ^ and j' Fig. 2, as also at all points where interference 



