ON INTERFERENCE IN THE MICROSCOPE. I^ 



assumes an angular aperture of objective =112** 52' — Diffractive 

 pencils beyond this limit would not be taken in under the given 



conditions.* 



Supposing that instead of a single opening (or transparent part) , 

 several were to come into play, the first and chief result would be 

 an augmentation of the effect described, ^since every equally 

 inclined diffraction pencil would necessarily cross the focal plane 

 at the same point q, and add to the effect. There the matter would 

 rest if we could assume that these diffraction pencils would not 

 occasion fresh interference amongst |themselves. This is not, 

 however, the case, for the diffraction pencils which proceed from 



neighbouring points are by no means without influence upon each 



other. Additional interference bands arise, particularly when there 



are many openings for passage of 



light 3 but an adequate description Fig. 3. 



and explanation of these phenomena 



would occupy too much space ; we 



refer, therefore, to the various 



treatises on physics for such details, 



and restrict ourselves here to a brief 



statement of the facts relating thereto. 

 Supposing the number of open- 

 ings or transparent parts to be 



numerous, and their mutual distances 



(interspaces) measured from middle 



to middle =d, then the laterally diffracted pencils (see fig 3) 



give maxima of light for all degrees of inflection at which the 



difference of travel, a c, is either one wave length or multiple of 



* Calling the wave length X and the width of the opening J, 

 then the diffracted pencils proceeding from a single opening give 



X , X - X 



bright \mQs for the several angles of inclination whose sines=f . r? 2"*Y' 2"* T 



etc. These sines have the same relation to each other as the odd numbers 

 3, S» 7, 9, &c. 



