446 Mr. L. N. G. Filon on certain Diffraction Fringes 



The successive maximum and minimum intensities do not 

 vary with a. Hence, what Mr. Michelson calls the measure 

 of visibility of the fringes, namely the quantity 



I, -Is 



Il+I*' 



where I l5 1 2 are successive maximum and minimum intensities, 

 does not vary with the distance between the slits. The only 

 effect of varying the latter is to make the fringes close up or 

 open out. Hence for a point-source of light the fringes 

 cannot be made to practically disappear. 



3. Consider now two point-sources of light whose geo- 

 metrical images are J 1? J 2 , and draw their 

 (fig. 3). 



FIr. 3. 



visible rectangles 



: J 



Jj 



To get the resultant intensity we have to add the in- 

 tensities at every point due to each source separately. 



Then it may be easily seen that the following are the 

 phenomena observed in the three cases shown in fig. 3: — 



(1) The two sets of fringes distinct. Consequently no 

 motion of the slits can destroy the fringes. In this case, 

 however, the eye can at once distinguish between the two 

 sources and Michelson's method is unnecessary. 



(2) Partial superposition : the greatest effect is round the 

 point K, where the intensities due to the two sources are 

 very nearly equal. If v' — v be the distance between Jj and 

 J 2 measured perpendicularly to the slits, so that (v' — v)/b is 

 the difference of altitude of the two stars when the slits are 

 horizontal, then over the common area the fringe system is 

 (a) intensified if v' —v be an even multiple of bX/Aa, (b) 

 weakened, or even destroyed, if v' — v be an odd multiple of 

 b\/4:a. For in case (a) the maxima of one system are super- 

 posed upon the maxima of the other, while in case (b) the 

 maxima of the one are superposed upon the minima of the 

 other. This common area, however, will contain only com- 

 paratively faint fringes, the more distinct ones round the 



