556 On the Orientation of the Slit in Interference Experiments. 



where 



d=a cos 2co + b for Fresnel's mirrors, 



= a + b for the biprism, 



= =^ — (a + b) for the divided lens ; 



and the visibility at the point is then the absolute value of 

 sin (iryk sec 0/X)/{iryk sec X). 



It thus follows that if the slit be inclined with its upper 

 part towards the interference apparatus, a rotation of the slit 

 in its own plane in a direction from y towards x causes the 

 point of maximum distinctness to move in the direction of 

 positive #*. 



If cj) = 0, the visibility is given by the absolute value of 



sin (iryk cos 0/X) sin (iryl sin 0/X) m 

 iryk cos 0/X myl sin 0/X 



which is independent of the length of the slit if 0=0, a 

 result that is obvious from other considerations ; and when k 

 is a small fraction of X/y, the visibility is given by the 

 absolute value of sin (nryl/sm 0/X) /(iryl sin 0/X), so that the 

 slit acts as a slit properly orientated of width equal to the 

 projection of the actual slit on a plane perpendicular to its most 

 favourable direction. This is M. Fabry's result mentioned 

 above. 



If = 0, </> = 0, the bands disappear when k = X/y, and in 

 this case a rotation of the slit increases the visibility, and 

 would theoretically cause a reappearance of the bands. A 

 consideration of the magnitude of the quantities involved 

 shows, however, that the increase of the visibility is too slight 

 to be noticed. 



When the slit is properly adjusted (0 = 0, </> = 0), the 

 bands attain their second maximum of distinctness when 

 &=l'4303\/7, their visibility being about J; if then we take 

 Lord Rayleigh's result f that the limit of visibility is reached 

 when the ratio of the illuminations at the darkest and brightest 

 parts of a system of bands is *975, which corresponds to a 

 visibility of -g- 1 ^, the bands will disappear when the slit is rotated 



* It is obvious that these phenomena cannot be observed in all cases. 

 Thus with a biprisni and sodium light, if /=1 cm., = 10°, the point at 

 which the bands would first disappear falls outside the field common to 

 the two streams, unless b tan d/(a-\-b) exceed '026, where 8 is the deviation 

 produced by the biprisni. M. Fabry has, however, observed the phe- 

 nomenon with Fresnel's mirrors (loc. cit. p. 33). 



t Phil. Mag. (5) vol. xxvii. p. 484. 



