476 Mr. J. Walker on the Admissible Width of 



point £ , 7j of the slit and traverse each one half of the lens is 



A = 2( 



a(b-t)-F{a + b-t)-F- ( I- ^-i«- ^— ?- {b-t) \ 



ft L r. r 2 ' i 



where 2e is the separation of the halves of the lens, 

 t is the thickness of the lens, 



a, h are the distances, measured along the axis, of the 

 slit and the screen from the surface of the lens 

 nearest the slit, 

 fi, r 2 , F are the absolute values of the radii of the 

 surfaces and of the focal length of the lens. 

 3. In each of these three cases the intensity at a point of 

 the screen due to an element of the slit of breadth d% distant 

 f from its central line may be written 



i-fl + 008^ («+/3* + 7f)}«, 



where a, fi, and 7 have the values proper to the case under 

 consideration ; and if the various parts of the width of the slit 

 act as independent sources of light — the condition, as 

 Lord Rayleigh bas shown {lor. cit. p. 81), most favourable to 

 brightness — the intensity due to the whole slit of width k is 



l = h f* /2 J 1 + cos^ (« + #» + 7?)} d % 

 J7 f,. sin irykjX 2ir . . , \ 



The visibility of the interference-fringes is thus given 

 by +sin (7ryk/\)/(7Tjk/\) ; this vanishes when <yk/\ is an 

 integer, while the maxima of distinctness occur when 



tan (7ryk/\) = iryk/X, 

 or when 



y k/y=0, 1-4303, 2-4590, 3-4709, 4-4747, , 



the corresponding values of the visibility being 



1 -217 -128 -091 -079 . . . ; 



when yk/\ = 0, the intensity is zero, but the visibility will be 

 considerable so long as 7#/\ is small. Now the linear width 

 of the bands (from bright to bright, or from dark to dark) 

 being 



A=X//3, 



the condition for maximum distinctness is that k must be a 



