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



Light from a distant source is allowed to pass through two 

 thin parallel slits. The rays are then focussed on a screen 

 (or the retina of the eye) and interference-fringes are seen. 

 If the distant source be really double, or extended, the fringes 

 will disappear for certain values of the distance between the 

 slits. This distance depends on the angle subtended by the 

 two components of the double source or the diameter of the 

 extended source. 



Mr. Michelson, however, in obtaining his results treated 

 the breadth of the slits as small compared with the wave- 

 length of light and their length as infinite. This seems un- 

 justifiable a priori. The present investigation takes the 

 dimensions of the slits into account. 



2. Suppose we have an aperture or diaphragm of any 

 shape in a screen placed just in front of the object-glass of a 

 telescope (fig. 1). 



Fig. 1. 



s* — - 



, -/ , 



< *: 



£^^1-, 



P 



A' 



/ J^' 



1 



A 



Let the axis of the telescope be the axis of z. Let the 

 axes of oc and y be taken in the plane of the diaphragm OQ 

 perpendicular to and in the plane of the paper respectively. 

 Let S be a source of light whose coordinates are U, V, W. 

 Let Q be any point in the diaphragm whose coordinates are 

 (#, y). Let A P be a screen perpendicular to the axis of the 

 telescope, and let (p, q) be the coordinates of any point P on 

 this screen. Let A'P' be the conjugate image of the screen 

 AP in the object-glass. 



Let b = distance of centre C of lens from screen AP. 



b'= „ „ „ „ image of screen AP. 



/= distance of diaphragm OQ from plane A'P'. 



Then if, as is usual, we break up a wave of light coming 



