by Apertures with Curvilinear Boundaries. 



299 



the same way to find the illumination at any point situated 

 inside the geometrical shadow. Thus, if in the diagram 

 (fig. 3) B be an opaque screen, the total effect is due to 



FiK. 3. 



the sum of strips like (n x rJ0 ) and (n 2 ^ ) and the effect 

 of each of these strips, as before, might be represented 

 by sets of waves sent out from the extremities n { and n 2 

 only. 



We may proceed now to consider the explanation of the 

 phenomena illustrated in the Plate. These are : — (a) the 

 luminosity observed along the evolute of the boundary of 

 the shadow when the edge is smooth or undulating, and not 

 highly corrugated ; (b) the dark and bright fringes running 

 nearly parallel to the evolute ; and (c) the special phenomena 

 observed whenever the edge is highly corrugated. 



(a) Any point on the evolute is situated at the centre of 

 curvature of some part of the boundary of the shadow 

 of the aperture. By simple geometry, it follows that waves 

 sent out from three contiguous points at the correspondino- 

 part of the boundary of the aperture, will reach that particular 

 point on the evolute in the same phase, and will conspire to 

 raise the amplitude there considerably above the amplitude 

 at neighbouring points on either side of the evolute. Conse- 

 quently the evolute itself of the boundary will be practically 

 a region of maximum illumination. 



(b) Consider the case of a point situated near any point 

 on the evolute on its concave side. A little consideration 

 will show that it is impossible from such point to draw any 

 normal to the shadow of the boundary (at any rate near to 

 that particular region of the boundary which corresponds 

 to the point on the evolute). Consequently, in the region 

 on the concave side, no two waves from the boundary can 

 arrive in the same phase, and this region will receive very 

 little illumination (unless of course a normal from some other 



