by Apertures with Curvilinear Boundaries. 291 



the transmitted pencil of rays. Further, on closer inspection 

 it is seen that running parallel to these arcs on the inner side 

 a tew dark and bright fringes appear, which are somewhat 

 analogous to the interference-fringes seen alongside a caustic. 

 The luminosity becomes fainter and fainter ;is we recede 

 from the centre of the field, but it does not terminate at the 

 cusps of the evolute, continuing beyond it in the form of two 

 horizontal brushes, which extend one on each side. (The 

 photographic plate was not large enough to cover this part 

 of the field.) Outside the region enclosed by the evolutes, 

 luminous streamers may also be seen radiating normally from 

 all parts of the elliptic boundary. 



The phenomena described above are always noticed 

 whether the incident pencil of rays is divergent or con- 

 vergent. But an interesting effect is observed in the case 

 of convergent light as the plane of observation approaches 

 the focal plane. The cross-section of the pencil and the 

 luminous arcs of the evolute appearing on either side of it 

 gradually contract and reduce to a point. The horizontal 

 brushes extending outwards from the cusps, however, persist. 

 These break up into beads of light on both sides which, when 

 the focal plane is further approached, ultimately join up and 

 form the elliptic rings usually observed in the Fraunhofer 

 pattern at the focus. 



Fig. In in the Plate shows the faint region of luminosity 

 inside the shadow of an elliptic disk. The four luminous arcs 

 forming the evolute of the boundary are clearly noticeable. 



3. The case of a Semicircular Aperture. 



This case is an instructive example of the importance of 

 studying the phenomena of large-angle diffraction. If we 

 exclude the outlying regions of faint luminosity, the dif- 

 fraction pattern of the Fresnel type is an approximately 

 semicircular patch of light, with fringes running inside it 

 parallel to the boundaries, and in fact this is how it appears 

 in a photograph reproduced in the paper by Gordon quoted 

 above. In this form, the Fresnel pattern bears not the 

 remotest resemblance to the diffraction figure of the Fraun- 

 hofer class due to a semicircular aperture as observed at the 

 focus of a heliometer objective. A study of the large-angle 

 diffraction, however, puts the case in an entirely different 

 aspect. Fig. c in the Plate shows the effects observed. It 

 will be noticeable that there is a long horizontal trail of 

 light proceeding to a great distance in either direction at 

 right angles to the diameter of the semicircle. Crossing 



