564 Notes. 



are exhibited outside the geometrical boundary of the normal beam, the 

 Fresnel bands within that boundary. Since in the case of a focused beam 

 of light the normal beam narrows to a point in the focal plane, it follows 

 that Fresnel bands disappear from the focal plane itself, and are therefore of 

 comparatively small importance in the theory of optical instruments. Fraun- 

 hofer bands on the other hand are best seen in the focal plane, and for this 

 reason they are of great importance for the theory of optical instruments, 

 where they give rise to the phenomena of the false disk, intercostal figures, 

 and the like — in one word, to the phenomena connected with what has been 

 called the antipoint. It is from this point of view that the Fraunhofer 

 diffraction phenomena have been exclusively studied, and consequently the 

 account given of them in the accepted text-books is limited to their appear- 

 ance in the focal plane. 



It was suggested in the paper that this restriction of the attention of 

 students to the phenomena exhibited in the focal plane leads to a misunder- 

 standing, both of the nature and of the importance of the Fraunhofer bands, 

 and in illustration of this point the author referred to an investigation of 



Fig. 130. Fig. 131. 



the Fraunhofer phenomena in planes other than the focal plane, some results 

 of which had been communicated in a paper read by him before the E.M.S. 

 in December last.* In the mathematical part of that paper it was shown 

 that if a mode of calculating the intensity of Fraunhofer rings is adopted, 

 which is applicable to rings lying in these afocal planes, these rings can be 

 shown to be in theory conical wave-fronts which, starting from the diffract- 

 ing aperture, travel down outside the surface of the normal beam, forming a 

 fringe of light having the form of a conical wave-front. This conical wave- 

 front intersects the surface of the normal beam at right angles, and forms a 

 tangential extension of the spherical wave-fronts occupying the interior of 

 the beam. The diagram, fig. 130, illustrates according to this theory the 

 anatomy of a focused beam of light. Here AA is the aperture defining 

 the beam, F the focal point. The circular arcs struck about F represent the 

 wave-fronts of normal light. CCC are traces of the dark intervals between 

 the Fresnel rings. DDD are the conical wave-fronts of the Fraunhofer ring. 



* J.R.M.S., 1905, p. L] 



