164. Lord Rayleigh on Methods for detecting small Optical 



the regular light from an infinitely fine slit may be cut off 

 suddenly, and that an irregularity will become apparent in 

 full brightness however little (in the right direction) it may 

 deflect the proper course of the rays. In considering the 

 limits of sensibility we must remember that with a finite A, 

 the image of the slit cannot be infinitely narrow, but con- 

 stitutes a diffraction pattern of finite size. If we suppose 

 the aperture bounding the field of view to be rectangular, we 

 may take the problem to be in two dimensions, and the 

 image consists of a central band of varying brightness 

 bounded by dark edges and accompanied laterally by suc- 

 cessions of bands of diminishing brightness. A screen whose 

 edge is at the geometrical focus can cut off only half the 

 light and, even if the lateral bands could be neglected 

 altogether, it must be further advanced through half the 

 width of the central band before the field can become dark. 

 The width of the central band depends upon the horizontal 

 aperture a (measured perpendicularly to the slit supposed 

 vertical), the distance / between the lens and the screen, 

 and the wave-length A. By elementary diffraction theory 

 the first darkness occurs when the difference of retardations 

 of the various secondary rays issuing from the aperture 

 ranges over one complete wave-length, i. e. when the pro- 

 jection of the aperture on the central secondary ray is equal 

 to \. The half-width (£) of the central band is therefore 

 expressed by %=f\ja. 



If a prism of relative index //,, and of small angle i, be 

 interposed near the lens, the geometrical focus of rays 

 passing through the prism, will be displaced through a 

 distance (//.— l)z/. If we identify this with f as expressed 

 above, we have 



(fi-l)i=\la, ...... (1) 



as the condition that the half maximum brightness of the 

 prism shall coincide with approximate extinction of the 

 remainder of the field of view. If the linear aperture 

 of the prism be b, supposed to be small in comparison with a, 

 the maximum retardation due to it is 



(in-l)ib = \,b/a; (2) 



and we recognize that easy visibility of the prism on the 

 darkened field is consistent with a maximum retardation 

 which is a small fraction of \. 



In Cheshire's application of Foucault's method (for I 

 think if should be named after him) the prism had an angle i 

 of 10°, and the aperture a was 8 cms., although it would 



