274 Mr. J. C. M c Connel on Diffraction- Colours, 



Hence, as usual, the illumination on the screen is given by 



. 2 7T«f . 3 TTO Sin 7 Tj 



q^sinV ln fX_ Sm — JT- 



The field is crossed by two sets of parallel dark bands, given 

 by a%lf\ and b sin 7 rj/fk being positive or negative integers 

 other than zero. There is a large central rectangle of dimen- 

 sions 2/X/a by 2f\/bsmy, surrounded by others of similar 

 shape but only a quarter the size. The brightest point is the 

 centre, and along the two principal directions the succes- 

 sive maxima have approximate values 0*046, 0017, 0'0085, 

 0*0050 . . . , that at the centre being unity, and are found at 

 distances given by 



of //X= 1-43, 2-46, 3-47, 4-47. 



Along the diagonals the numbers for the successive maxima 

 are the squares of the above, viz. 0-0021, 0*00029, 0*00007 . . . , 

 so the diminution is much more rapid. 



It is obvious from (2) that the linear dimensions of the 

 diffraction-pattern are proportional to X, and its brightness 

 proportional to \~ 2 . Thus, if the source send out white light, 

 the central patch will be bluish in the middle and tinged with 

 yellow and red at its edges. Along one of the principal direc- 

 tions, e. g. ?7 = 0, we have, governing the colour of the light, 

 the factor m wa ^ 



Sm JK < 8 > 



As will be explained in the next section, the colours are those 

 of Newton's rings, though their relative brightness is very 

 different. Along the diagonals for which aZ = bsmyr], the 

 colour-factor is tirn t 



tf^T? W 



So that the tints are much richer, though the intensity is yerj 

 feeble. 



Babinet's Principle, 



Suppose now that b sin 7 is much greater than a, so that 

 our aperture becomes a narrow slit. We are intending to 

 deal, not with slits in an opaque screen, but with filaments in 

 the open sky. This case may be immediately derived from 

 the other with the aid of Babinet's principle. But it is 

 desirable, I think, to examine the application of the principle 

 in some detail. Replace the slit by a very much larger aper- 

 ture, say 500 times as long and 10,000 times as broad. The 



