Interference- Bands. 83 



small as the interval between trie D lines ; but for this purpose 

 the first slit had to be rather narrow, and the direction of its 

 length accurately adjusted, so as to give the greatest distinct- 

 ness. Since the wave-lengths of the two D lines differ by 

 about y^oo P ai % spectral bands of this degree of closeness 

 imply interference with a retardation of 1000 periods. 



Much further than this it was not easy to go. When the 

 bands were rather more than twice as close, the necessary 

 narrowing of the slits began to entail a failing of the light, 

 indicating that further progress would be attained with 

 difficulty. 



Indeed, the finiteness of the illumination behind the first 

 slit imposes of necessity a somewhat sudden limit to the 

 observable retardation. In this respect it is a matter of 

 indifference at what angle the reflector be placed. If the 

 angle be made small, so that the reflexion is very nearly 

 grazing, the bands are upon a larger scale, and the width of 

 the second slit may be increased, but in a proportional degree 

 the width of the first slit must be reduced. 



The relation of the width of the second slit to the angle of 

 the mirror may be conveniently expressed in terms of the 

 appearance presented to an eye placed close behind the 

 former. The smallest angular distance which the slit, con- 

 sidered as an aperture, can resolve, is expressed by the ratio 

 of the wave-length of light (X) to the width (w 2 ) of the slit. 

 Now, in order that this slit may perform its part tolerably 

 well, io 2 must be less than ^A ; so that, by (2), 



\/w 2 > 2b/D (5) 



The width must therefore be less than the half of that which 

 would just allow the resolution of the two images (subtending 

 the angle &/D) as seen by an eye behind. In setting up the 

 apparatus this property may be turned to account as a test. 



The existence of a limit to n, dependent upon the intrinsic 

 brightness of the sun, may be placed in a clearer light by a 

 rough estimate of the illumination in the resulting spectrum ; 

 and such an estimate is the more interesting on account of 

 the large part here played by diffraction. In most calcu- 

 lations of brightness it is tacitly assumed that the ordinary 

 rules of geometrical optics are obeyed. 



Limit to Illumination. 



The narrowness of the second slit would not in itself be an 

 obstacle to the attainment of full spectrum brightness, were 

 we at liberty to make what arrangements we pleased behind 



