CLASSICAL THEORY OF LIGHT 



733 



The contour of the rulings of a grating does, on the other hand, 

 affect the relative intensities of the various diffraction-maxima and 

 the details of the distribution of intensity throughout the diffraction- 

 pattern. If they are grooves or troughs, their profiles in cross-section 

 have influence upon the pattern; if they are slits with bars between, 

 the ratio of width of slit to width of bar must be taken into 

 account. In crystals the arrangement of the atoms in the groups 

 controls the intensity-ratios among the diffraction-maxima and con- 

 versely is deduced from observations made on these. Even the dis- 

 tribution of electricity in the separate atoms of a crystal may be read 

 from the details of the diffraction. These effects however can 

 intrude upon the measurement of wave-lengths only in the cases — 

 comparatively rare — in which some of the diffraction-maxima are 

 actually blotted out, so that the uninformed observer may misinterpret 

 those remaining. Except for cases such as these, one may derive the 

 formula for computing the wave-length by assuming any convenient 

 form of grating; and therefore we may think about a grid of slits and 

 bars. 



P(a,/3,r) 



Fig. 1. 



Consider then an alternation of slits of width a and bars of width b, 

 occupying the plane x = 0. A beam of plane-waves, monochromatic 



