732 BELL SYSTEM TECHNICAL JOURNAL 



The Diffraction Grating 



The ideal diffraction grating of theory is a sequence of equally-wide 

 perfectly vacant slits, separated from one another by strips absolutely 

 opaque and equal in width to one another though not necessarily to 

 the slits. Actual gratings seldom resemble this picture, though Fraun- 

 hofer's first — the most important instrument, I suppose, in the story 

 of spectroscopy — was an approximation to it which he made by winding 

 a wire around and around a pair of screws held parallel and wide apart, 

 soldering it in place and cutting away the alternate strands. So were 

 some of his others, composed of gold-leaf mounted on glass and 

 scratched along parallel lines with a diamond. So-called reflection 

 gratings would also conform with the picture, if they consisted of 

 bands of perfectly smooth reflecting metal separated by absolutely 

 non-reflecting bands; for then the result would be the same as if the 

 light came through the reflecting strips from a virtual image of the 

 source located behind. Practical reflection gratings are not usually 

 very like this conception, for the entire surface of the metal block is 

 ploughed up into roughly-shaped furrows. In fact one could scarcely 

 define the word "grating" less generally than as a periodically-repeated 

 obstruction, or better yet a periodically-repeated device for perturbing 

 the free onward flow of a beam of light. 



Nevertheless the theory of the ideal grating contains most of what 

 is required for the theory of the practical appliance. The reason is, 

 that the action of the grating upon the light can be separated into two 

 factors, each of which produces its own separate effect, each of which 

 may be studied apart from the other. Commonly there is a set of 

 maxima of brilliance in the diffraction-pattern; otherwise expressed, 

 there are certain directions in which the intensity of the diffracted light 

 is exceptionally great. From the locations of these maxima, the 

 wave-length of the light is calculated. Now these locations are deter- 

 mined by the spacing of the units — be they slits and bars, furrows 

 and ridges on a reflecting surface, planes of atoms in a crystal, or 

 what not — whereof the exact repetition in sequence constitutes the 

 grating. Thus if we know that a certain grating is ruled with 1000 

 "lines" to the inch, we can compute the wave-length of sodium light 

 from the positions of the maxima in its diffraction-pattern, without 

 knowing or caring whether the rulings are slits, grooves, triangular 

 indentations, wavy ripples, or rough-bottomed troughs. If we know 

 that in a crystal a certain grouping of atoms repeats itself one million 

 times in a centimetre, we can calculate the wave-length of an X-ray 

 beam or an electron-beam from the locations of its diffraction-maxima, 

 without knowing anything about the arrangement of atoms in the 

 group. 



