530 HENRY A. KOWLAND 



or a compound groove, the higher orders may exceed the lower in 

 brightness and it is mathematically possible to have the grooves of 

 such a shape that, for given angles, all the light may be thrown into 

 one spectrum. 



It is not uncommon, indeed, very easy, to rule gratings with im- 

 mensely bright first spectra, and I have one grating where it seems as 

 if half the light were in the first spectrum on one side. In this case 

 there is no reflection of any account from the grating held perpendicu- 

 larly: indeed to see one's face, the plate must be held at an angle, in 

 which case the various features of the face are seen reflected almost 

 as brightly as in a mirror but drawn out into spectra. In this case all 

 the other spectra and the central image itself are very weak. 



In general it would be easy to prove from the equation that want of 

 symmetry in the grooves produces want of symmetry in the spectra, a 

 fact universally observed in all gratings and one which I generally 

 utilize so that the light may be concentrated in a few spectra only. 



EXAMPLE 1 SQUARE GROOVES 



When the light falls nearly perpendicularly on the plate, we need 

 not take the sides into account but only sum up the surface of the plate 

 and the bottom of the groove. Let the depth "be X and the width equal 



to*. 

 m 



The intensity then becomes proportional to 



'N T S T ~rn r T" 

 This vanishes when 



N = m , 2m , 3m, etc., 



or = 0, 1, 2, 3, etc. 



The intensity of the central light, for which N = 0, will be 



* - / * ]T\ 



rein(* T XJ. 



This can be made to vanish for only one angle for a given wave- 

 length. Therefore, the central image will be colored and the color 

 will change with the angle, an effect often observed in actual gratings. 

 The color ought to change, also, on placing the grating in a liquid of 

 different index of refraction since A contains 7, the index of refraction. 



It will be instructive to take a special case, such as light falling per- 

 pendicularly on the plate. For this case 



