164 ELEMENTS OF LABORATORY WORK 



would come from the portion G a 7 may be considered to con- 

 sist of two portions which will be in opposite phases. One of 

 these being intercepted, a band is visible in the direction P a 7) 

 and so on, for all portions of the grating, where the corre- 

 sponding distances differ by any whole number of wave-lengths. 

 The position of these images will be determined solely by the 

 length of the light-waves, and will vary for different colours. 



If d denote the distance a 2 a 3 , &c., that is, the interval 

 composed of an opaque and a transparent portion of the 

 grating (a distance which is usually known for each grating), 

 and X denote the wave-length of the light used, then, by con- 

 struction, for the position of the first image, 



i=sin 61. Or \=d sin V 



when 6 is the angle a- 3 a. 2 I or, which is the same, the angle 

 o P 3 ; for the second image and the second angle 9 , 



\=~ sin 2 , and so on. 



It is advisable in this observation to take the mean angle, 

 obtained by measuring the corresponding images on each side 

 of the main image. Precisely the same results, explicable in 

 the same manner, may be obtained by reflexion from lines 

 ruled upon polished metal. When white light is used a series 

 of pure spectra may be obtained with either reflexion or 

 refraction gratings, since we shall have each monochromatic 

 image of the slit replaced now by a band, representing the 

 superposition of successive images, caused by the radiations of 

 successive wave-lengths. By constructing a diagram which 

 shall include radiations of different wave-lengths, the difference 

 in position of the images will be made clear. 



104. Explanation of Reflexion and Refraction, The RJUHU 

 principle of interference of light may now be applied to 

 explain the observed laws of reflexion and refraction in 

 isotropic media that is, media which do not interfere by their 

 structure with the spherical propagation of ether- waves. 



