DIFFRACTION. 109 



only rays concerned in the production of the fringes ; but 

 that the light which passed by these edges at sensible dis- 

 tances was also deviated, and concurred in their forma- 

 tion. Fresnel was thus forced to seek a broader foundation 

 for his theory. 



(124) In this theory the phenomena of diffraction are as- 

 cribed to the interference of the partial, or secondary waves, 

 which are separated from the grand wave by the interposi- 

 tion of the obstacle. In applying this principle, Fresnel sup- 

 poses the surface of the wave, when it reaches the obstacle, to 

 be subdivided into an indefinite number of equal portions. 

 Each of these portions may, by the principle of Huygens, be 

 considered as the centre of a system of partial waves ; and the 

 mathematical laws of interference enabled him to compute the 

 resultant of all these systems at any given point. This re- 

 sultant vibration, Fresnel has shown, is in general expressed 

 by means of two integrals, which are to be taken within limits 

 determined by the particular nature of the problem. Its 

 square is the measure of the intensity of the light ; and it is 

 found that its value has several maxima and minima, which 

 correspond to the intensities of the light in the bright and 

 dark bands. 



The problem of diffraction was thus completely solved; 

 and its laws derived from the two principles to which the 

 laws of reflexion and refraction are themselves referred, the 

 principle of Interference, and the principle of Huygens. It only 

 remained to apply the solution to the principal cases, and to 

 compare the results with those of observation. The cases of 

 diffraction selected by Fresnel are those whose laws have 

 been already stated ; viz. the phenomena produced 1, by a 

 single straight edge ; 2, by an aperture terminated by parallel 

 straight edges ; and 3, by a narrow opaque body of the same 

 form. The agreement of observation and theory is so com- 



