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[ 51 ] 



VI. A new Proposition in the Theory of Diffraction, and its 

 Application. By J. Fkohlich, of Budapest. 



THE mathematical expression which serves for the calcula 

 tion of the intensity of diffracted light leads, after a fe 

 simple reasonings, to a peculiar connexion between the kinetic 

 energy of the diffracted light issuing from an element of a 

 luminous surface and incident upon an infinitely large receiving 

 screen, on the one hand, and, on the other, the energy of the 

 light proceeding from a very large luminous surface and yet 

 incident upon only one element of the screen. 



This relation is specially note-worthy on account of its faci- 

 lity of application ; for it gives a simple method of observa- 

 tion which permits the question of the equality of the kinetic 

 energy of the incident and the diffracted light to be at once 

 decided experimentally for any aperture. 



For the deduction of this proposition we make the following 

 suppositions: — 



Let there be a diffracting aperture $ (fig* 1)? bounded by 

 any pane- or space-curve, y\<*. l. 



the dimensions of which 

 relative to the wave-length 

 of the light are very great, 

 so that the amplitude of 



the diffracted light pos- ^ F l____—^^__ 

 sesses a finite value only \ '^P'trfr ^^ ^A 

 when the angle of diffrac- \ L 



tion is small, but other- ^ 

 wise vanishes. Further, let there be a uniformly luminous 

 source of light of the form of a spherical surface F F, from 

 which the light, after diffraction by %, arrives at the likewise 

 spherical-surface-shaped receiving screen //. The radii of the 

 surfaces F F and//, p r and p , are very long in proportion to 

 the dimensions of the aperture; and their common centre 

 lies in the aperture or its immediate vicinity. 



Let the amplitude of the light-motion which emanates from 

 the element dF be, at unit distance, (5l5dF)* (since each ele- 

 ment dF vibrates quite independently of the rest) ; conse- 

 quently there arrives at the diffracting aperture a motion the 



amplitude of which is >™°d ) a , which we shall in future de- 

 Pi 

 note by %; hence it is the amplitude of the incident light 

 proceeding from dF. 



* Translated from Wiedemann's Anncden, 1878, No. 9. 

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