THE 

 LONDON, EDINBURGH, and DUBLIN 



PHILOSOPHICAL MAGAZINE 



AND 



JOURNAL OF SCIENCE. 



[FIFTH SERIES.] 



FEBRUARY 1891. 



IX. The Elementary Treatment of Problems on the Diffrac- 

 tion of Light, By Arthur Schuster, F.R.S.* 



THE complete investigation of problems relating to the 

 diffraction of light involves the discussion of certain 

 definite integrals which often cannot be introduced at the 

 stage at which students begin to learn the important subject 

 of Physical Optics. Most of our text-books give therefore 

 a more elementary treatment of the question in which the 

 wave-front is broken up into elements or zones, the effects of 

 which are added up algebraically. This elementary treatment 

 suffers from a very serious defect, if anything more than a very 

 general explanation is aimed at, for the considerable difference 

 of phase in the resultant effect of the first and subsequent 

 elements is altogether neglected. Prof. Mascart, in his excel- 

 lent book on Optics, obtains numerical results from such 

 elementary considerations ; but he takes without justification 

 the phase of the central element to be the same as that of the 

 others, and his treatment is therefore open to the objection 

 which I have indicated. It is true that the intensities of the 

 diffraction-bands at the edge of shadows, as calculated in 

 the elementary way, do not differ much from those ob- 

 tained by a more rigorous analysis ; but the position of the 

 bands is not correctly given, and the question of the resultant 

 phase is altogether left out of account. Even to those who 

 can follow the complete investigation by means of Fresnel's 

 integrals, the method of breaking up the wave-front into 



* Communicated by the Author. 

 Phil. Mag. S. 5. Vol. 31. No. 189. Feb. 1891. H 



