160 Prof. Stokes on the Polarization of Diffracted Light. 



and the predictions of a theory in which it is assumed that the 

 office of the opake body is merely to stop a portion of the inci- 

 dent light. But when diffraction is produced by a fine grating, 

 the angle of diffraction is no longer restricted to be small ; and 

 it becomes an open question whether the precise circumstances 

 of the diffraction may not have to be taken into account, and not 

 merely the form and' dimensions of the apertures through which 

 the light passes. If so, the problem becomes one of extreme 

 complexity. In my memoir on the Dynamical Theory of Dif- 

 fraction, published in the ninth volume of the Cambridge Philo- 

 sophical Transactions, I investigated the problem on the hypo- 

 thesis that in diffraction at a large angle, as we know to be the 

 case in diffraction at a small one, the office of the opake body is 

 merely to stop a portion of the incident light. I distinctly stated 

 this as a hypothesis, and I always regarded it as rather pre- 

 carious. I was guided by the following consideration. Let AB 

 be the section of a transparent interval by the plane of diffrac- 

 tion, supposing for simplicity the diffraction to take place in air 

 or in a homogeneous medium, and not at the confines of two 

 different media; let AB = &; let /3 be the angle of diffraction, 

 and A, the wave-length in the medium. Supposing the light to 

 be incident perpendicularly on the grating, the difference of 

 phase of the secondary waves which started from A, B, respect- 

 ively, will be determined by the length of path b sin /3 within the 

 medium. In experiment this will usually be a considerable 

 multiple of \. In the line AB take two points, A', B', equidistant 

 from A, B, respectively, and comprising between them as large a 

 multiple as possible of X cosec /3. If we suppose the influence 

 of the opake body insensible at the distance AA' or BB' from A 

 or B, the secondary waves which start from all points in the in- 

 terval A'B' will neutralize each other by interference, so that the 

 whole effect will be due to the secondary waves which start from 

 AA' and BB'. Suppose the angle ^ to belong to the brightest 

 part of a "spectrum of the first class" (Fraunhofer) ; then 

 'AA' + BB' = iA. cosec /3, X. referring to mean rays, so that AA' or 

 BB' is only equal to ^X- cosec yS. If, for example, yS=30°, AA' 

 is only equal to iX. At such very small distances it may well 

 be doubted whether the influence of the opake body may not 

 have to be taken into account. 



When diffi-aetion takes place at the confines of two different 

 media, suppose air and glass, the problem is still further com- 

 plicated. We may, however, apply the theory to which reference 

 has been made on the two extreme suppositions, first, that the 

 diffraction takes place wholly in the first, secondly, that it takes 

 place wholly in the second medium. The results of my own ex- 

 periments were very fairly represented by theory, the vibrations 



