fine Lines or transmitted by narrow Slits. 357 



It may be well to recall that in the results which we have 

 obtained the angles a, <£ are measured from the surface and 

 not, as is usual in Optics, from the normal. Again, if it be 

 desired to attach significance to the sign of II, we must re- 

 member that in one case we were dealing with c* and in the 

 other with R. 



The above given theoretical investigation was undertaken 

 in order to see how far an explanation could be arrived at of 

 some remarkable observations by Fizeau*, relating to the 

 light dispersed at various angles from fine lines or scratches 

 traced upon silver and other reflecting surfaces. In every 

 case the incident and dispersed ray is supposed to be per- 

 pendicular to the lines, so that the problem is in two dimen- 

 sions. The most striking effects are observed when the 

 incident and dispersed rays are both highly oblique and upon 

 the same side of the normal to the surface. The dispersed 

 light is then strongly, sometimes almost completely, polarized, 

 and the plane of polarization is parallel to the direction of the 

 lines, L e. perpendicular to the plane of incidence. A silver 

 surface, polished by rubbing with ordinary rouge in one 

 direction, shows these effects well, and even a piece of tin- 

 plate, treated similarly with cotton-wool, suffices. The plate 

 is to be held obliquely and the incident rays should come 

 from a window or sky-light behind the observer. It is of 

 importance to avoid stray light and especially any that could 

 reach the eye by specular reflexion. Observation with a 

 nicol shows at once that the light is strongly polarized and 

 in the opposite way to that regularly reflected from a glass 

 plate similarly held. 



Under the microscope a single line may be well observed, 

 especially when strongly lighted by sunlight. Fizeau found 

 that when the incidence is oblique and the observation normal 

 (a = small, </> = 90°), or equally when the incidence is normal 

 and the observation oblique (a = 90°, cf> = small), the above 

 specified polarization obtains, provided the line be very fine ; 

 otherwise the polarization may be reversed. When the in- 

 cidence is oblique and the light nearly retraces its course 

 (a and <£ both small and of the same sign), the polarization 

 is more complete and also less dependent upon extreme 

 fineness. When u and <fi are both in the neighbourhood of 90°, 

 the polarization becomes insensible. If the incidence is 

 oblique and the angle of observation in the neighbourhood of 

 the regularly reflected light, traces of reversed polarization 

 are to be detected. 



* Annates de Chimie, lxiii. p. 385 (1861) ; Mascart's Traite d'Optique, 

 § 645. 



