134 REPORT OX PHYSICAL OPTICS. 



But in the first application of the principle of interference to 

 the colours of crystalline plates there arose a difficulty to which 

 the known laws afforded no answer. So far as this explanation 

 went, the phenomena of interference and of colour should be 

 produced by the crystal alone, and in common light, without either 

 polarizing plate or analyzing plate. Such, however, is not the 

 fact ; and the real difficulty seemed to be, not to explain how the 

 phenomena are produced, but to show why they are not always- 

 produced. It occurred to MM. Arago and Fresnel to inquire how 

 far the state of polarization of the two pencils might modify the 

 known laws of interference ; and the results of this inquiry* have 

 happily furnished an account of the difficulty, and completed the 

 solution of the problem. It was found that two rays of light 

 polarized in the same plane interfere, and produce fringes, under 

 the same circumstances as two rays of common light ; that, when 

 the planes of polarization are inclined, the interference is diminished 

 and the fringes decrease in intensity ; and that, finally, when the 

 angle between these planes is a right angle, the rays no longer 

 interfere at all. Hence the two rays which emerge from a crystal- 

 line plate, being oppositely polarized, cannot interfere ; and, to 

 produce the phenomena of colour in perfection, their planes of 

 polarization must be brought to coincidence by the analyzer. 



The non-interference of rays oppositely polarized is a necessary 

 result of the mechanical theory of transversal vibrations. Fresnel 

 has shown, on the principles of that theory, that the intensity of 

 the light resulting from the union of two such rays is constant,. 

 and equal to the sum of the intensities of the components, what- 

 ever be the phases of vibration in which they meet. But though 

 the intensity of the light does not vary with the phase of the 

 component vibrations, the character of the resulting vibration will. 

 It appears from theory that two rectilinear and rectangular vibra- 

 tions compound a single vibration, which will be also rectilinear 

 when the phases of the component vibrations differ by an exact 

 number of semiundulations ; that, in all other cases, the resulting 

 vibration will be elliptic ; and that the ellipse will become a circk, 

 when the component vibrations have equal amplitudes, and the 

 difference of their phases is an odd multiple of a quarter of a 

 wave. These results of theory have been completely confirmed 



" Mcmoire s.ir 1' Action qu 5 b s Rayons de la Lumicre polarisee exercent les uns 



sur lea autref," ^nnales c'e C/n'mic, ton-, x. 



