REFRACTION OF LIGHT, REFRACTOMETRY AND INTERFEROMETRY 



width within which the spectrum is con- 

 tinuous. 



A discussion of group-velocities falls out- 

 side the scope of this article, except where 

 the refractive index is concerned. 



The group-velocity U is related to the re- 

 fractive dispersion by the formula: 



U = C/[n - {\-dn/d\)] 



{20) 



Since dn is large compared to d\, U tends to 

 become much smaller than C, which repre- 

 sents a maximum: the refractive index n = 

 C/U for the bundle becomes greater than 

 that for any one of the radiations it contains. 



The group-velocity concept has recently 

 acquired a fundamental importance, as the 

 cornerstone of a generalized theory of Re- 

 fraction. This new theory is now capable of 

 encompassing the situations arising when 

 the radiation emitters are in fast motion 

 relatively to the medium of index n. These 

 phenomena include the emission of the 

 Cherenkov-Vavrilov polarized radiation, the 

 Doepler effect at super-light velocitj^, and 

 others. They have an immense practical im- 

 portance for the interpretation of all high- 

 energy high-velocity phenomena involved 

 in nuclear energy investigations. The com- 

 plete theory of interferences at superlight 

 velocities how^ever, remains to be fully de- 

 veloped. 



The optical pathway Li of light through 

 a transparent medium is related to the time 

 t required to traverse it by 



If one of the media is a vacuum (no = 1), it 

 results that the optical path length is the 

 product of the geometrical length of a me- 

 dium l\y its refractive index relative to 

 vacuum (ni). This important relation is the 

 basis for the determination of relative re- 

 fractive indices by the interferometric 

 methods, involving a direct comparison of 

 the products nL in two media, one of which 

 is known. 



In Huygens vibrational theory it is 

 postulated that "something along the path 

 of a light ray is vibrating according to a 

 sinusoidal function of the general type : 



L = A sin 2t ^^ - ^ + a) 



(24) 



t = Li/Fi , or Li = t-Vi 



(21) 



A similar relation holds for any other me- 

 dium in which the velocity will be V2 . If 

 during the same time t, light traverses a 

 layer Li of medium 1 and a layer L2 of 

 medium 2, one can write: 



The correctness of this theory became ap- 

 parent when Thomas Young succeeded 

 (1813) in composing the vibrations issued 

 from two synchronous light sources (pin- 

 holes lighted from the same primary source) 

 whose interference thus extinguished the 

 light. 



By application of Huygens theorem to 

 the space between the primary source of 

 radiant energy and the plan containing 

 Young's twin apertures, it is possible to 

 demonstrate that the rays issuing from these 

 apertures are formed of synchronous vibra- 

 tions. Such rays are said to be "coherent". 



In this memorable experiment two syn- 

 chronous point sources of light A and B, sep- 

 arated by a distance a produce two narrow 

 beams of light falling upon the same area c 

 on a screen placed at the distance d. 



The amplitude L of the synchronous vi- 

 bration X issued from A and B is: 



L = An sin 27r 



iH 



(25) 



UIU = ^Fl/F2 



{22) 



Since F1/F2 = n2 or relative index of me- 

 dium 2 compared to medium 1, one has 



h\ = TfltLl 



{2S) 



The difference p between the paths of the 

 light rays Ac' and Be' falling on c' (c — c' = 

 z) is: 



p = Be' - Ac' = X2- xi (26) 



and the difference of phase <^, of the two 



504 



