REFKACTION OF LIGHT, REFRACTO.^IETRY AND INTERFEROMETRY 



the shape of the wave-front realized. This 

 proved occasionally to be of considerable 

 value in discovering newer applications of 

 known arrangements. The wave front shapes 

 involved are: (a) plane wave fronts, (b) 

 curved wave fronts with spherical geometry, 

 (c) irregularly curved fronts (Gouy). 



The meaning of these distinctions will be- 

 come apparent after a discussion of the dif- 

 fraction phenomena taking place in every 

 interferometer. 



Finally, from a didactic standpoint, it is 

 still convenient to follow the classical dis- 

 tinction of two groups of interferometers 

 based upon the reciuired means of observa- 

 tion, as is done in the next two sections: 

 apparatus producing localized fringes, and 

 apparatus producing non-localized fringes. 



The practical implications of this last 

 classification become apparent by consider- 

 ing the Raveau's rule: "when the two rays 

 of light, resulting from the splitting of a 

 single ray emitted from the center of a 

 source S, after its passage through an inter- 

 ferential apparatus, are superimposed at a 

 real point S', the fringes are visible at this 

 point even if the source S is large." 



Apparatus Producing Localized Fringes 



The oldest apparatus of this category was 

 conceived by Newton. The difference of 

 optical path p, is given by: 



p = 2ni-cos r 

 the order of the fringes being: 



Pl = pi/X, P2 = PsA, 



(38) 



etc. 



From this expression, it appears that the 

 fringes will be apparent under two sets of 

 conditions, both practically important: (a) 

 with parallel light (/• = cte) and variable I: 

 the fringes will represent the zones of uni- 

 form thickness of layer L; (b) with an opti- 

 cally parallel plate (Z = cte) and diffused light: 

 the fringes then represent the locus of the 

 impact of rays of identical incidence. 



Fringes of Equal Thickness. A first type 

 of interference produced by Newton rings 

 has wide applications as a checking method 

 in the manufacturing of all sorts of mechan- 

 ical parts. The classical arrangement is still 

 that originally proposed by Fizeau. 



When the flint surfaces of the plane p are 

 altered, Sleator and Martin (81) observed 

 that a ring system with black center was ob- 

 tained, although the conditions were such 

 that a white centered system should be pro- 

 duced (flint index 1.72, lens index 1.53, oil 

 medium index 1.62, in their experiment). 

 This effect disappeared after re-polishing 

 the flint. Conversely, this observation sug- 

 gests the utilization of Newton's rings for 

 the study of the superficial layers and of 

 their alterations. 



When the medium interposed between 

 the plane p and the lens L is air (ri = 1), a 

 measurement of the diameter of the fringe 

 gives the radius R of the lens as a function 

 of k and d: 



rf2 = 4:Rk 



(39) 



where k is the order of the fringes considered, 

 and d is the fringe diameter. 



If it is desired to measure the refractive 

 index, the transparent medium whose re- 

 fractive index is to be measured is placed 

 between the lens L and the plane p, in opti- 

 mal contact with both (for instance, a small 

 closed cell is built to contain the liquid, and 

 this cell is completely filled up). The method 

 of measurement is based upon the fact that, 

 while the square of the diameters of succes- 

 sive fringes of the same color (black, for 

 instance) are as the order of the natural 

 numbers, these diameters are related to the 

 thickness I of the corresponding refracting 

 layer, and to the radius R of the lens by the 

 relation : 



dV4 = 2RI UO) 



On the other hand, one has also: 



2nl = kX, or I = k\/2n (41) 



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