REFRACTION OF LIGHT, REFRACTOMETRY AND INTERFEROMETRY 



In this case, the new vakies Xi and X2 will 

 be the optical pathways Xi = Xi'-ni , and 

 x-i = Xi-Ui , respectively, according to equa- 

 tion {S3). Consequently, the measurement 

 of Ic , at point c' should lead to the calcula- 

 tion of the refractive indices, rii , for in- 

 stance, if the other, n2 , and the values of: 

 a, d, z, and X are known. This determination 

 can be effected more easily by considering 

 only the distance from point c on the screen, 

 of the points where the intensity Ic is either 

 zero (minimum) or maximum (4^^), thus 

 avoiding photometric measurements. One 

 demonstrates that the maxima of light (cen- 

 ter of bright fringes) are located in the points 

 where the difference of optical pathways 

 X2 — a;i is either zero or an exact integer K = 

 0, 1, 2, 3, 4, etc., of the wavelength X: 



or 



p = K\ 



(SI) 



Similarly, the location of the minima (cen- 

 ter of dark fringes), w^here L = for any 

 value of t, is such that : 



TTp 



COS — = 0, or IT 



A 



(:)= 



+ kir, 



{S2) 



or p = (2A' + 1) 



One demonstrates that the locus of all the 

 points satisfying equation {28) is a series of 

 hyperboloids of revolution centered on A and 

 B. Only for the lowest values of the order K 

 of the black fringes are these fringes appear- 

 ing straight in the zone where the observa- 

 tion plan on the screen c intersects the hyper- 

 boloids. 



A last simplification is derived from the 

 relationship existing between the difference 

 of pathways p and the geometrical dimen- 

 sions of the apparatus, a and d: 



p = x-i-n-i — x\-ni = a sin 6 = az/d {33) 



Combining {32) and {33), the distance from 

 z to the centers of the black fringes (order 

 K = 1) is given by: 



{2K + l)d-\ 

 2a 



Obviously, the distance h between the cen- 

 ters of two consecutive black fringes is 



h = d\/a 



(35) 



If the geometrical dimensions: Ac = Be = 

 I are constant but the two interfering beams 

 of light rays traverse two different media of 

 refractive indices rii and 712 , respectively, 

 equation {33) becomes: 



p = l{dn) = a-z/d 



(36) 



The middle fringe (and also the whole sys- 

 tem) moves away from the point c to an- 

 other point c' which is distant from c by the 

 width 2h of an interfringe when: 



, , ad\ 

 l(dn) = —- = X 

 ad 



(37) 



az/d = {2K + 1) X/2 



(34) 



Therefore, a single measurement of the 

 displacement of the fringes on the screen 

 gives directly dn, if X, a, and d are fixed. 



The various interferometric methods differ 

 by means utilized to produce two coherent 

 beams of light. The selection of an instru- 

 ment depends upon the application con- 

 templated. 



Classification of Interferometers 



Several classifications of interferometers 

 are possible, according to the predominant 

 point of view. 



If one considers mainly the utilitarian as- 

 pect, two broad groups can be distinguished: 



Instruments with widely separated beams of 

 light. This group includes instrument types 

 based upon the original experiment of 

 Thomas Young, and those based upon the 

 properties of semireflecting surfaces. The 

 former type is realized in devices identified 

 by their inventor's name: Young's, Fresnel 

 mirrors, Fizeau, Soleil, Mascart, Billet's 

 lenses and prisms, Desains, Rayleigh, Ray- 

 leigh-WiUiams (Hilger Mfg.), Le ChateUer, 



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