INTEKFEKOMETRIC METHODS 



Combining (40) and (41) gives: 

 n = 4Rk\/d^ 



im 



With this method, the measured diameter 

 d varies only as the square root of the re- 

 fractive index. 



Fringes of Equal Incidence. The ar- 

 rangement of the optical parts is similar to 

 that used to produce Newton's rings, but 

 there is no lens, and the plane p is formed of 

 a parallel-face transparent plate of thickness 

 I and index n. A large monochromatic light 

 source is used (sodium lamp). The fringes 

 are circular and centered around the point 

 corresponding to the incidence of rays per- 

 pendicular to the plate (r = 0). The center 

 of the system is black. The difference of 

 pathway between the two reflected beams of 

 rays is equal to 2 nl. The angular radius of 

 the first ring is : 



«! = nX2/po 

 the order of this first ring being: 



po = 2nl/\ 



(43) 



iU) 



The angular radius a of any ring of order k 

 is given by: 



a = n\ 2/730 • k (45) 



With thicknesses successively 0.1, 1.0, 10, 

 and 20 mm, the following radii are found: 

 6', 2', 38'', and 27'', respectively. 



Even with a plate deviating from paral- 

 lelism by as much as 30" (seconds of arc), the 

 fringes are still visible, provided the zone ob- 

 served is less than 0.5 mm in diameter (ocu- 

 lar/ = 60 mm, objective / = 30 mm, mag- 

 nification X0.5, with an ocular diaphragm 

 of 1 mm forming on the plate a virtual image 

 of 0.5 mm diameter). 



This arrangement is very convenient the 

 verification of optically parallel transparent 

 plates: a variation of thickness of dl = X/ 

 2n = 0.18 produces a variation of diameter 

 equal to the thickness of one fringe. Con- 

 tinuous photographic recording is possible. 

 This apparatus, as well as Fizeau's, is fre- 

 quently used in dilatometric studies. 



The standard ultraviolet refractometer of 

 Lowry and Allsopp (82) uses the formation 

 of fringes by a wedge comprised between 

 two semi-platinized glass flats, mounted on 

 the Hilger Co. stand. The separation of the 

 fringes depends only on the wavelength 

 and the index of the medium filling the 

 wedge. The spectrograph is set at right 

 angles to the fringes. The fringes' separation 

 can be measured at any wavelength, on the 

 spectrograms, by reference to a set of en- 

 graved lines. The theory of the fringes pro- 

 duced by a wedge is that of Fabry and 

 Perot interferometer. 



Instruments Producing Non -localized 

 Fringes 



Instruments of this type possess two well- 

 separated beams of light. They are adaptable 

 to measurements by application of equation 

 (37). The first observations made along this 

 line were those of Thomas Young. Since this 

 memorable experiment, the procedure al- 

 ways involves producing two synchronous 

 (coherent) pencils of light from one single 

 narrow slit or a small circular aperture. From 

 there on, the means employed to divide the 

 light along these pencils vary. 



The simple arrangement of the Fresnel 

 double mirrors dates from 1816. Fresnel's 

 double-prism setup, dating back to 1819, 

 and his triple mirror interferometer of 1820, 

 described in most textbooks, utilize the same 

 principle. Other interferometers of the same 

 general design were subsequentlj^ built by 

 Lloyd (1837), by Haidinger (1849), by 

 Fizeau, and by Mascart. 



Billet's half -lens and his half -prism inter- 

 ferometers are based upon the principle of 

 homo-focality, and date back to 1858. The 

 apparatus of Dessains is of considerable 

 historical interest for the metrologists. 



The apparatus built by Jamin between 

 1856 and 1858 was established on the work 

 of Brewster on the interferences produced by 

 thick glass plates (circa 1817). In this ap- 

 paratus the separation of the two light beams 



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