70 THE INTERFEROMETRY OF 



vertical and horizontal axis. The thickness of the efficient air-film is thus e- 

 and H and G may be brought to touch or to recede from each other several 

 centimeters. L is the collimator (slit and lens), furnishing intense white sun, 

 light or arc light, and the beam, after traversing the system, is viewed by 

 the telescope T (direct beams, fig. 51), or D (diffracted beams). 



The plate H is half-silvered, but the grating G is left clear. In this case, 

 however, only the fine fringes are seen strongly on transmission. The others 

 appear on reflection at G, preferably in the second order of spectra. Fine 

 fringes are not well reflected, but the medium and coarse fringes are very 

 strong and clear, and the first observations were made by means of them. 



Thereafter the ruled face of the grating was half -silvered. This largely 

 destroys the reflected field, D f , except the fine fringes, but the transmitted 

 field D is now strong, particularly in the second order of spectra, for all the 

 three sets of fringes in question. Mr. Ives's direct-vision prism grating 

 shows the fine fringes well in the direct beam T. The lines are always rigor- 

 ously straight, so far as they can be observed; i.e., it is impossible to bring 

 H and G rigorously in contact, not only because of dust, but since the grating 

 (at least) is not optical plate. The fine fringes may always be found in the 

 principal plane of a telescope, but the medium and coarse fringes usually lie 

 in other focal planes differing from each other. By placing the ocular it is 

 thus possible to eliminate any of the interferences or to show a single set in 

 the field only. 



To find the fringes, the direct white-slit images are made to coincide through- 

 out their extent, and the same may be done with a pair of spectrum lines in 

 the superposed spectra. The proper e is then to be sought. Owing to imper- 

 fect plane parallel plates, it may be necessary to correct this by the adjustment 

 screws on the mirror until sharp, strong fringes are seen in the corresponding 

 focal plane. 



31. Equations. The equations for the three useful interferences in ques- 

 tion are for r<6 m and a similar group for r > 6 m 



(1) n\ = 2e/j.cosr 



(2) n\ = 2en cos d' m 



(3) n\ = 2Ai(cos r cos 0'' m ) 



where X is the wave-length of the color used, n the order of the interference, 

 e the thickness of the sheet to be measured, and (j, index of refraction, if i is 

 the angle of incidence of the white light on the grating, r the angle of refrac- 

 tion in the plate (ju) , and Q' n the angle of diffraction of the mth order of spec- 

 tra therein. If the sheet is an air-space, these equations become simplified, 

 since n = i and r is replaced by i, tf m by m , the angle of diffraction in air. 

 Thus, since positive values are in question, 



(4) n\ = 2ecosi 



(5) n\ = 2e cos d m 



(6) n\ = 2e(cosi cos m ) 



