CHAPTER IX. 



THE USE OF COMPENSATORS, BOUNDED BY CURVED SURFACES, IN 

 DISPLACEMENT INTERFEROMETRY. 



63. Introduction. -The method of increasing the sensitiveness of the dis- 

 placement interferometer by increasing the dispersion of the grating readily 

 suggests itself, but unfortunately the interference pattern loses sharpness in 

 the same ratio and ultimately becomes too diffuse for practical purposes. 

 Similar sensitiveness is secured when the air-paths and the glass-paths of the 

 component beams of light are respectively identical, with the same inadequacy 

 in the huge mobile figures, for the purpose of adjustment. In fact, if for sim- 

 plicity we consider the incidence normal (I = R = o, linear interferometer), 

 the sensitiveness becomes 



de/dn = \ z /[2eD cos 0. 



where 6 is the angle of diffraction for the wave-length X, e the thickness of the 

 plate of the grating, /* its index of refraction, D the grating space, n the order 

 of the fringe, and b, N, constants. Hence, other things being equal, dQ/dn 

 increases as D and e grow smaller, where e = o is obtained by a compensator 

 counteracting the thickness of the plate of the grating. 



It occurred to me that the difficulty of diffuse interference patterns might 

 be overcome, in part, by the use of compensators with curved faces, when the 

 case would become similar to the conversion of the usual interference colors 

 of thin plates into Newton's rings. Naturally a cylindric lens with its elements 

 normal to the slit is chiefly in question, though an ordinary lens also presents 

 cases of interest, chiefly because of the easy conversion of elliptic into hyper- 

 bolic patterns, and the lens is more easily obtained. 



Other methods were tried. For instance, on using a Fresnel biprism with 

 its blunt edge normal to the slit, two sets of interference patterns, one above 

 the other in the spectrum, are obtained. When the blunt edge is parallel to 

 the slit, either side of the prism gives its own interferences, but they can 

 not be made clearly visible at the same time. A doubly reflecting plate or a 

 thin sheet of mica covering one half of the beam will produce two intersecting 

 patterns, but these also are of little use for measurement. 



64. Lens systems. -If but a single compensator is to be used, i.e., compen- 

 sation in one of the component beams only, the lens in question must be of 

 very small focal power; otherwise the adjustment will be impossible, as the 

 two direct images of the slit will be in very different focal planes. Moreover, 

 the focal power should be variable. All this makes it necessary to use a 

 doublet, preferably consisting of lenses of the same focal power, respectively 

 convex and concave. If these lenses are themselves weak, say i meter in 

 focal distance, both slit images may easily be seen in the telescope and be 



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