90 



DISPLACEMENT INTERFEROMETRY BY 



trum images may be small enough to be separated. In case of clear glass, 

 however, there is practically but one pair of bright images, and they carry 

 fringes when properly superposed. 



66. Equations. One internal reflection. The first question to be elucidated 

 is the nature of the conditions of refraction. From figure 88, in view of the 

 symmetry of the arrangement, if b is the breadth of the ray parallelogram and 

 R the radius of the cylinder and h the distance of the chord C from the axis A , 



(1) sin i = sin 2r = b/2R 



(2) smr=h/R 

 and the index of refraction 



(3) M = sin j'/sin (2/2) which reduces to p. = 2 cos r = b/2h. 



20 



/9 



18 



/e 



56789 Worn, 



The relations remain the same if b/zR is constant. If the (small) value 

 b= 10 cm. is inserted into the equation, the results are such as shown by the 

 graphs for i and n in figure 90. It is seen, therefore, that for diameter 2R 

 between 10 and n cm., the available indices of refraction of the glass would 

 increase from 1.4 to 1.7 roughly, while the angle * falls from 90 to about 65. 

 Hence the experiment requires the interfering rays to impinge near the outer 

 limits of the cylinder; but it is otherwise quite feasible. By narrowing the 

 outside beam, only a small part of the caustic within the cylinder will be used. 



It is next in order to consider the possibly observable conditions of apparent 

 ether drag. The velocity within the refracting medium of index fj, is usually 

 written (or follows from the theory * of relativity) in the form 



(4) c/^v(i-i/^ 



where v is the velocity of the medium in the direction, or contrary to the 

 direction of the velocity of light c. It remains therefore to determine the 

 average speed of the beam along the chord C of figure 86. From this figure 



(5) C = 2R cos r = iJ.R, and b = 2fj.h 

 whence, 



(6) 



b = 



- 



* The insufficiency of this equation has been shown by Zeeman (Amsterdam Acad 

 Sept. 1914 and Sept. 1915). But an estimate only is above in question. 



