70 C, Barus — Rotation of Interference Fringes 



is practically a plane wavefront, perpendicular to the rays in 

 8', /S', 7, and the diffracted rays J"/, T/, T 3 \ are also practically 

 parallel. Hence in case of symmetry and coincidence of J/^A 7 ,, 

 the points 8\ fi'y, 8',a'e, are in the same phase (diffraction 1 ). In 

 other words, there is no path difference between T^+A'and 

 Y + A", whether the angle of incidence is zero or not ( Y l + X l 

 and I 7 "/ -f- A','). The whole field in the telescope must there- 

 fore show the same illumination (homogeneous light, wide slit) 

 between the maximum brightness and complete darkness. 

 Interference fringes can only occur when the opaque mirror 

 J/, is displaced parallel to itself, out of the symmetrical posi- 

 tion. If J/, and JY, are symmetrical, as in figure 3, the dis- 

 placement of G', fore and aft, parallel to itself, is without 

 influence. 



This reduces the whole discussion to the normal displace- 

 ments of the system G\ M u A T ,, given in figure 4. Let the 

 mirror M l be displaced over a normal distance, e m , to the posi- 

 tion M ti A 7 ", remaining in place. Then the image of G' will 

 be at G./, at a perpendicular distance e from its original position 

 (f/. The path difference so introduced, since 8', /3', 7, then 8\ 

 a', e', finally e', 77, £, are in the same phase, is 



2e m cos 8/2 



8 being the double angle of reflection, and the displacement per 

 fringe will be 



2 cos 8/2 



which is very nearly equal to A/2, as in most interferometers, 

 remembering that e and 8e refer to the displacement of the 

 virtual image of the grating G' and e m to M x . Two interfer- 

 ing rays will be coincident. 



If the mirror 3£ l is further displaced normally to J/ 4 the 

 image of G' will be at G,' (the total displacement being e'), 

 and the rays in e and /j, (at a distance c apart on the grating 

 G,') will correspond with the path differences 



2e„,' cos 8/2 



while per fringe 8e = 8e' . 



In the next place, e and 8e may be reduced to the corre- 

 sponding displacements e m and de m of the mirror M x . From 

 figure 3 



sin o72 . 



e m = e — -. — - — = ie sec oy 2. 

 sin o- " ' 



If 6r" is displaced parallel to itself, 8e will not be modified, 

 since each virtual image G/, G/ moves in parallel in the same 



