66 THE INTERFEROMETRY OF 



tion G'I. The path-difference so introduced, since a and b (ab normal to the 

 ray Y z impinging on M 3 at c and reflected to b) are in the same phase, is 



ze m cos 6/2 



and the displacement per fringe 1 will be 



X 



wt/ m < / 



2 COS 6/2 



which is nearly equal to X/2, as in most interferometers, remembering that 

 e m and de m refer to the displacement of the mirror Mi. Two interfering rays 

 will be coincident at b. 



In the next place e and 8e may be reduced from the corresponding displace- 

 ments e m and de m of the mirror Mi. In figure 48 the figure fdbe is approxi- 

 mately a parallelogram with the acute angles 6/2. Hence, since 2 = ( 5+00/2 



2C m COS (7/2 =6 



as is also otherwise evident. Thus per fringe, if the length g = c 



\ = de cos 6 2+ 8c sin 2 

 since dc = 2 5e m sin (7/2 . 



If G' is displaced parallel to itself, 8e will not be modified, since each virtual 

 image G\ and G's moves in parallel, in the same direction, by the same amount. 

 If then the grating G' is rotated around an axis at G', perpendicular to the 

 diagram, figure 47, over a small angle, <p, the result (apart from the super- 

 posed rotational effect) is equivalent to a displacement of the mirrors MI and 

 Ni in opposite directions, producing a virtual distance apart e and the cor- 

 responding interference fringes. In other words, the rotational effects may be 

 explained here in the same way as in the preceding paragraph. 



The angle zdd, within which the interference rays lie, per fringe, is sub- 

 tended by 8e m , and this may be put roughly (N= 162 cm., normal distance) 



2dd=(28e m sin 5/2)/JV= (X tan 8/ 2 )/N 



This angle is very small, scarcely icr 8 X3.2 radians, or less than o.oi second 

 of arc. Hence all pencils consist of practically parallel rays. 



An important result is the angular size of the fringes; i.e., if e m and X are 



given 



d6 2 _ X _ Dz sin 2 

 dn e m sin 6/2 e m sin 6/2 



D 2 being the grating space. 



Thus they become infinitely large when e m passes through zero. The angu- 

 lar size is independent of the distance between the gratings. It ought, there- 

 fore, to be easy to obtain large interference fringes, which is not the case. 

 The reason probably lies in this : that the two opaque mirrors are not quite 



1 The differential symbol 5 is unfortunately also used to designate the double angle of 

 reflection 5. But it is improbable that this will lead to confusion. 



