24 



THE INTERFEROMETRY OF 



of the coarse sagittate phenomena into the hair-like striations, as a and b 

 move farther apart, may then be accounted for in accordance with the general 

 theory of diffraction; i.e., if. the distance apart of a and b is d and the principal 

 focal distance of is R, 



d~R 



where z is the distance between the two fringes of wave-length X. Hence z 

 will increase as d decreases, agreeing with the effect of fore-and-aft motion, 

 or with the effect of simultaneous, large (2.5 cm.) displacement of both 

 mirrors, neither of which destroys the symmetry of the interfering rays. 



I W 



10 



The motion of a single mirror, M or N, for instance, does destroy the sym- 

 metry, and it was shown in 12 that the limiting range of displacement of 

 0.25 cm. moves either a or b 0.096 cm. out of symmetry. The interferences 

 thus vanish without much changing in form or size, and vanish in all focal 

 planes. 



The breadth of the blades of light aa' and bb f , figure n, capable of inter- 

 fering is x on the grating and 



x cos ^ = 0.096X0.808 = 0.078 cm. 



normally. Since the rays are parallel after leaving the collimator, this would 

 be about half the breadth of the effective beam on the objective of this appur- 

 tenance. Thus 2 Xo.o776 = o.i 55 cm., increased by the width of the refracting 

 edge of the prism, is the width of the strip of white light which, after separa- 

 tion by the knife-edge of the prism, furnished the two component beams which 

 potentially interfere on recombination. It is reasonable to suppose that the 

 elements of these beams come from a common source and that the width in 

 question is produced by the diffraction of the slit. 



This datum is more appropriately reduced to the angle at the slit a, within 

 which lie the rays capable of interfering with each other after the interferom- 

 eter cleavage. As the collimator used was / = 22 cm. from slit to lens, 



a = 2#cos 6/1 = o.i 55/22 =0.0070 



Hence the angular width of the wedge of white light, with its apex at the slit 

 of the collimator and containing all the rays which can mutually interfere, 

 is about 0.007 radian, or less than half a degree of arc. One would infer that 

 a long (/) collimator (i.e., one with weak objective) is advantageous, as the 

 blade of parallel rays issuing is proportionally wide and the range of displace- 



