Reflected-Dlffracted and Diffracted- Reflected Rays. 57 



Suppose the remote glass face makes an angle dr/2 with 

 the surface of the grating. Then the DR ray of the strong 

 interferences has its angle increased by dd = dr, whereas the 

 RD ray receives an increment of but 



cos a 



Hence if the DR and RD rays were parallel for parallel 

 surfaces, they would be at an angle corresponding to 



d6 — dr cos r— cos (9±\ 



~dr~~ = c^s~0 ? * ' " ' ^ } 



where dr/2 is the angle of the wedge. If DR is negative in 

 character, opposite conditions will hold, since dr and dO 

 change signs together. 



Rays all but parallel will cross each other in front 

 (convergent) or behind (divergent) the grating, depending 

 on their mutual lateral positions. As a ray moves from the 

 right to the left of the normal, the phenomenon may change 

 from divergence to convergence, and vice versa. 



These relations are very well brought out by the inter- 

 ferometer of which the mirror M may be inclined at pleasure. 

 If small values of deviation only are in question, this instru- 

 ment becomes a means of measuring small horizontal angles 

 7 between mirror and grating as these involve less change of 

 focus. 



In fact, if h is the vertical height of the illumination at 

 the mirror M } and the corresponding obliquity of fringes is 

 equivalent to an excess of N fringes crossing the bottom of 

 the cross-hairs as compared with the top for a wave-length X, 

 ry = NSe/h ; or 



NX 



ry — — m 



21i(cos 0' — cosi) 



The question next at issue is thus the value of li. It will 

 be noticed that if parallel rays fall upon the slit, they will be 

 brought to a focus by the collimator objective first, and 

 thereafter by the telescope objective placed at a diametral 

 distance D beyond it. Then if S is the vertical length of 

 slit used, and/c and/* the focal lengths of the two objectives 

 respectively, it follows that the length h = S is virtually 

 illuminated. Hence 



7 = 2S(cos<9'-eos 2 ) ^ 



For since the angle 7, or a ratio, is in question, Nhejli is 



