544 Prod. Trowbridge and Mr. Orandall on Groove-Form 



considering only that part of the wave-front diffracted from 

 the portion AG of the groove. Referring to fig. 4 c : 



29 is the angle between collimators, 

 AA' is the oncoming wave-fro„nt, 

 AD is the diffracted wave-front, 

 i is the angle of incidence, 



6 — i = h is the angle of deviation of the grating from 

 the position of the central image. 



The retardation of the one end of the wave-front over the 

 other is seen to be 



p=AO(cos A'CA + cos DCA), 

 since 

 cosA'CA = cos{90 o -(f-f23 o )}=sin( ? , + 23°), 



and 



cosDCA = cos{2<9 + ^A'CA}=cos {90- (i+ 23° + 20)} 



= sin (i + 23°-20), 



/ o = AC{sin(i + 23 o ) + sin(i + 23 o -20)} 

 = 2 AC sin (i+ 23° -6) cos 0, 



or, since 6 — i = S, we have 



p = 2ACsin(23°-8) cos d *. 



The value of AB is '00123 cm., the ratio - = "802, so that 



_. ri -00123x0-802x2 nn91 _ 



2AC = -— r„ = 002136 cm., 



cos 26 7 



while the half angle between collimators is 9°' 6. The curve 

 showing the relation between p and 8 is given in fig. 5. 

 Obviously the retardation must vanish when 8 = 23°, i.e., 

 when the grating is turned so that the oblique image is 

 viewed by the collimator. The retardation for any position 

 of the grating may now be read off the curve, and if this 

 were an exact multiple of the wave-length diffracted into 

 the collimator for this setting, we should expect the order 

 naturally occurring at this point to be extinguished. How- 

 ever, due to the assumptions made, and the fact that the 

 plane AC is not a good enough mirror to define the oblique 



* If the side BO were vertical, it would, under some settings of the 

 grating, cut off a portion of the diffracted wave-front so that a varying 

 portion of the line AO must be used in deriving the formula. This is 

 taken into account in the more general formula, since b = c in this case 



