GRATINGS IN THEORY AND PRACTICE 527 



The direction of the diffracted light will then be defined by the 

 equations 



' 2 + p* + r * =0, 



whence 



Fff^J-Jf-If, 



a 



In the ordinary case where the incident and diffracted rays are per- 

 pendicular to the lines of the grating, we can simplify the equations 

 somewhat. 



Let <p be the angle of incidence and (p of diffraction as measured from 

 the positive direction of X. 



A = /' cos <f + I cos <p , 



N = fi = /' sin y + / sin </> , 

 a 



where I is the wave-length in vacuo. 

 In case of the reflecting grating 1 = 1' and we can write 

 A = I\coa<p + cos <^}, 



N=. ii = I\ sin a> + sin <p\. 

 a 



This is only a very elementary expression as the real value would 

 depend on the nature of the obstacle, the angles, etc., but it will be suffi- 

 cient for our purpose. 



The disturbance due to any grating or similar body will then be very 

 nearly 



(* r e ib[R- Vt to-ny-vz + KW + y' + tfrtclg^ 

 where ds is a differential of the surface. For parallel rays, K = 0. 



PLANE GRATINGS 



In this case the integration can often be neglected in the direction 

 of z and we can write for the disturbance in case of parallel rays, 



aib(R Vt) I I (, il>[ AX ny] /7 

 J J 



