Interference Phenomena. 545 



inversely as the squares of the distance compared to those 

 terms which alone are of importance, unless the point under 

 consideration is close to the surface, we find 



^-JJ-£^-jj*-Ji.£J<.-j-)«. 



To apply this equation to the special case treated in § 8 we 

 take (j> at the surface to be independent of that direction 

 which is parallel to the lines of the grating and measure s at 

 right angles to the lines ; if 21 is the width of the grating, 

 h its length, r the value of r for that line which is drawn 

 from any point P to the centre of the grating, j3 the angle 

 between r and the normal, and if finally r is taken to be 

 very large, 



M(0 = ! L^il C +l d J t _ i sin/3 U. 



rw ar Q J dt^\ a J 



The amplitude of the disturbance at the focal plane of a 

 telescope varies inversely with the focal length ; hence, if 

 instead of receiving; the light on a screen at an infinite 

 distance, we collect it by means of a lens of focal length F, 

 we must substitute F for r in the above expression. Let 



now yfrlt J be the disturbance in the incident beam which 



falls on the grating at an angle a, and let, as in § 8, the 

 grating act in such a way as ,to reduce -\Jr in the ratio cos qs. 

 The value of <£ at the grating will for the reflected beam 

 become 



<j>{t)=cosgsf(t+— a -j, 



and if we put y=s(sin/3— sin a), 



_ , , N h cos 8 C d , . . N , 



2?r0(O= aF J cos qs ^ir(t-ys/a)ds. 



This is the equation we have made use of for the displace- 

 ment produced at the focus of a lens, of focal length F, by a 

 simple grating the lines of which are at a distance 2ir/q } the 

 displacement in the incident beam being given as sjr(t — a:/a). 



