116 Prof. S. Banerji on the Radiation of Light 



The total disturbance at Q in the focal plane is therefore 



I I rsm*27rU ^ ?-\dOdr. . . . (1) 



%JQ */0 



The rays from the various elements r'dd'dr' of the second 

 aperture may be regarded as meeting in the field of the 

 observing telescope proceeding at an angle <f>' with the axis 

 and producing the observed effect. The total disturbance 

 in this direction due to the second aperture is therefore; 



r0;p-*(H 



cos 6 sin (j) 



X 



'!cos 0' sin d>'\ _ __ _ , _.. 

 ^ ^-jdrdddr'dO'. (2) 



Since (f> and $' are small quantities, the above expression 

 can be written as 



p, p p p^ t ^ , t ^ ^, reos # 



Jo Je! Jo Jo ^T X 



This expression can be reduced to the form 



»27T (* K~ 



x f T' c ° s ( 27r ^x°^) *" d 4 (4) 



the other integral being zero on account of symmetry of the 

 diffracting aperture. 

 But the integral 



Therefore the expression (4) becomes 



ffW,^(f^').^(>), w 



neglecting a constant factor. 



If / is the focal length of the lens, then $=j. The- 



