Interference-Fringes in the Focus of a Telescope. 257 



senting the distribution along the radius be i = ^(r) y then the 

 element of intensity of a strip y x dx will be 



I 





and it has been shown that the visibility-curve in this case is 



fa(x) cos kx 



fr(a)da 



This may be proved as follows : — 



The intensity of the diffraction-figure of a luminous point 

 in a telescope with a symmetrical aperture is * 



I 2 = \\\ cos Kfi^Y cos icv x yxd x \ dy\\ ' • • • • (X) 



in which k = 2tt/\, fi x and v x are the angular distances from the 

 centre of the image, and x x and y l are the coordinates of the 

 element of surface of the aperture. 



If fju and v are counted from the axis of the telescope and 

 x, y, r, are the coordinates of the luminous point, the expres- 

 sion becomes 



12 = LI) C ° S Y ~ f)* 1 C ° S K Y~~r) yid * ldy ^\ ' ' ^ 



If now the source is a luminous surface whose elements 

 vibrate independently, 



l=^l 2 dxdy (3) 



For the case of two equal apertures t whose centres are at 

 x x = — Ja u and x l = +|a n , 



I* i= I2 C osH«%i(/*-Q (4) 



This substituted in (3) gives 



1=11 1 2 cos 2 i«a n ( fi — Jdxdy. 



* ' Wave Theory of Light,' Rayleigh. 



t More generally, for m equal equidistant apertures whose total area is 

 constant, 



t __t sin § miefwi 

 m sin ^ Kfxa 



