Lord Rayleigh on Pin-hole Photography. 97 



the number of wave-lengths by which the extreme ray is 

 retarded relatively to the central ray ; for 



v(W)+v /^ + ,2)- a -i = £„+> approximately . 



According to (26) the aperture should be enlarged until the 

 retardation amounts to jfh,. 



In the image of a double star the curves of brightness 

 proper to the two components are superposed. If the com- 

 ponents are equal, resolution will be just beginning when the 

 distance of the geometrical images asunder is the double of 

 the value of ? for which I 2 has about one-half its maximum 

 value. By inspection of the curve for y — ^ir we see that 

 there will not be much appearance of resolution until 

 zj^/2 = 1*5. The corresponding angular interval between 

 the two components is 



?= ^—Vt/) ^ 



This may be regarded as defining the maximum separating 

 power as a function of A. and/. 



Passing on from the theoretical discussion, I w r ill now 

 describe certain laboratory observations upon the defining 

 power of various apertures. A succession of such, of gradually 

 increasing magnitude, were perforated in a piece of thin 

 sheet zinc, and were measured under the microscope. The 

 diameters, in fractions of an inch, are as follows : — a 



(1) (2) (3) (4) (5) (6) 



•0210, -0240, -0262, -0290, '0326, -0366. 



The objects, whose images were examined, are (1) a grating 

 cut out of sheet zinc, and (2) a pair of equal round holes a 

 quarter of an inch apart. The period of the grating is also a 

 quarter inch, and the transparent and opaque parts are equally 

 wide. Behind the grating, or double hole, was placed a 

 paraffin lamp and a large condensing lens. The distance a 

 between the objects and the apertures under test was about 

 18 feet. 



The best image with a given aperture is obtained by 

 bringing the eye immediately behind, without the use of a 

 focusing lens. But the image formed at a sufficient distance 

 beyond, and examined with a focusing glass of low power, 

 is nearly as good. Thus at a sufficient distance (b) the 



