an Optical Paradox. 129 



centrally upon the telescope objective C, is alone considered. 

 In order to deal adequately with what happens when the 

 source of light though central is of sensible size, the inves- 

 tigation needs to be extended to the case where the image of 

 a point-source falls excentrically upon C. When this is done 

 some instructive results emerge into view. 



Lord Rayleigh's experiment, and others related to it, can 

 be most conveniently made with the microscope, which, 

 besides, enables us to experiment with numerical apertures 

 up to 28 times the numerical aperture of an ordinary 

 refracting telescope"*. 



To see that the experiment can be made with the micro- 

 scope — Remove lens L of the apparatus represented by the 

 figure in the text, and replace it by two lenses 1/ and I/', of 

 which lens L' collimates the light from A, while L" con- 

 centrates the collimated beam to a focus at C. It is obviously 

 legitimate to make this substitution. When the experiment 

 is made with a microscope, the source A is to be light passing 

 through a small hole (or slit) in a stop placed under the con- 

 denser. The condenser of the microscope then takes up the 

 duties of lens I/, and at the same time the objective of the 

 microscope discharges the functions of the combination con- 

 sisting of lens L" together with lens C. The image of A 

 produced at C then becomes that image of the hole (or slit) 

 which may be seen in the u Concentration Image " of the 

 microscope — i. e., in the image which comes into view on 

 removing the eyepiece and looking down the microscope tube. 

 Furthermore, when the experiment is made with the micro- 

 scope, any desired object can be put upon the stage of the 

 microscope and becomes the object to be resolved. So far 

 as the writer knows, far the best object to employ is one of 

 the bands of Grayson's Rulings, supplemented by observa- 

 tions upon a single pair of lines such as may here and there 

 be seen to project from one or other end of a band. The 

 hole in the stop may, if desired, be made to behave as a self- 

 luminous source of light, by focussing the light of the lamp- 

 flame or other luminary upon the stop. This will be found 

 in no degree to impair definition, whether the hole in the 

 stop be large or small. 



* The numerical aperture ( i.e. the sine of half the angular aperture) 

 of the objective of an achromatic telescope is seldom so large as O05 ; 

 while the numerical apertures of dry microscope objectives and con- 

 densers range up to 0*95, and the numerical apertures of immersion 

 objectives and immersion condensers range up to 1*4. 



Phil Mag. 8. 6. Vol. 10. No. 55. July 1905. K 



