NUMERICAL APERTURE. 



161 



Fig. 3. 



Produce the lines A F and B F through the focus to F and K. 

 Draw M N through F, perpendicular to D C. Now, the angle 

 E F K is equal to the angle A F B, and if air is on both sides of 

 M N will represent the angular amount of light coming from air 

 into the lens, but if there is another mcdmm instead of air, the 

 angle E F K will not represent it. 



In the case of the microscope, if a medium is placed between 

 the lens, it is always a denser one than air, and consequently angle 

 A F B represents a much larger angle in air, such as J F L. 



For, let m = refractive index of the medium. 

 Let a = angle AFC = | A F B. 

 Let b =^ \ angle J F L. 

 Then sin b ^ ;;/ sin a. 



Thus, it is necessary to take the angle J F L as the true angle 

 of aperture for the whole cone of rays, because if the cone of rays 

 represented by A F B are fully utilised, they are re-given out in 

 air. 



The actual amount of light, of course, varies with the squares 

 of these quantities ; but, as in all microscopical work, it is found 

 more convenient to treat of linear equivalents. 



Taking the same figure, suppose G H to be a lens of the same 

 diameter as A B, with a longer focus, but still at F, and G F H 



New Series. Vol. I. 

 1888. 



M 



