NUMERICAL APERTURE. 

 P 



Firi JTI 



and A a luminous 



XX' represent the limiting surface between the two media, the 

 oblique rays AO, BO, CO, instead of passing through in a 

 straight line, like AOa', are squeezed together, and brought 

 nearer the normal OP ; and, — vice versa, — rays passing out of a 

 dense medium into a rarer one are expanded. The effect of this 

 is that in the dense medium the waves of light are shortened, 

 and a given area in a dense medium contains more light-waves 

 than the same area in a rare one. 



In applying this to our present question, it is to be re- 

 membered that the medium into which the pencil emerges is 

 always air. 



If, in Fig. IV., BC represents a lens, 

 point placed at its focus ; then, 

 if there is air between the lens 

 and the object, the cone Bx\C 

 will represent the extreme a- 

 mount of light which can pass 

 through the lens ; if, on the 

 other hand, a denser medium 

 than air be interposed, the cone, Bx\C, will include, for the 

 above reasons, a larger amount of light-waves, represented in 

 air by the larger cone Di\E : consequently, the angle of the 

 emergent pencil is increased, and the aperture enlarged. 



The density of the medium, between the objective and the 

 object, must therefore be taken into account in estimating the 

 aperture ; although it in no way alters the angular magnitude 

 of the entering pencil of light. 



The next question is, how are we to get an expression for 

 aperture which will enable us to compare lenses with reference 

 to each other? 



