IG-t NUMERICAL APERTURE. 



From B, and with a distance, ^^B D, describe an arc cutting 

 B H in F. The waves of light must touch this circle simul- 

 taneously to arrive along the equal radii at B together. From F 

 let fall F E perpendicular to B D, and meeting it in E, then F E 

 will represent the linear semi-opening =« and B F=B D=^. 



_=sm B =c sui A^= -^ sm A, 

 d a 



a^mf sin A, 



^ ■ A 



- ^ =w sm A. 



Now, if the ray A G F B represents the most oblique ray 

 which passes in and out of the system, 



a 



^= -,^w sin \ angular aperture ; 



or the ratio of the linear semi-aperture of any system to the focal 

 length of that system is equal to the sine of 1 angular aperture 

 multiplied by the refractive index of the medium between the 

 object and the lens. This is the numerical aperture. 



As the angle B, in the case of the microscope, is always very 

 small if the arc F D or the tangent to H D was taken, the differ- 

 ence between their ratios to the distance B D and that of the sine 

 F E would be inappreciable, so this aperture is half the clear 

 opening of the back lens. 



. • . If half the angle of aperture is represented by (T, and N 

 is the numerical aperture, 



N = w sin a 



In the case of a dry lens rii is of course unity. 



There may be a slight feeling of dissatisfaction at taking 



E = the magnifying power = — ; 



but as a matter of fact this exactly expresses what we mean by an 

 objective of a certain focus. 



For instance, take a ^ objective. We know this objective does 

 not focus a y% inch away from the object. We mean, however 

 that its magnifying power is that of a lens whose focus is in a cer- 

 tain ratio to the distance of distinct vision, which is always taken 



