THE MICROSCOPE AND MICROSCOPIC METHODS 23 



8. Fig. 9 shows the change which is introduced by the use of 

 an eye-piece of higher magnifying power. 



It will be noted that the objective and lower lens of the eye- 

 piece bring the beam to a focus forming a real image, and that 

 the rays diverging again from this image are again brought to a 

 focus on the retina by the upper lens of the eye-piece and the op- 

 tical structures of the eye. The magnification represented in the 

 first image is the quotient of the sine of the angle of the opening 

 limb of the beam divided by the sine of the closing angle. The 

 subsequent magnification between this and the eye is the quotient 

 of the sine of the opening angle of the rays proceeding from this 

 image divided by the sine of the closing angle of the rays approach- 

 ing the retina. The closing angle at the formation of the first 

 image and the opening angle of the beam proceeding from it are 

 obviously equal, so that the total magnification equals the sine 

 of the first opening angle divided by the sine of the last closing 

 angle in the system. It will be noted that the eye-piece of higher 

 power narrows the beam and decreases the closing angle. 



In the above discussion, the refractive index of the vitreous 

 humor has been disregarded. This is not the same as that of 

 air (in reality it is about 1.3) and the peripheral beam is there- 

 fore bent toward the axis of the eye instead of proceeding in its 

 former direction, the magnification being thereby reduced by 

 precisely the fraction 



refractive index of air 



or 



refractive index of vitreous 1.3 



This brings us to a definition of numerical aperture. The 

 numerical aperture of the closing limb (n.a.) is the sine of half 

 the angle of the converging beam multiplied by the refractive 

 index of the medium (in this instance the vitreous humor). 

 This is commonly designated as n.a. The numerical aperture 

 of the opening limb of the beam (N.A.), proceeding from a point 

 in the object to the objective, is the sine of half the angle of this 

 beam multiplied by the refractive index of the medium through 



