THE MICROSCOPE AND MICROSCOPIC METHODS 23 



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 

 optical 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. 



By placing the eye about two feet above the eye-piece, one 

 may measure the width of the beam as it emerges from the latter. 

 Now by changing to an eye-piece of higher power he can readily 

 demonstrate the consequent narrowing of the beam. This 

 narrowing of the beam makes more important the obscuration 

 caused . by any defect in the optical system of the eye itself. 

 Microscopic vision is disturbed by floating shadows and hazy 

 definition due to such partial obscuration especially when the 

 beam has been too much liarrowed. For ordinary work , therefore, 

 an eye-piece of low power will prove more satisfactory. 



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 ^^ i 



refractive index of vitreous i . 3 

 This brings us to a definition of numerical aperture. The numer- 



