THE APEKTUHE OF THE OBJECTIVE. 7] 



Eured by the expression of its absolute diameter or 

 " opening." No such absolute measure can be applied 

 in the case of microscope-objectives, the largest lenses 

 having by no means the largest apertures, but being, 

 in fact, found with the low powers, whose apertures 

 are but small. The capacity of a microscope- objective 

 for receiving and transmitting rays is, however, as will 

 be seen, estimated by its relative opening, that is, its 

 opening in relation to its focal length. When this 

 relative opening has been ascertained, it may be 

 regarded as synonymous with that denoted in the 

 telescope by absolute opening. That this is so will be 

 better appreciated by the following consideration : 



In a single lens, the rays admitted within one meri- 

 dional plane evidently increase as the diameter of the 

 lens (all other circumstances remaining the same), for 

 in the microscope we have, at the back of the lens, the 

 same circumstances as are in front in the case of the 

 telescope. The larger or smaller number of emergent 

 rays will therefore be measured by the clear diameter, 

 and as no rays can emerge that have not first been 

 admitted, this must also give the measure of the admit- 

 ted rays. 



If the lenses compared have different focal lengths 

 but the same clear " openings," they will transmit the 

 same number of rays to equal areas of an image at a 

 definite distance, because they would admit the same 

 number if an object were substituted for the image ; 

 that is, if the lens were used as a telescope-objective. 

 But as the focal lengths are different, the amplification 

 of the images is different also, and equal areas of these 

 images correspond to different areas of the object from 

 which the rays are collected. Therefore, the higher 

 power lens with the same opening as the lower power, 

 will admit a greater number of rays in all from the same 

 object, because it admits the same number as the latter 

 from a smaller portion of the object. Thus, if the focal 

 lengths of two lenses are as 2 : 1, and the first ampli- 

 fies N diameters, the second will amplify 2 N with the 

 same distance of the image, so that the rays which are 

 collected to a given field of I mm. diameter of the 



