46 VISION WITH THE COMPOUND MICROSCOPE 



cally, the clear, effective diameter of the back lens. The emergent 

 pencil from a microscope -objective converging to a relatively distant 

 focus has its rays approximately parallel, and the conditions are 

 once more similar to those of the telescope-objective on the side of 

 the object. The diameter of this emergent pencil, whether it emerges 

 from a single lens or from a composite system, must therefore always 

 have the same signification. The influence of the power on focal 

 length also remains the same as in the case of the single lens. An 

 objective with a focal length equal to half that of another admits, 

 with the same linear opening, twice as many rays as the latter, 

 because the amplification of the image at one and the same distance 

 is doubled, and the same number of rays consequently are admitted 

 by the higher power from a field of half the diameter. And this 

 will hold good whether the medium around the object is the same 

 in the case of both objectives or different ; for an immersion system 

 and a dry system always give the same amplification when the focal 

 length is the same. 



Thus we arrive at the general proposition for all kinds of objec- 

 tives. First, when the power is the same, the admission of rays 

 varies with the diameter of the pencil at its emergence. Secondly, 

 when the powers are different the same admission requires different 

 openings in the proportion of the focal lengths, or, conversely, with 

 the same opening the admission is in inverse proportion to the focal 

 length that is, the objective which has the wider pencil relatively 

 to its focal length has the larger aperture. 



Thus we see that, just as in the telescope the absolute diameter 

 of the object-glass defines the aperture, so in the microscope the 

 ratio between the utilised diameter of the back lens and the focal 

 length of the objective defines its aperture. 



This definition is clearly a definition of aperture in its primary 

 and only legitimate meaning as ' opening ' that is, the capacity of 

 the objective for admitting rays from the object and transmitting 

 them to the image ; and it at once solves the difficulty which has 

 always been involved in the consideration of the apertures of 

 immersion objectives. 



So long as the angles were taken as the proper expression of 

 aperture, it was difficult for those who were not well versed in 

 optical matters to avoid regarding an angle of 180 in air as the 

 maximum aperture that any objective could attain. Hence, water- 

 immersion objectives of 96 and oil-immersion objectives of 82 

 were looked upon as being of much less aperture than a dry objective 

 of 180, whilst, in fact, they are all equal, that is, they all transmit 

 the same rays from the object to the image. Therefore, 180 in 

 water and 180 in oil are unequal, and both are much larger aper- 

 tures than the 180 which is the maximum that the air objective can 

 transmit. 



If we compare a series of dry and oil-immersion objectives, and, 

 commencing with very small air-angles, progress up to 180 air- 

 angle, then taking an oil-immersion of 82 and progressing again to 

 1 80 oil-angle, the ratio of opening to power progresses continually 



