8 THEORY OF THE MICROSCOPE. 



focus placed at E will, in fact, depict an image of the object <> h 

 (Fig. 4), which will be exactly similar to b* a* ; in order to 

 coincide with I* a*, however, the former image must be displaced 

 along the axis parallel with itself to a distance equal to that 

 between the two principal planes. 



The focal lengths of a system of lenses are measured by the 

 distances of the focal points from the respective principal points, 

 consequently by the lines F E, E* F*. We have hitherto' 

 regarded them as equal to one another, because this equality 

 actually exists when the terminal surfaces of the system are 

 bounded by the same medium, as is usually the case in the Micro- 

 scope. Where this condition is not fulfilled the two focal lengths 

 vary as the refractive indices of the corresponding media. If, for 

 instance, the incident ray passes into water, and the emergent ray 

 into air, the anterior focal length is to the posterior as 1J to 1 

 (1J being the approximate refractive index of water). On this 

 supposition a ray directed to E is not only displaced to E*, but is, 

 in addition, refracted as though at E it passed out of water into air. 

 The ray of direction, as the ray passing through unrefracted is also 

 in this case usually called (in accordance with the terminology f< r 

 one refraction), can, therefore, no longer be drawn through E and 

 E*, but must be drawn through points, of which the first is at a 

 distance from its nearest corresponding focus equal to that of the 

 posterior focal length, and the latter at a distance equal to the 

 anterior focal length. These two points, which in the present 

 case share with one another the function of the optical centre of a 

 single lens, are called the nodal points. In the following examin- 

 ation of the Microscope, however, the introduction of these nodal 

 points is superfluous, since the immersion of the objective in water, 

 as well as the effect of the thin glass cover, can be as well taken 

 into account afterwards. 



If we represent the distance of the object from the first principal 

 plane by p, the distance of the image from the second principal 

 plane by p*, and the focal length by /, we obtain the equation 



1 1 1 



/' 



"*" :: T 



which agrees with that above established for a single refraction. 

 The quantities p and p* are called the conjugate focal lengths ; 

 p* is to be taken as negative, when image and object lie on 



