Formula and Methods connected ivith Lenses, 451 



The ratio of the two focal lengths will always have the 

 same value, the magnifying-power of the whole, wherever the 

 division is made. 



When, for the purposes of celestial photography, a telescope 

 has a camera attached at the eye-end, the question arises how 

 tar the eyepiece must be racked out in order to obtain an 

 image on the plate. 



If the optical properties of the eyepiece are known, i. e. its 

 focal length and the positions of its principal foci, then of 

 course the distance of the camera-plate from the second 

 principal focus is known. But the camera-plate must be in 

 the second principal focus of the whole system. Hence the 

 distance from the second principal focus of the eyepiece to 

 the plate must be the travel of the principal focus due to the 

 application of the object-glass, i. e. 



f* -k 



where / is the focal length of the eyepiece, c is the distance of 

 the photographic plate from the second principal focus of the 

 eyepiece, and k is the amount of racking out required from 

 the position in which the focal length of the telescope is 

 infinite. 



If we have a lens system, and coaxial with it a mirror, 

 either plane or spherical, and light is passed first through the 

 lens in a direction towards the mirror, and after reflexion at 

 the mirror, back through the lens in the reverse direction, 

 the combination forms a virtual mirror to which the following- 

 very simple rules apply: — 



The virtual mirror's surface is conjugate with the real 



mirror's surface by the lens. 

 The virtual mirror's centre of curvature is conjugate with 

 the real mirror's centre of curvature by the lens. 



These rules enable one at once to determine the genera] 

 facts of the image-formation in any given case. 



If the virtual mirror is a plane one, its radius of curvature 

 is infinite, and either its surface or its centre of curvature 

 must be at infinity, while the other must be at a finite 

 distance. 



Hence to form a virtual plane mirror either the surface or 

 the centre of the real mirror must be in the second principal 

 focus of the lens. 



If the surface of the mirror makes this coincidence, the 

 surface of the plane virtual mirror will be at infinity ; but its 

 centre is not so, and may be easily found experimentally, as 



212 



