Determination of the Powers of Lenses. 147 



obtained by taking a convergent lens of suitable power and 

 adjusting it with respect to tho cross-wires until a real image 

 ■of the same size is formed on a second screen. The image 

 will then be at one of the " negative principal points" of 

 Toepler, or " symmetric points" of S. P. Thompson, and the 

 distance between the cross-wires and the auxiliary lens will be 

 approximately twice the focal length of the latter. This posi- 

 tion having been found, the auxiliary lens support is fixed 

 rigidly to the screen carrying the cross-wires, and the two are 

 adjusted until an image of the latter is formed by the diver- 

 gent lens on the fixed screen. The power, m — 1, is then read 

 off directly as before. 



By paying due regard to the signs of m and D both 

 equations may bo written in the form 



D = l-m. 



A little care is necessary in the choice of the auxiliary lens 

 :as, if its focal length is too small, it will not be possible to 

 form the virtual object in the required position ; while if, 

 •on the other hand, it is greater than is necessary for this, the 

 distance between the lens and cross-wires may be incon- 

 veniently great. Thus, for a —ID lens, the magnification 

 will be 2 and the virtual object will be midway between the 

 lens and the screen, i. e. 50 cm. from the lens. This is there- 

 fore the minimum distance between the cross-wires and the 

 auxiliary lens, so that the minimum focal length of the 

 latter is about 25 cm. This method, unlike the previous 

 •one, is applicable to lenses of less than —ID but, for the 

 reason just indicated, becomes less convenient as the power 

 of the lens decreases, the minimum distance between cross- 

 wires and auxiliary lens being about 67 cm. for a — 0*5 D lens. 

 For a similar reason the method is inconvenient in practice 

 for convergent lenses of less than +1D. 



For thick lenses and lens systems, the screen must be 

 1 metre from the second principal point which can be readily 

 found by the usual methods, 



The writer wishes to thank one of his students, Mr. W. 1\. 

 Lynas, for kindly making the diagrams. 



L2 



