Determination of the Powers of Lenses. 



145 



For this reason it has been suggested recently (W. 

 Swaine, Optician, Dec. 17 & 24, 1920) that trial lenses be 

 re-marked according to vertex powers instead of, as now, the 

 powers referred to the principal points. The vertex system 

 was originally suggested by Biot in 1844, and has been 

 employed since by several authorities. A useful method for 

 the direct determination of the power of a convergent 

 (positive) lens was described by the late S. P. Thompson in 

 1899, but does not appear to be generally known or used. 



It depends on the fact, pointed out by Toepler, that the 

 lateral magnification of an" image formed by the refraction 

 of paraxial rays through a centered system of spherical 

 surfaces is proportional to the distance of the image from the 

 principal focus of the image-space, being zero at this point 

 and increasing by unity in distances equal to the focal 

 length of the image-space. 



The optical imagery is shown in fig. 1, in which O l5 2> 



Fig-. 1. 



Convergent Lens 



and 3 ..., represent successive positions of an object-point on 

 a ray parallel to the principal axis, and I l5 I 2 , and I 3 ..., the 

 corresponding positions of the image-point formed at distances 

 of 1, 2, 3... focal lengths from the principal focus F, the 

 magnification being indicated by numbers after the manner 

 suggested by Blakesley. If, therefore, a screen be placed at 

 a fixed distance of 1 metre from a convergent lens of focal 

 length /metres mounted on an optical bench and the cross- 

 wires be adjusted until an image I is focussed on it, the 

 numerical value of the magnification, m, is given by the 



relatioi 



whence 



m/+/=(m + l)/=:L 



The power of the lens, in dioptres, is thus simply (Magnifl 

 cation + 1). 



Phil. Mag. S. G. Vol. 42. No. 247. July 1921. 1. 



