Focometry of Lens- Combinations. 159 



and, consequently, HgHi is also divided externally by in a 

 ratio equal to the magnification. The position of thus 

 depends on the magnification. I£ this is zero, coincides 

 with H 2 (as in the ordinary way of using the nodal slide) ; 

 if it is infinity, coincides with H^ If is to the left of H 2 , 

 the magnification lies between unity and zero, and if to the 

 right of H l5 between + °° and unity. If it lies between H 2 

 and H x the magnification is negative, and may have any value 

 between zero and — <x> . 



The position of can be found with the nodal slide, 

 and then OP x and OP 2 can be measured, thus determining 

 the magnification either for a converging or diverging 

 combination. The combination can then be displaced towards 

 or away from the object, the new position of found, and 

 the corresponding value of the magnification. The focal 

 length and the positions of the cardinal points can then be 

 found by calculation. 



The following example of a rough determination of the 

 focal length of a diverging combination will make the 

 method clear. An auxiliary convex lens was used, which 

 enabled an image to be formed on a screen and the position 

 of P 2 to be found. having been determined with the 

 nodal slide, 0~F X was found to be 51*0 cm. and OP 2 9'0 cm. 

 The combination was then moved towards P x and again 

 determined. OP 2 was then 9*5 cm., OP! 24*5 cm., and the 

 distance through which the combination was moved 26'9 cm. 



Thl,s 1=5-7, -=2-6, 



mi m 2 



and , 26'9 



cm. 



The advantages of the method are that there is no 

 adjustment for parallel light, and no transparent scales 

 necessary for measuring the magnification, which is more 

 accurately determined by measuring OPi and OP 2 . 



