158 



Prof. A. Anderson on the 



If the combination be now reversed, H x and Fj may be 

 found in the same way. Or, without reversing the combi- 

 nation, it is easy to make the light emerging from the 

 combination parallel. Its parallelism can be tested by 

 allowing it to fall on a convex lens with a screen placed at 

 its focus. If the light be parallel, an image will be formed 

 on the screen, which will not be displaced when the com- 

 bination is turned about a vertical axis through H x . 



But these methods are only applications of particular cases 

 of a general theorem which may be stated as follows. If V 1 

 be the object and P 2 the image of P x formed by light passing 

 through any lens-combination, there is always one point 0, 

 and only one, on the axis, a vertical through which has the 

 property that if the combination receive a small rotation 

 about it, the image P 2 will not be displaced. 



In the figure P^ is the object and P 2 N 2 the image. Let 

 the system be rotated about through a small angle PiOX^ 

 The points H 1? H 2 , F 1? F 2 will now occupy the positions 

 H/, H 2 ', F/, F 2 '. It is clear that, if N 2 keep the same 

 position, we must have 



mXjNiH- 0p^- PiXi 



where m denotes the magnification. 

 Thus 0P 2 



*Ni, 



OP: 



P 1 X 1 = mPiX 1 , or m — 



OP, 



OP, 



The point 0, therefore, divides P 2 Pi externally in a ratio 

 equal to the value of the magnification. 



Thus 



m = 



QP 2 

 OPa 



rLPo OH 



_ 1 - t 2- L 2 _ 



HJV OHx' 



