512 Focometry of Diverging Lens- Combinations. 



Hence, if u= —2/, v = 2f; or, if light converge to a point Si 

 such that H 1 S 1 = 2/, it will, after passing through the com- 

 bination, diverge from S 3 , where H 2 S 2 = 2/. Si and S 2 are 

 the symmetric points, and it is clear that S 1 F 1 = F 2 S 2 =/. 



The combination A B should be fixed on a support which 

 is capable of a lateral motion at right angles to the length of 

 the optical bench, so that the axis of the combination may be 

 placed in or out of the axial plane of the bench at pleasure. 

 The additional parts required are two supports which can 

 slide along the bench, each furnished with a convex lens and 

 cross wires. The line joining the intersections of the cross 

 wires should be parallel to the bench and coincident with the 

 axes of the lenses and that of the combination when in the 

 axial plane. The lenses should be of exactly the same focal 

 length, and the cross wires of both should be placed outside 

 (or away from the combination) at equal distances, greater 

 than this focal length, from the lenses. It would be an 

 advantage if the positions of the cross wires could be altered 

 relatively to the lenses, but in making a measurement they 

 should be at equal distances from them. 



Suppose, now, the focal length of a diverging combination 

 has to be measured. A telescope furnished with cross wires, 

 and which has been focused for parallel rays, is used to view 

 the cross wires of one support through the convex lens of 

 that support and the combination, the support being moved 

 along the bench till the cross wires are seen without parallax. 

 The combination is then moved out of the axial plane, and 

 the position of the image of the cross wires formed by the 

 rays passing through the convex lens observed. This gives 

 one of the focal points, and the position of the other can be 

 found in the same way, using the other sliding support. 

 Transparent micrometers may now be placed at these points, 

 as in Prof. Thompson's method. The two supports are then 

 placed so that their cross wires are at equal distances from the 

 micrometers, and moved along the bench through equal dis- 

 tances in opposite directions till the image of the cross wires 

 of one support coincides with the cross wires of the other, the 

 combination having of course been previously moved back 

 into the axial plane. The combination is then again moved 

 out of the axial plane, and the micrometers are moved till 

 the images of the cross wires are seen in them. The distance 

 moved through by either is the focal length of the com- 

 bination. 



It should, if necessary, be possible to remove the convex 

 lenses and replace them by others more suitable for the actual 

 •combination to be measured. Of course the apparatus with- 



