FOCAL LENGTH. 183 



anterior surface upwards, a suitable object (for instance, a 

 slip of glass blackened over a candle-flame) is adjusted on the 

 work-table or on the window at a distance of *2 to 1 metre or 

 more. The illuminating mirror, which must be plane, is adjusted 

 to reflect the image of the object in the optic axis of the 

 objective to be tested, which consequently forms a small dioptric 

 image above ; the diameter of this image is directly measured 

 with suitable amplification. The magnitudes D and d are now 

 known ; the distance p* is then measured with the scale, to which 

 the distances from the object to the mirror and thence to the 

 objective must be added. If necessary, a horizontal position can 

 be given to the Microscope, and the object may be viewed 

 directly. 



If the focal length of one objective has been accurately de- 

 termined, that of another can be readily found by comparison. 

 From the formula for the magnification 



ffl 1 & nrft 



m = 1 *- we obtain/ = ^ , or, if m is regarded as posi- 



j ffi 1 



.* 



tive,/ = ~ - , that is, the focal lengths are in inverse ratio to 



ffl -p L 



the objective amplifications increased by 1. Since the latter are 

 proportional to the linear dimensions which the images of a given 

 object occupy in the eye-piece micrometer, we have only to read 

 off the divisions from one end to the other, in order to determine 

 the ratio of the known focal lengths to one or more unknown, 

 which may thence be calculated. 



The focal lengths of single lenses may, of course, be determined 

 similarly. Where, however, the curvatures are very shallow, and 

 the focal lengths amount to several centimetres, it is generally 

 sufficient to measure the distance of the image of the sun from 

 the lens, or one of the simple methods described in the text-books 

 of Physics may be employed. 



