THE AMERICAN 



MONTHLY 



MICROSCOPICAL JOURNAL, 



Vol. VI. Washington, D. C, August, 1885. No. 8. 



A Practical Method of Finding the 

 Optical ('entre of an Objective, 

 and its Focal Length. 



BY PKOP\ W. F. DURAND, ASSISTANT 

 ENGINEER U. S. NAVY. 



The term optical centre, as usually 

 defined in the text-books on optics, is 

 that point in a lens through which if 

 a ray pass, it enters and emerges in 

 parallel lines. This definition will 

 not exactly suit the point referred to 

 in the following article, and it maybe 

 well to show exactly what is meant 

 by the term. 



In the diagram (Fig. 21) let a 6 he 

 an object. Then it is simply a matter of 

 experiment to show that in some way 

 the rays radiating from a, for exam- 

 ple, are brought to a focus at some 

 point a on the opposite side of the 

 centre line, and at a distance from it 

 depending on the distances of a from 

 the centre line, and from the objec- 

 tive. Likewise the rays radiating 

 from 6 are brought to a focus at 6', 

 and thus is formed the inverted real 

 image a' b' . Suppose that a and a 

 be joined with a straight line, and 

 likewise b and b' . Without attending 

 at all to the actual course of the rays, 

 which, in an objective of two, three, 

 or four systems is very complex, it is 

 evident that ao b and a o b' are simi- 

 lar triangles, and that we have 

 a b' a o CO 



a b 

 a b' 



oc 



Now, — — is evidently magnifica- 

 a b 



tion, and by the equation this equals 

 That is, the magnification equals 



o c 



the ratio of the distance of the image 



from a certain point, 0, to that 

 the object from the same point, 

 the position of 

 o be known, it 

 is evidently an 

 easy matter to 

 find the magni- 

 fication when 

 the positions of 

 c and c are 

 known. Fur- 

 thermore, if we 

 wish to adopt 

 the lo-inch 

 standard for the 

 vague quantity 

 called tube 

 length, o is evi- 

 dently the point 

 from which to 

 start, and in 

 this case we 

 have c o r=^ 10 

 inches, and the 

 magnification 



equals 



^ CO 



Now, this point 

 o possessing the 

 foregoingprop- 

 erties is the 

 point which, 

 for want of a 

 better name, is 

 here designated 

 the optical cen- 

 tre of the objec- 

 tive. It is near, 

 but does not 

 coincide with 

 the point an- 

 swering the 

 definition in the text-books. 



of 

 If 



