ZOOLOGY AND BOTANY, MICROSCOPY, ETC. 



621 



The most convenient ray to employ for this purpose is the one proceeding 

 from a point such as h in the object in a direction parallel to the optical 

 axis. Such a ray after refraction passes through the principal focus F 

 of the objective, and if the incident ray from h and the refracted ray 

 passing through F are produced until they intersect at V, then by 

 definition a plane V a! perpendicular to the optical axis and containing 

 this point is the upper cardinal plane of the objective, and its distance 

 a' F from the principal focus of the objective, or the upper focal 

 plane as it is usually called, is the equivalent focus of the objective. 



. Now, it is immediately apparent that a' V F and A B F are similar 

 triangles, and as a' V is equal in size to the object a h, and a' F is the 



Fig. 100. 



equivalent focus, we can immediately deduce the proportion, that A B, 

 the size of the image, is to a b, the size of the object, as the distance A F 

 between image and upper focal plane is to a' F, or the equivalent focus 

 •of the lens. Or in mathematical form 



{AB^ab) = (AF-^a'F) 



(A B -^ a J) is the magnification of the image A B, and we will intro- 

 duce the symbol M for this, as well as the symbol / for the equivalent 

 focus of the lens, and our expression thus becomes 



I. M = (AF-^/) 



which is the simple equation used in Abbe's method of determining the 

 •equivalent focus, all the apparatus required being a stage micrometer 

 and an eye-piece micrometer divided to the same unit, that is to say both 

 in fractions of millimetres or both in fractions of inches. 



As is obvious from the diagram, no lens must intervene between the 

 objective being measured and the magnified image A B, and if the eye- 

 piece micrometer is to be used in the usual Microscope eye-pieces of 

 Huyghenian type, it is absolutely necessary that the field-lens of the eye- 

 piece be removed, as otherwise totally erroneous results must be 

 obtained. 



By observing how many divisions of the eye-piece micrometer corre- 

 ;spond to a division of the stage micrometer, we determine directly the 

 magnification M in our equation I. 



By measuring off the position of the eye-piece micrometer with 

 regard to the upper end of the Microscope tube, we can also determine 

 the point A in our diagram, but the point F cannot easily be determined 

 by the same method, and therefore both quantities of the right hand 

 side of our equation must be regarded as unknown and two observations 



