USEFUL TO THE MICKOSCOPIST 1125 



q 



ft = -, and the distance between the surfaces, that is B A 7 , = 1-8; t the 

 2 



3 3 



thickness of the field lens = - - ; and t' that of the eye lens = ; A .D = 



(ii); BE = -* = --2 (ii). Similarly A'D' = 0; B'E'=-i = - 1 (ii) ; 



fl \i 10 



= -2 4-1-8 = 2. Now 



'' 



3x1 3 



We see, therefore, that the equivalent focus is 1^ inch, but the 

 principal point G', from which the focus is measured, is 1 inch to the left 

 from E' ; therefore the focal point is ^ inch to the right from E'. Now as 

 E' is ^ inch to the left of B, the plane surface of the eye lens, it follows 

 that F, the focal point, is ^ inch to the right of the plane surface of the 

 eye lens. If this problem is worked by the simpler formula (xxiii), the 

 answer will be -44 from the plane surface of the eye lens ; this is only an 

 error of -04 in excess. 



This explains ' the microscope objective of 10-ft. focus.' 

 The equivalent focus of the objective was 10 ft., but the principal point 

 G' from which that focus was measured was 9 ft. 11 inches from the 

 objective, which would give inch as the working distance of the lens. 

 The objective in question has a double convex back lens and a plano- 

 concave front ; a small decrease in the distance between the lenses, such 

 as a ^ inch, has the effect of causing the principal point G' to recede 

 many feet, and of causing a great increase in the equivalent focus. 



With regard to the tube length, which is equal to d in (xxvi), the 

 position of the principal points of a combination plays an important part. 

 Suppose the Huyghenian eyepiece, in the preceding example, were 

 mounted as an objective; the tube length would have to be measured 

 from the first principal point of the eyepiece, wherever that might be, to the 

 second principal point of the objective, which in the example before us is 



..... (xxiv) 



G is therefore measured 3 inches to the right from the point D ; D is, 

 as we have seen, coincident with A, the convex vertex of the field lens. 

 So anyone measuring the tube length from the field lens, which is the 

 posterior lens of our supposed objective, or from the middle of the 

 combination, would be 1^ or 3 inches in error. The correct point from 

 which the measurement should be made lies one inch in front of the eye 

 lens, which is the front lens of our supposed objective. 



The importance of this cannot be over-estimated, as the optical tube 

 length has a direct bearing on the power. If Q=the distance of vision 

 (say 10 inches), M = the magnifying power, F = the equivalent focus of the 

 eyepiece, F' = the equivalent focus of the objective, O = Prof. Abbe's 

 ' Optical Tube length,' viz. the denominator in the fraction in formula 

 (xxvi) ; then 



If - the focal length of the entire microscope, N.A. = the numerical 

 aperture, and e = the diameter of the eye-spot, then 



Journal B.M.S. 



