TO FIND THE INITIAL POWER OF A LENS 289 



a myopic observer. Let us investigate the case of one whose accom- 

 modation distance is five inches. 



Here he will be obliged, in order to see the object distinctly, to 

 form the virtual image from the eye -piece at a distance of five inches. 

 To do this he must cause the objective conjugate focus to approach 

 the eye-lens ; consequently he must shorten his anterior objective 

 focus. In other words, he must focus his objective nearer the 

 object. This will have the effect of causing the posterior conjugate 

 focus to recede from the objective towards the eye -lens, and the fact 

 of bringing the inverted objective image nearer the eye-lens brings 

 also the virtual image of the eye-lens nearer. 



Shortening the focus of the objective has the effect of increasing 

 its power ; but as this alteration is proportionately very little, the 

 increase in power is very small ; but the shortening of the eye-piece 

 virtual from ten to five inches has the effect of nearly halving its 

 power. Consequently the combined result of the eye-piece and 

 objective, in the case of halving the eye-piece virtual, is to nearly 

 halve the power of the microscope. The increase of the objective 

 power is practically so small that it may be neglected. 1 In practice 

 it is found by us that if the image is projected on a ground-glass 

 screen ten inches from the eye-piece, the image is nearly the same 

 size whether focussed by ordinary or myopic sight. This is in 

 harmony with Abbe's demonstration that both images are seen 

 under the same visual angle. But, on the other hand, if a myopic 

 sight compares the image with a scale, the magnification will be 

 less than with ordinary vision, because the observer with myopic 

 sight must bring the scale to a shorter distance than ten inches 

 in order to see it. 



To find the precise initial power of any lens, or to find the exact 

 multiplying power of any eye-piece, is not so easy. A laborious 

 calculation, involving the knowledge of the distances, thickness, and 

 refractive indices of the lenses, is required. But a very approximate 

 determination, sufficiently accurate for all practical purposes, may 

 be easily made, especially if one has a photo-micrographic camera at 

 hand. The principle is as follows : 



Select a lens of medium power a J-inch is very suitable. Now, 

 with the microscope in a horizontal position, and with a powerful 

 illumination, project the image of the stage micrometer on to a screen 

 distant five feet, measured from the front lens of the objective. If no 

 photo-micrographic camera is at hand, it will be necessary to perform 

 the experiment in a darkened room, shading the illuminating source. 

 Divide the magnifying power thus obtained by 6 ; the quotient will 

 give the initial powder of the lens at ten inches to a very near approxi- 

 mation. 



The reason why the result is not perfectly accurate is that the 

 ten inches must be measured from the posterior principal focus of 

 the lens, and that is a point which is not given. But in the case of 

 a power such as a J, it is, in practice, found to be very near the front 

 lens of the objective. So by taking a long distance, such as five feet, 



1 English Mechanic, vol. xlvi. No. 1185. Article on measurements of magnifying 

 power of microscope objectives, by E. M. Nelson. 



