Virtual Images if - Initial Magnifying Power. By E. M. Nelson. 18.1 
If m is the magnifying power, i the image, and o the object, 
in, therefore, may be practically determined 
i = m o, or in = - , 
o 
by direct measurement of i and o, but it can also be found from 
purely optical considerations, because the proportion between i and o 
7/73 73 
is identical with that between p' and p, so - = - , and in — - • 
o p p 
Therefore, if we know the distances of the object and the screen 
from the lens, we can find the magnifying power. 
It is now that / the focal length of the lens, becomes so useful, 
because, although p' is either known or can be measured, p is not 
usually known, and often cannot be conveniently measured. If, 
however, f is known, p can be expressed in terms of / and p, and so 
all knowledge of p can be dispensed with. 
In the simple Microscope there is no screen, p' is the nearest 
distance of accommodation, p however is not known, but as we know 
p' and f we can find p, and so determine in the magnifying power of 
any lens. The argument is as follows : — 
p’f 
t p 
m = - = - 
o p 
111 ,, 
— [ — ( = therefore p = . „ , 
PI/ P ~f 
putting this value instead of p in the denominator of the fraction in 
ithe first equation and simplifying we get 
P' P' i 
m = , j - = - 1 . 
P f f 
P' ~ f 
So in a simple Microscope we may readily find the power if we 
know / the principal focus of the lens, by substituting d the least 
distance of accommodation for p . 
One or two points require to be noticed with regard to this 
formula : — 
(1) p is positive, but in the simple Microscope / being measured 
from the lens to the image, or from right to left, is negative. There- 
fore in will be negative, which indicates that the image is virtual. 
When, however, a real image is received on a screen, p is positive, 
and m is also positive, because when p is less than / no image can 
be formed on the screen. 
(2) The formula in the case of the simple Microscope assumes the 
eye to be placed close to the lens. When, however, the eye is placed 
at the back principal focus of the lens, p' is not equal to d, but is 
equal to d — / Dropping, therefore, the negative sign for the 
virtual image, and considering d a positive quantity, we obtain the 
following formulas for a simple Microscope: — 
(i.) When the eye is held close to the lens 
d , 
».= 7 + i . 
