The Penetrating Power of the Microscope. By E. M. Nelson. 337 
normal and the longer accommodation is infinite, then vanishes 
° w 
and the depth becomes ^ - which may be written . 
1 w M' 
The focal depth is practically the latitude of focus which must be 
allowed for fluff. An object has really a precise and definite focus, 
but because the eye is unable to perceive very minute alterations in the 
image, that very precise and definite focus cannot be found, because 
the eye allows a slight range on either side of the true focus. This 
range is focal depth. Its amount can be easily determined. The 
first point to ascertain is the amount of fluff to be allowed, or in other 
words the diameter of the circle of confusion. I think it is better to 
take for this the least separable distance s, at the usual distance of 
accommodation or w. If we call this 1/200 in. at 10 in. it will 
probably not be far from the average, although it is a larger amount 
than I allow for my own sight. The focal depth is then directly 
proportional to p the refractive index of the medium the object is 
mounted in, and /the focal length of the lens or entire Microscope, 
and inversely proportional to the numerical aperture N.A. 
The focal depth is therefore — -~ S - - which may be written 
N.A. • W J 
p s 
The values for s and w ought to be determined for each individual 
case ; the following, however, will serve for general purposes : — Normal 
or emmetropic vision : s = • 005 in. = • 127 mm. ; w = 10 in. = 250 
mm. Myopic sight: s = • 0035 in. = • 09 mm. ; w' = 6 in. = 150 mm. 
The total visual penetration for emmetropic sight is therefore 
ff— j ^- S — which may be written 
M 2 + M • N.A. J 
sx> 
(O 
For myopic sight the expression will be somewhat longer. 
fJL ( w / w \ s ) 
m in V 1 “ V) + nTa.J' 
Thus far we have only been explaining and simplifying Abbe’s 
formulae, so if his values for the different terms are put in, results 
identical to his will be obtained. 
Examples. — Emmetropic sight, tv = 250 mm. ; D = 250 mm. ; 
magnifying power M = 10; N.A. = -1; g. = 1-5; co = -0005; 
s = • 127 mm. 
1892. 2 b 
