The Photometry of a Bull's-Eye Lens. 
393 
Fig. 3 (2) shows the bull’s-eye at a distance x = 300 mm. 
from source. The axis of each bundle of light passes through the 
centre of the lens, and thus from similar triangles the relative 
diameters of the source and its image are [in Fig. 3 (1)] 1 to 3 
and [Fig. 3 (2)] 1 to 1/3. 
These are the two positions — namely, when the lens is at 
100 mm. and 300 mm. from the source of light — where with a lens of 
75 mm. focal length images can be formed in the given total distance 
of 400 mm. To ascertain the brilliancy the diameter of the bull’s- 
eye must be considered, and we may take this as L = 58 mm. 
As the lens is circular its area is 2642 mm., and for convenience 
we may call this L' 2 . 
Firstly, when the bull’s-eye is at a distance of 100 mm. from 
the source of light, it receives from the source a total quantity of 
light, as if it were the screen in the previous case, of 
KS 2 L' 2 _ K 100 x 2642 
10,000 
26*42 K. 
The whole of this light is transferred to the object, but is spread 
out over an area which is the size of the image of the source of 
S 2 x 2 
light. The area of this image is 2 , and the total quantity of 
light must be divided by this area to obtain the intensity of unit 
area — namely, 
K S 2 L' 2 
K L' 
K -2642 
90,000 
K 
32 
The formula shows that the brilliancy is only dependent upon 
the intrinsic brilliancy of the source K, the area of the bull’s-eye 
L' 2 , and the distance of the bull’s-eye from the object x\ In the 
case under consideration the brilliancy of the object — is 50 times 
as great as when illuminated by the direct beams 
1600' 
This mav 
appear a large increase, but to obtain a correct impression of what 
is required in a microscope it must be remembered that magnifying- 
power is not reckoned by the increased area of an object, but by 
the increased length, and an object magnified 7 diameters has an 
area 49 times as large as the original. Therefore, to obtain suffi- 
ciently increased illumination to allow of the use of a microscope 
magnifying 7 diameters without loss of light, we require 49 times 
