FOCUS AND OPTICS 45 
pinhole, and a circle of light will be found on the front glass 
of the lens; the diameter of this circle will be the true aper- 
ture of the stop, and dividing the focal length by this gives 
the true ratio aperture. As it is sometimes difficult to see the 
circle of light on the glass, the latter may be dusted with talc, 
which makes it more readily visible. Or a small piece of 
bromide paper may be cut and placed inside the cap of the 
lens, and a fairly long exposure given to the light passing 
through the pinhole and the lens. On development the 
diameter of the black circle is the diameter of the ratio 
aperture. Another method is to focus a bright spot of light 
at infinity or a great distance, and then move the focussing 
screen until the spot of light becomes a disk of any definite 
diameter, say, half an inch. Then the distance the focussing 
screen was moved divided by the diameter of the disk of light 
is the diameter of the ratio aperture. To find the diameter 
of the stops for a lens, the following approximate method 
may be adopted: Find the equivalent focus F of the lens, 
measure the distance between the two outer surfaces of the 
front and back lens, call this d; then the diameter of the stop 
f:x will be (F— Yd) +x. Example: focus of lens, 16 
inches, distance between the surfaces or d, 2 inches; if the 
desired stop is f:8, then 16— (4% X 2) +=8= 16—1~— 8 
— 1% inches, the diameter for f: 8. 
Piper’s TaBLeE oF ANGLES OF ViEw.—To find the angle 
included on any given plate, divide the diagonal of the plate 
by the equivalent focus of the lens. The quotient T is equal 
to twice the tangent of half the angle, but the value of the 
angle can be found very nearly from the following table: 
ii ais The angle Tides The angle 
less than is less than less than is less than 
0.3 vee eZ 81° 
0:35 20° 1.8 84° 
