14 Mr Barlow On the Practical Construction 
it is proposed to give, in words at length, some preliminary rules 
for determining the foci of simple lenses, when the refractive 
power and radii of curvature are given, or the converse : for, 
notwithstanding these rules may be familiar, in some form or 
other, to practical opticians, yet, as we should wish this paper 
to contain every rule requisite in the construction of an object- 
glass, we shall, it is hoped, be excused for introducing them in 
a concise form in this place. 
14. Rules for determining the Focal Length of lenses of given 
curvature *. 
1 . To find the focal length of a double convex lens for 'parallel 
rays, the radii of curvature and the index of refraction being 
given. 
Rule. — Multiply the two radii together : then add the two 
radii together, and multiply their sum by the decimal part of 
the index of refraction. And the former product, divided by 
the latter, will be the focal length. ' 
Example. — The radii of curvature of a flint lens being 4 in- 
ches and 10 inches, and its refractive index 1.601, required the 
focal length. 
Here 4^ < 
r 4 
10 i and . 
) 10 
> _ 
40 ' * 
" 14 
.601 
8.414)40.000(4.75 inches focal length. 
2. When the two radii are equal, the rule becomes more simple, as 
follows . 
Divide the radius of curvature by double the decimal part of 
the index for the focal length. 
* The algebraical formulae embracing all these rules may be stated as follows : 
viz. 
r R 
For parallel rays, / = 
See Encyclopaedia Metropolitana , — Optics. 
Where /is the focal length, a the decimal part of the index of refraction, and r 
and R the radii, which are to be both positive when both surfaces are convex, and 
negative when concave. 
