determining the dispersive ratio of glass , &c. 
Whence the index 1 -j- x is known. 
As also, <p x (q 1) = r' - - (3). 
267 
(? + 0 
- (4). 
<p x 
The radii sought. 
27. In order to determine the index of a given concave lens, 
we must combine it with any proper convex lens to produce 
a compound focus. Let this focus be <p, that of the convex 
lens/, and the required focus of the concave x , then by known 
principles -j- = -j- + -j ■ 
Whence x becomes known. Having then measured the radii 
of curvature as already stated, and calling them r, r', and 
index 1 + a > we have 
a 1 (— -4- — r) — , 
\ r 1 r ! x ’ 
and since r, r* , and x are known, a! and 1 + d will of course 
be known also. 
