| Δ = − | nr1 | + d + | nr2 | . |
| n − 1 | n − 1 |
Writing R = Δ(n − 1), this relation becomes
R = n(r2 − r1) + d(n − 1).
We have already shown that f (the first principal focal length of a compound system) = −f1f2/Δ. Substituting for f1, f2 and Δ the values found above, we obtain
| f = | r1r2n | = | r1r2n | , |
| (n − 1)R | (n − 1) {n (r2 − r1) + d(n − 1)} |
(10)
which is equivalent to
| 1 | = (n − 1) { | 1 | − | 1 | } + | (n − 1)2 d | . |
| f | r1 | r2 | r1r2n |
If the lens be infinitely thin, i.e. if d be zero, we have for the first principal focal length.
| 1 | = (n − 1) { | 1 | − | 1 | }. |
| f | r1 | r2 |