By the same method we obtain for the second principal focal length
| f′ = | f′1f′2 | = − | nr1r2 | = −f. |
| Δ | (n − 1)R |
| Fig. 8. |
The reciprocal of the focal length is termed the power of the lens and is denoted by φ. In formulae involving φ it is customary to denote the reciprocal of the radii by the symbol ρ; we thus have φ = 1/f, ρ = 1/r. Equation (10) thus becomes
| φ = (n − 1) (ρ1 − ρ2) + | (n − 1)2 dρ1ρ2 | . |
| n |
The unit of power employed by spectacle-makers is termed the diopter or dioptric (see [Spectacles]).
We proceed to determine the distances of the focal points from the vertices of the lens, i.e. the distances FS1 and F′S2. Since F is represented by the first system in F2, we have by equation (2)
| x1 = | f1f′1 | = | f1f′1 | = − | nr12 | , |
| x′1 | Δ | (n − 1)R |
where x1 = F1F, and x′1 = F′1F2 = Δ. The distance of the first principal focus from the vertex S, i.e. S1F, which we denote by sF is given by sF = S1F = S1F1 + F1F = −F1S1 + F1F. Now F1S1 is the distance from the vertex of the first principal focus of the first system, i.e. f1 and F1F = x1. Substituting these values, we obtain
| sF = − | r1 | − | nr12 | = − | r1 (nr1 + R) | . |
| n − 1 | (n − 1)R | (n − 1)R |