Past exam of the mathematics course of the University of Cambridge / 2019 / iii / Paper 338 / 3 / b / ii / Solution

At the intermediate $d$ reference wavelength, the lensmaker's equation gives $1/f_{id}={\rho }_i(n_{id}-1)$. Therefore the curvature-factor ratio from the previous part impliesand henceThe last equality uses the Abbe number definition and expresses the achromatic doublet power balance in terms of component focal lengths.