Past exam of the mathematics course of the University of Cambridge / 2017 / iii / Paper 338 / 1 / c / ii / Solution

At the $d$ line, the focal lengths obey $1/f_{id}=(n_{id}-1){\rho }_i$. ThusRearranging givesThe last equality uses the Abbe number definition. The minus sign signifies a converging and a diverging component, with the normal optical glass convention and nonzero finite focal lengths.