= 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 implies
$$
\frac{f_{2d}}{f_{1d}}=\frac{\rho_1(n_{1d}-1)}{\rho_2(n_{2d}-1)},
$$
and hence
$$
\boxed{\frac{f_{2d}}{f_{1d}}=-\frac{(n_{2F}-n_{2C})/(n_{2d}-1)}{(n_{1F}-n_{1C})/(n_{1d}-1)}=-\frac{V_{1d}}{V_{2d}}.}
$$
The last equality uses the <Abbe number> definition and expresses the <achromatic doublet power balance> in terms of component <focal lengths>.
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