Achromatic doublet power balance
= Achromatic doublet power balance
For two thin lenses in contact, achromatism requires $\Phi_1/V_1+\Phi_2/V_2=0$, where $V_i$ are their <Abbe numbers>. With total power $\Phi=1/f$, the component powers are $\Phi_1=\Phi V_1/(V_1-V_2)$ and $\Phi_2=-\Phi V_2/(V_1-V_2)$. A positive doublet using a larger-$V$ <crown glass> element and smaller-$V$ <flint glass> element therefore uses a converging crown and a diverging flint.