I have a problem with the determination of the correct focal curve of an achromatic double. I'm considering here a doublet formed by a biconvex Flint Glass lens attached to a plano-concave crown glass lens. ( I know that the typical design of the doublet is a biconvex crown lens attach to a plano-concave flint glass lens. but here I'm interested in the opposite.) I'm also assuming that I aim to achromatize the C and F Fraunhofer lines. The optical powers of the two lenses are: P1 = n_flint * (1/R1-1/R2) P2 = n_crown*(1/R3) [ I assume that R4=∞, since this is a plano-concave lens ] I also know the optical power (Pt) of my system at the D Fraunhofer line. The classic textbook formulas say that the conditions required to design a doublet are: P1 = Pt * Δ2/(Δ2-Δ1) P2 = -Pt * Δ1/(Δ2-Δ1) Where Δi = (ni_F - ni_C) / (ni_D-1) ( i=1,2 stands for the first or second lens, respectively), and n_F, n_C and n_D are the refractive indexes of the respective glass. We have 2 equations and 3 unknowns ( R1,R2 and R3), so in order to solve this problem I must choose an arbitrary radius R1 for example. My problem is that after I solve the system and find the required radius, when I plot the focal shift of my system it yields a focal shift of 1*10^-15 in the whole visible spectrum, when in theory the focal shift should only be zero valued for the C and F lines.. Can anyone Explain me what I'm doing wrong? Thank you in advance.