The equations in the diagram below are used to calculate the dioptric powers of the lens elements of a “thin-lens” achromat. The dioptric powers are then used to create the starting form for a real thick lens design.
The radii of curvature of the elements for the starting form are calculated for an achromat comprising an equi-convex crown glass lens, Element A, cemented to a negative flint glass lens, Element B.
https://www.dropbox.com/s/wwo4qi88zt61exx/Achromat%20Element%20Powers.xls?dl=0Suitable lens element thicknesses can be assigned to yield a real lens form in which lens aberrations can be minimized and lens radii and thickness set to satisfy manufacturing and mounting requirements.
A spreadsheet is provided at the link, “Achromat Element Powers”, so that the designer can experiment with different glasses. A design objective is to arrive at relatively low lens element powers by choosing glasses with a large difference in V-number. Reducing the lens element powers generally alleviates the problem of correcting spherical aberration and coma in the real lens design. Limitations on glass selection are often effected by other factors including the glass refractive index and partial dispersion, environmental, mechanical, and thermal properties, as well as optical shop workability, cost and availability.