The exact solution for the centre thickness of spectacle and contact lenses.

The available methods for the exact calculation of centre thickness presuppose that one knows simultaneously both surfaces of the lens and that the lens' power is determined afterwards. However, this approach is of secondary importance in practical situations. The issue in daily practice is the determination of the centre thickness of lenses that already have explicit vertex powers. In such cases one can set only one surface. The other has to be calculated following the prescription, the known surface and the optical effect of the centre thickness. Exact solution for this problem leads to four expressions, reflecting the number of ways one can treat it. Two of them are complete second-order algebraic equations and the other two, complete third-order algebraic equations. The practical value of the latter is limited by the fact that one cannot always obtain their three roots by pure algebraic procedures.