Design
The first-order design of an achromat involves choosing the overall power of the doublet and the two glasses to use. The choice of glass gives the mean refractive index, often written as (for the refractive index at the Fraunhofer "d" spectral line wavelength), and the Abbe number (for the reciprocal of the glass dispersion). To make the linear dispersion of the system zero, the system must satisfy the equations
where the lens power is for a lens with focal length . Solving these two equations for and gives
Since, and the Abbe numbers are positive-valued, the power of the second element in the doublet is negative when the first element is positive.
Read more about this topic: Achromatic Lens
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