= Achromatic lens
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An <achromatic lens> combines <optical lens> elements with different <optical dispersion> so that two specified <wavelengths> have the same <focal length> in the <paraxial approximation>. This brings their parallel incoming <light rays> to a common <optical focus>, helping an <optical camera> form a sharper image under mixed-colour illumination. A common implementation is an <achromatic doublet>: a positive <crown glass> element paired with a negative <flint glass> element. https://farside.ph.utexas.edu/teaching/302l/lectures/node142.html[Fitzpatrick, Chromatic aberration, compound lenses]{ref}.
The <achromatic doublet> does not require either material to have zero <optical dispersion>. Instead, the positive element gains positive <optical power> toward blue, while the negative element becomes more negative. Suitable <Abbe numbers> and signed <optical powers> let these changes cancel even though their reference <optical powers> do not cancel. For example, the <achromatic doublet power balance> calculation below combines $+10\,\mathrm D$ with $-5\,\mathrm D$ to obtain $+5\,\mathrm D$, or <focal length> $0.2\,\mathrm m$, with zero primary F–C <optical power> difference. The smaller <Abbe number> of the negative element makes its weaker reference <optical power> sufficient to oppose the positive element's colour change.
An <achromatic lens> is corrected at two chosen <wavelengths>, not necessarily at every <wavelength> between them. The remaining <focal length> variation is the <secondary spectrum>. Correcting <axial chromatic aberration> also does not automatically remove <lateral chromatic aberration> throughout an imaging system, <spherical aberration>, or <diffraction>. Actual designs therefore need <ray tracing> with the intended <wavelengths>, element thicknesses, separations and <apertures>. https://imaging.nikon.com/sport-optics/guide/fieldscopes/choosing/choosing_03/[Nikon, ED glass and secondary spectrum]{ref}; <AY 105 Lab Experiment 3: Optical aberrations by California Institute of Technology>[Caltech AY 105, Optical aberrations, 2011, Part A: doublet ray tracing and through-focus comparison]{ref}.
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