Solution (source code)

= Solution

A simple converging <optical lens> bends different <wavelengths> through different <angles> because of <optical dispersion>. For a fixed shape in air, the <lensmaker's equation> gives $1/f\propto n(\lambda)-1$: the larger short-<wavelength> <refractive index> gives a shorter <focal length>. Different colours therefore form sharp images at different axial positions, causing <longitudinal chromatic aberration>, blur and coloured fringes in a white-light image. Off the <optical axis>, colour-dependent <transverse magnification> can also give <lateral chromatic aberration>. An <achromatic doublet> combines suitable <optical glasses> and curvatures to reduce this wavelength dependence.