Rob Pike
Fun watching the hacker news commentators try to understand how achromatic (and apochromatic) lenses work. I was utterly confused by this myself when I was a kid. Despite devouring Newton's Opticks I couldn't figure it out.
But it's pretty easy.
The refractive index (bending power) of optical materials varies with wavelength; this is called dispersion.
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Rob Pike
A fun detail is that Newton figured this out, but managed to use two materials of essentially the same dispersion, so his experiment failed and he gave up. But he had the right idea.
Rob Pike
This allows to make, say, a two-element lens with less chromatic aberration.
We make a too-strong convex (positive) lens using low-dispersion material, then a concave (negative) lens behind, of lesser power but higher dispersion. If you choose the two materials correctly, you can (partially) cancel out the spread of colors. The two different dispersions can be adjusted to compensate perfectly while allowing a positive optical power to remain.
Do the same with more lenses for better correction.
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