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Comment by itishappy | Hacker News Reader

It's a bit buried, but this (to me) is the most interesting sentence :

> Fluorite lenses are also unique in their extraordinary partial dispersion tendencies: the red to green wavelengths are dispersed with the same tendencies as glass, but the green to blue wavelengths are dispersed more than glass.

It has both low dispersion (less overall aberrations) and a unique shape to the dispersion curve (more control). Glasses typically all have similar dispersion curves. The weird shape of fluorite's dispersion curve gives your optimization function an extra lever to play with.

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Does this mean it has an index of refraction that depends on wavelength? How can that be? Is the bond length some multiple of blue (or green/red), where there's some quick "change" in what the photon "sees"?

Amazing question! Yup. Refractive index is a function of wavelength. I bet you already knew that on some level, because that's why prisms do their thing. As an extreme example, imagine X-rays: they barely refract at all, they just pass straight through stuff! Also, the change is actually quite smooth.

https://refractiveindex.info/

https://en.wikipedia.org/wiki/Dispersion_(optics)

It's a consequence of the relationship between absorption and index of refraction in glasses, which follow the Karmers-Kronig relationship [0]. As the wavelength approaches atomic resonance, the index increases or decreases depending on which side of the absorption peak the wavelength is.

0. https://en.wikipedia.org/wiki/Kramers%E2%80%93Kronig_relatio...

This is, I think, just one of those spots where "all models are wrong, some models are useful" is true. From the wikipedia page on Refractive Index (https://en.wikipedia.org/wiki/Refractive_index):

> The refractive index may vary with wavelength. This causes white light to split into constituent colors when refracted. This is called dispersion. This effect can be observed in prisms and rainbows, and as chromatic aberration in lenses.

--- snip ---

> For most materials the refractive index changes with wavelength by several percent across the visible spectrum. Nevertheless, refractive indices for materials are commonly reported using a single value for n, typically measured at 633 nm.

So we were all lied to in our introductory optics classes. n isn't a constant for a given material but rather n(lambda) but weakly.

Glass has this too. it's why achromats and apochromats were developed (using rather clever ideas like pairing two different types of glass, which cancel each other's dispersions.

All the physical explanations I've seen invoke the EM equations and quantum mechanics to explain it (and I don't understand it well enough to translate).

3Blue1Brown has a nice animated video about this: https://youtu.be/KTzGBJPuJwM?si=ssBPKL8LVhsQ3wNZ

Glass has an index of refraction that depends on wavelength; this is how a prism works. This is also why chromatic aberration exists at all.

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