Abbe numbers and refractive indices

I'm a refractor guy.

I've seen these things called Schmidt-Cassegrains, and someone told me they can do astronomy with mirrors. One day I might be beguiled by the hyperbolic surfaces of a Ritchey-Chr├ętien, or the pure beauty of a well-machined truss tube. For now, though, I reckon that if it was good enough for Galieo, Kepler, Brahe and Copernicus, then it's good enough for me.

But refractors have their problems. Chromatic aberration, where the different colours components in the light from stars don't focus at the same point, is the bugbear of the design.

Of course, other designs do have their problems. Newtonians have coma, Schmidt-Cassegrains have astigmatism, and Ritchey-Chr├ętiens have an air of intolerable smugness (with apologies to the late Douglas Adams)

So how do we manage chromatic aberration?

We have two main ways of controlling the way light changes as it passes into and out of a glass lens.

First, the amount the light bends is determined by the refractive index (RI) of the glass (and that of the air). have a look at these two prisms:

The top prism has a lower index than the bottom one. The one at the top bends the light much less than the one at the bottom, even though the prisms are the same shape. RI is typically a number between 1 and 2.

The second way of controlling light as it passes though glass is dispersion, or how much white light splits into a rainbow. In the photo, the top prism is showing low dispersion - you can only see the beginnings of a rainbow off to the right. The bottom prism shows a Pink Floyd level of dispersion.

Dispersion is measured by the glass' Abbe number. This pretty simple formula compares RI numbers of the lens for three different colours. A high Abbe number indicates low dispersion and vice-versa.

So now, lens makers can make different coloured light travel on different paths through groups of lenses. The paths are determined by the different Abbe and IR numbers.

It's complicated, but eventually the light of different colours focuses at the same point.

Optical lens designers: 1. Chromatic aberration: nil.

Image: SCHOTT AG

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