> While investigating Wikipedia, I came across a fleeting suggestion that a 
> material's optical properties are somehow related to its electrical and 
> magnetic properties.

Of course they are, "optical" properties are just how a material responds to 
a certain frequency band of electro-magnetic waves.  We just think of the 
optical wavelengths differently to the others because that's what our eyes 
respond to.

For example, you know how light "bends" when it enters eg glass, well how 
much it bends is related to the refractive index of the material.  And if 
you know the "electrical" properties you can calculate this refractive index 
exactly (it's the square root of permittivity times permeablility of the 
material).

> Obviously, this seems *highly* implausible, given the abundance of 
> materials with similar optical qualities but highly disimilar electrical 
> properties, and vice versa.

There is no fixed standard rule, but you can see patterns.  For example how 
good electrical conductors also tend to be good thermal conductors, and 
completely opaque to light.  Finding a good conductor that is transparent or 
soft is difficult.  Ditto things that are soft tend to not conduct 
electricity.  An exception is ceramics, which are hard and opaque, but very 
good insulators, that's why they are used on electricity pylons (rubber or 
plastic would suffer much worse weathering).  As always, it's all in the 
atomic level detail, but you can make higher level generalisations.

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