Fiber optics also uses _exceptionally_ clear glass.
If the ocean were as clear as your average long-distance fiber cable, you would see down to the bottom of the Mariana Trench (also in the range of visible light, AFAIK).
Silica glass behaves differently from ZBLAN (fluorozirconate glass).
Which goes to show how complicated EM interactions with media can be. It's generally easier to just empirically measure attenuation through some medium and use the empirical measurements as a model.
It's exceptionally clear compared to e.g. window glass even in the visible spectrum of light. You can shine a red light source into a 10 kilometer standard G.657 fiber (optimized for 1310/1550nm, i.e. deep infrared) and it will still be visible just fine on the other end. If you did that with regular glass, it would hardly go ten meters.
What are the relative contributions of the total internal reflection property of the fiber optic cable and the particular low-attenuation material it's made of?
The total internal reflection is to keep it focused, it's in a sense a different question.
IIRC, when Corning Co. first started working on optical fibers, the best available glass would be good for sending signals about ten meters. What was improved was not the total internal reflection; it was the purity of the glass.
Oh yeah. I'm not saying otherwise. Someone replied "Clear glass blocks about 5% visible light". I guess "clear glass" is pretty subjective. At what level of attenuation would someone consider glass not clear? xD
If the ocean were as clear as your average long-distance fiber cable, you would see down to the bottom of the Mariana Trench (also in the range of visible light, AFAIK).