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.
