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enter image description here

The critical angle is given by:

c = arcsin(n2 - n1)

For a typical optical fibre, it says on the web that refractive index (n2) for cladding is higher than that of the glass core (n1) but it's only a few percent higher.

enter image description here

For instance, let's calculate c (critical angle) for this example.

c = arcsin(1.45/1.55) = 1.21 rad = 69°

For angles much closer, this can go even higher (like 80°)

This would mean light has to maintain angles lower than 10-20° with the core (since critical angle is about 70-80° from normal).

How are such low angles maintained? enter image description here

These angles for instance, seem much greater than the angles 10-20° from glass core.

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  1. Fiber optics are used in different ways. When it's needed to make light really bend around, I believe the fiber is plastic with no cladding, so that the difference in refractive indices is much higher.

  2. Fiber optic lines for telecommunications are only ~100 $\mathrm{\mu m}$ thick. So your last picture seems exaggerated. As long as the bends in the fiber are on a large enough scale relative to the fiber's diameter, then the light has ample time to more gently bounce around the bend at shallower angles. And from what I can find, according to The Fiber Optic Association, fiber optics aren't supposed to be installed with a bend radius less than 10x the cable diameter, and each cable is a larger bundle of individual fibers. This is to prevent damage to the cable, but I suppose it doubles as satisfying this condition for the total internal reflection.

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  • $\begingroup$ Huh. So if this difference in Indices of Refraction suffices, then wouldn't ANY plastic pipe (like that of a pen's refill) provide TIR for incoming light rays close enough to the surface? Does that mean there's nothing special in the optical fibre's core's material? $\endgroup$
    – Maddy
    Commented Oct 28, 2023 at 8:18
  • $\begingroup$ @Maddy For TIR, yes, the refractive index is the important bit. But the core material is chosen for some other properties as well. Glass fibers can be made with very low absorption which enables longer cable lengths, etc. $\endgroup$
    – HiddenBabel
    Commented Oct 28, 2023 at 9:02

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