Total internal reflection. Light inside a denser material that meets the wall above the critical angle, measured from the normal, is reflected completely. Acrylic in air: 42.2°.
Why bends leak. In a loop each ray keeps the same impact parameter, so the angle at the outer wall shrinks as the radius shrinks. Below critical, part of the light refracts out. It only happens on the outside of the bend.
Telecom fibre. The wall is glass too: the cladding. Core index is only ~0.36% higher (≈1.449 vs ≈1.444 at 1550 nm, derived from Δ = 0.36%), so the critical angle is 85.1° from the normal, within ~4.9° of the axis. Refracted into air through a flat face that is ≈7° (index NA ≈0.12).
Ray picture is a simplification. Standard single-mode fibre carries one mode. Its mode field (10.4 µm @1550 nm) is wider than the 8.2 µm core, and ~1/5–1/4 of the light runs in the cladding. On a bend, the part on the outside would have to outrun light in the cladding, so it radiates. Loss rises roughly exponentially as the radius shrinks, and generally with wavelength.
Safety. Never look into a fibre end. The real beam is infrared and invisible, and some systems are powerful. The laser switches off in the X-ray view.
Honest labels. Traced numbers carry RAY MODEL. Telecom bend figures are ITU maximum limits per turn for bare fibre on a mandrel, never extrapolated. The glow is illustrative.