I love this optic fibre demo. It is just a bent piece of Perspex. The Perspex has a higher refractive index than the air so light speeds up as it leaves the Perspex. If the angle is big enough, bigger than the critical angle, all of the light reflects back into the glass and thus is able to zig-zag round the curve to emerge at the end.
But look - light does escape out of the side of the fibre on the most curved sections. You can see that these parts are lit up.
I have reasoned that this is because when bent there is less space to fit in light between the critical angle and the top of the fibre so more of the light is below the critical angle and escapes.
