A beam of light usually spreads into the space around it. An optical fibre does something useful: it guides light along a narrow path. The trick begins at the boundary between two materials.
Two kinds of glass, one useful boundary
A fibre has a central core surrounded by cladding. The core has a slightly higher refractive index than the cladding. Refractive index describes how light propagates in a material relative to a vacuum. At a boundary, the difference in refractive index determines how a ray bends or reflects.
For light travelling from the higher-index core towards the lower-index cladding, a sufficiently large angle of incidence—measured from the normal to the boundary—produces total internal reflection. In the simple ray model, the light stays guided rather than passing out through the boundary. Total internal reflection — The Fiber Optic Association.
This does not mean that any beam entering from any direction will be trapped. The fibre and the way light is launched into it determine which light can be guided.
The optional equation
Guided does not mean lossless
A real fibre still has losses. Absorption and scattering reduce the optical power that arrives at the other end. Bending can also increase loss. The fact that light is guided explains why the path works; it does not imply that the signal survives any distance unchanged. Fibre terminology and loss mechanisms — Corning.
That is why the larger communication system matters. The transmitter, fibre, amplifiers and receiver must work together to carry information reliably.
A useful question to take back to the main story is this: which parts of a cable protect the glass physically, and which parts preserve the information carried by the light?
EXPLORE THE IDEA
When does the light stay inside?
Increase the angle past the critical value and watch the outgoing ray return into the core.
Ray model at one core–cladding interface, with illustrative indices n(core) = 1.48 and n(cladding) = 1.46. Angles are measured from the normal. Below the critical angle, reflection and transmission coexist; only the transmitted branch is drawn. Real fibres guide electromagnetic modes.