An optical fibre keeps light inside by arranging for the incident angle to be:

1. Fibres rely on light never escaping the core. 2. The critical angle produces an angle of refraction that grazes the surface. 3. If the incident angle is greater than the critical angle, all light is reflected back into medium 1. 4. That condition is total internal reflection. 5. So the fibre is built so the incident angle stays above the critical angle. _Source: OpenStax College Physics for AP Courses 2e (CC BY 4.0), Ch 25 'Geometric Optics', sections 25.1-25.7_