Light travels in optical fibre irrespective of its shape because it is a device by which signals can be transferred from one location to another. It is based on the phenomenon of:

Optical fibers are thin strands of glass or plastic designed to transmit light signals over long distances [t6]. The fundamental principle governing light propagation in these fibers is total internal reflection (TIR) [t3, t4]. When light travels from a medium with a higher refractive index (the core) toward one with a lower refractive index (the cladding) at an angle exceeding the critical angle, it does not refract out of the fiber [t6, t8]. Instead, the light is reflected entirely back into the core [t6, t7]. This continuous internal reflection allows the light to follow the path of the fiber regardless of its shape or bends, ensuring minimal signal loss [t4, t9]. While refraction occurs at the initial entry point, the guiding mechanism that enables signal transfer through the length of the cable is strictly total internal reflection [t2, t6].

Sources

1. [1] https://www.sciencedirect.com/topics/engineering/light-propagates