How do light waves within a fiber optic cable travel around corners?

Light waves in a fiber optic cable travel around corners through a principle called total internal reflection. When light hits the boundary between the fiber's core and cladding at a steep angle, it reflects back into the core instead of refracting out. This allows the light to bend around corners without escaping, maintaining the signal's integrity. The design of the fiber, with a core that has a higher refractive index than the cladding, facilitates this process.