The correct answer is option 4: successive total internal reflections occur as a ray moves through the fibre.

Optical fibers are made of a core material surrounded by cladding material. The core is designed to have a higher refractive index than the cladding, which allows for total internal reflection to occur at the boundary between the two.

When light enters the fiber at an angle greater than the critical angle, it undergoes total internal reflection at the core-cladding boundary. This means that instead of passing through the boundary, the light bounces back into the core. As it continues to propagate through the fiber, it undergoes multiple total internal reflections, which keep the light trapped within the core and guide it along the fiber`s length.

Because of these successive total internal reflections, the light rays can travel along an optical fiber in a zigzag path to reach their destination. This property of optical fibers allows for efficient transmission of light signals over long distances, as the light can bounce back and forth without significant loss or dispersion.

Therefore, the option stating that successive total internal reflections occur inside the fiber is the correct explanation for why light rays can move in zigzag paths through an optical fiber.