Fiber optic cables are made out of many concentric layers of transparent material (usually glass or plastic), each with a slightly different index of refraction. how can these transparent cables keep light inside?

Transparent cables can keep light inside by the phenomenon of total internal reflection.

Explanation:

Optical fibers are often made from glasses or plastics.

when light rays falls on the glass or plastic with an angle greater than the critical angle, we have what is known as TOTAL INTERNAL REFLECTION

The total internal reflection causes the fibre to act as a wave guide. For a good glass or plastic when the rays of light falls, the ray converges and for a bad plastic or glasses, the rays are dispersed.

Therefore, transparent cables can keep light inside because of total internal reflection.

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explanation: