Question

Why does total internal reflection occur in a bicycle reflector?

Answer 1

Total internal reflection is a phenomenon that occurs at the boundary between two mediums, such that if the incident angle in the first medium is greater than the critical angle, then all the light is reflected back into that medium.

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Answer 2

Because no light is absorbed.

It is not the fact of "total reflection" that is important here (a simple mirror does that), but the fact that the light should go more-or-less back to where it came from so that the car driver (say) does actually see the cyclist. This is a much more complicated problem.