When light passes close to a black hole, it is deflected from its original direction.
The grey disk marks the region inside the event horizon. From here, neither light nor matter can escape to the outside.
Outer three rays:
Far away from the black hole the deflection is small, but sufficiently close it may be quite large.
Inner three rays:
Light that comes very close to the black hole is caught: the photons cross the event horizon and end up in the singularity.
The most interesting region is in between: the region where photons are just caught or just barely escape.
In this intermediate region, a photon can, e. g., make a three quarter turn around the black hole ...
... or make several turns before it escapes ...
... or make several turns before being caught.
The limit between escaping and non-escaping photons is a circle with 1.5 times the circumference of the event horizon. A photon which just turns exactly into that circular orbit, will circle the black hole forever. If it stays a little bit farther out, it may circle the black hole many times and will eventually escape. If it gets a little bit further in, it is eventually caught, possibly after circling the black hole many times.
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