Light that is directed towards the center of a black hole

In theory, yes. There is a region called the photosphere where a photon can orbit a black hole. This, however, is a temporary situation. The orbit is unstable and will not persist.

 

If you go nearer and nearer to the event horizon, the effect of gravity gets stronger and stronger unlimitedly. So, I think, you can always find balancing radius for a photon to orbit a black hole. But, light as wave diffuses by diffraction. So, it will not last long.

 

"dip" is impossible. Anything inside the EH can not go out of the EH. This is the definition of EH. Furthermore, I think, anything can not go into the EH in our (= observers far from the black hole) frame of reference because progress of the time stops there. Following link shows further discussion.
http://en.doppolaboratory.com/engli...tions/is-the-distance-to-a-black-hole-finite/

 

“Kruskal–Szekeres coordinates“ shows that light can cross the event horizon. But, I think, the crossing can take place after the end of our spacetime. I calculated the time for light to reach the surface of a black hole from a certain point by simply integrating well-known equation. It went infinite. This is shown in eq. (7) in the web page cited in comment #4 above.

 

All I wanted to say is that eq. (7) seems simple enough to convince me.

 

defracts off what?

 

the photon sphere is at radius 3M around a black hole (where the event horizont is at 2M)

close to the photon sphere, light can orbit many times before escaping

see https://www.physicsforums.com/library.php?do=view_item&itemid=268 for details

 

A laser pointer can spot a point sharply at a screen 10m ahead. But it can’t spot a point 100m ahead because the beam diverges and brightness of the spot decreases. This is because of diffraction. Additionally, because of strong tidal effect, the divergence must be accelerated. So, I think all photons will escape or fall into the black hole before long.