* Michael Richmond:

It does however not explain multiple images. Instead, it just asserts
that they can occur "if [the background source and the lens] line up
well enough that the true position of the background source falls within
the Einstein ring radius of the lens". I don't understand that.

There is no way around the math; you'll have to read the technical
literature on gravitational lensing if you want to understand. One
early paper you might read is by Bourassa and Kantowski. The ADS
entry for it

http://adsabs.harvard.edu/cgi-bin/np...f6510b0d827235

includes a scanned version of the entire paper. Somewhat more
complicated models are included in another early paper in the field,
by Padmanabhan and Subramanian:

http://adsabs.harvard.edu/cgi-bin/np...f6510b0d829377

Good luck.

Yes, thanks, it seems luck is the key word in dechiphering that first
mentioned paper, even the presumably clarifying figures... ;-)

Here is then my limited understanding, disregarding for now (until last
paragraph) the impenetrable paper.

Consider three points in space: source, point lens, receiver, not in a
straight line. These three points define a plane P. Now the source can
emit a photon that goes somewhat to the side of the lens, wrt. to the
direction from receiver to lens, and we can vary the distance out from
the lens, and for at most one distance for a particular side (assuming
the photon doesn't go around the lens one or more times, which I in my
naivete think is impossible) it can strike the receiver.

Since there are only two sides of the lens in plane P, photons in P can
at most define two images of the source. That's what I meant when I
wrote that it's easy to visualize _two_ images. But not identical.

If the source emits a photon that is not in plane P then the photon path
plus lens defines a new plane Q, and the receiver is not in that new
plane Q unless the source, lens and receiver are in a straight line. So
assuming first they're not in a straight line. In order for that photon
to strike the receiver the lens will then have to deflect the photon in
a direction normal to the plane Q defined by the original path + lens.

I haven't heard of gravity having any sideways effect before.

Assuming next that source, lens and receiver are in a straight line.
Then the photon can strike the receiver among any of an infinite number
of paths, namely those that pass through a cirle or oval around the
lens. Which gives the "Einstein ring" effect.

Now the only simplifying assumption I see in that is the one about point
source, point lens and point receiver. But as far as I can decipher the
paper you linked to it claims that -- possibly with spatial extension
in the picture -- five or even seven distinct images can appear. I
can see that spatial extension can give an "Einstein ring" even when the
line-up isn't perfect, but I fail to see how photons can arrive at the
receiver when passing through five or seven points around the lens (or
in the case of "Einstein's cross", four points), and _not others_.

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