# In gravitational lensing, if the source is infinitely far away how can we have an image on the same side of the lens?

In the standard picture of gravitational lensing, we have a picture like the one you can see as Figure 1 of this paper (I don't know if I can copy/paste it). In it, the source S and the observer O are both at a finite distance from the lens L, and both on the same side. Light curves a little bit around the lens, and an image is formed on the same side of the lens as the source.

Now, in almost every situation one makes the approximation that the source and the observer are infinitely far away from the lens, like this:

This feels weird, because as you can see the image and the source are always on opposite sides of the lens, which is not always the case in realistic situations (for example, with the lensing of a star by the sun). How can this be explained? Is it that the approximation has to be applied only sometimes?

• I have edited in the abstract of the cited paper, as this is customary and covered under fair usage policy. If my edit is approved shortly, could you please just review it, and ensure that your post is the way you want it, thanks.
– user167453
Commented Sep 8, 2017 at 20:03
• @Countto10 Well, I gotta say, I don't really see the point of including the abstract. After all, I just cared about the picture. Commented Sep 8, 2017 at 20:05

"How can we...?" - something like this,

That is, for a small deflection the object and image are on the same side of the lens. However this cannot be detected by conventional observations, as I now explain.

A lensed object is detected by comparing direct light with a lensed image.

If the object is on the same side as of the lens as the image then the light that would be direct (this is the red line from object 1 to the observer in the diagram) also passes through the gravitational lens and never reaches the observer.

If the object is deflected sufficiently (to the other side of the lens) direct light will be able to avoid the lens altogether.

• But the issue is that if you move the observer farther back along the direction of the light ray, you eventually move to the other side. I feel like it might have to do with how exactly you send the observer to infinity. Commented Sep 8, 2017 at 23:16
• Yes as the observer moves further back, his sight line to the lens changes angle. Eventually it will cross the image. (picture updated) Commented Sep 8, 2017 at 23:22
• I mean may. In my diagram unfortunaly the Image is not sufficiently deflected. Commented Sep 8, 2017 at 23:31
• But what troubles me is that if source and observer are infinitely far away, the image will always be on the other side of the lens. This approximation is always taken, and no one doubts its validity, and yet in real situations the image is often on the same side of the lens. Commented Sep 8, 2017 at 23:34
• modified pic again. Commented Sep 8, 2017 at 23:35