# Doubts about gravitational lens magnification

A gravitational lens approximately follows a $1/r$-curve, meaning that rays closer to the lensing object get bent more than those away. My question is, wouldn't that shrink any image as opposed to magnify it?

Consider, for example, the sketch below.

The top ray from the star (that reaches the target) has to come out at a lower angle or else it wouldn't be converged by the gravitational lens (it'd go outward as shown by the uppermost ray). This means that the top and bottom ray have to meet at a smaller angle at the target (which would make a smaller image).

Even when you have an Einstein ring, the rings should be thinner than the object by the same reasoning.

Under what circumstances can something get magnified? Is there a circumstance where the area is necessarily larger and brighter?

• Don't bother drawing any of the rays that don't reach your eyeball. The ones that reach your eyeball are the only ones that explain what you see because they are the only ones that you are able to see. Jun 5, 2018 at 18:44

The geometry is a bit involved, but it turns out that if $\theta$ is the angle the rays make with the optical axis (the observer-lens line) at the observer, $\alpha$ is the deflection angle, and $d\gamma$ is the angular size of the source with no lensing, then
$$\frac{d\theta}{d\gamma} = \frac{1}{1-d\alpha/d\theta},$$
which, since $d\alpha/d\theta < 0$, is smaller than 1 as you said.