A search of these boards proved fruitless, as did Google. (Lots of statements that minus lenses make things look smaller, but no explanations of why.)
I got my first pair of glasses 2 years ago, but didn’t think much about this until I recently saw some diagrams of light being bent by a lens and going into an eye. Minus lenses scatter the light–two parallel beams entering the lens will diverge upon leaving it–so if anything, I’d guess that it would make things look bigger. What gives?
Optics guy here.
I always told my students to work through these problems by ray tracing. Draw an arrow as your object on one side of the lens, with the arrow base on the optic axis and the tip some distance away from it. Now draw a line from that arrow tip parallel to the optic axis to the lens. After it passes through the lens it will, as you say, diverge away from the axis. You can draw the line by placing one point on your ruler at the focal point on the same side of the lens as your object (for a thin lens, this will be one focal length from the lens) and the other point where your ray parallel to the optic axis hit the lens. Draw a dashed line from the focal point to the lens, and a solid line from the lens onwards.
Now trace a ray from the tip of your arrow (where the other one started) towards the focal point on the other side of the lens. It will get closer to the optical axis, until it hits the lens. By the laws of paraxial optics, this line will now end up travelling parallel to the optical axis, so draw the transformed ray of the other side as parallel. Extend the parallel line through the lens, but make it dashed . If your object was on the left side of the len, you should now have two dashed lines on the left side of the lens. The point where they intersect is the location of the virtual image. Notice that it’s closer to the lens, and smaller than the original. It seems smaller because your eye follows the solid rays on the right side of the drawing back toward the object. These rays bend at the lens, but your mind imagines them going unbent, and they meet at the head of the virtual image – “virtual” because light doesn’t actually pass through that point, and if you put a screen there you would not get an image.
By “minus lens” I assume you mean a concave lens.
http://www.gunn.palo-alto.ca.us/~cbakken/p1A/optics/obookshelf/ccimages.html
That site explains it reasonably clearly.
Basically, the light from the object you are looking at is diverged by the lens, as you said, so it appears to be coming from a virtual object closer to the lens, and smaller than the actual object.