The only thing you have to know to understand how all lenses work is that light, when going from air into glass, will bend away from the surface of the glass. This is shown in the picture below:
The light (red line) starts in the air and hits the glass in the bottom half of the picture. As it enters the glass, it bends away from the surface as shown. (It is actually more correct to say that it bends toward the dashed line, which is perpendicular to the surface, but don't worry about it).
When light travels from glass into air, the exact opposite thing happens: It will bend toward the surface, like in the next picture:
If we put these pictures together, we can understand both convex and concave lenses. A convex lens can take parallel light rays and bend them together, as shown below.
Light comes in from the left, hits the glass and is bent inward (away from the surface). When it gets to the other side of the lens it is bent again on the way out, this time toward the surface, changing its direction even more.
A concave lens can take parallel light rays and bend them apart, as shown in the final picture. Again, each light ray is bent away from the surface in the way into the glass and toward the surface on the way back out.
(published on 10/22/2007)
Hi Bess- I'm putting up a quick answer so you'll have something to help right away in class. We may improve it as we find better illustrations, etc. I've marked your question as a follow-up to an old one that has some pictures of how light rays bend as they pass through lenses.
On the second question, I think the key thing is to use lots of pictures. Draw a little figure, with rays of light coming off say the head and the foot. Trace how those rays would go through the lens. As the rays reach an eyeball, they each come from some direction.Tracing them backward to where they seem to come from shows that the concave spreading makes them look like they're coming from points closer together than they really were. Maybe that's what you've already done. This site has some useful sketches: http://2.bp.blogspot.com/-fElj_9DV-Cc/UgIG7vnCtpI/AAAAAAAAB84/EWcp7SmVzdg/s1600/17-caoncave-convex.jpg. As I said, we'll look for some better figures, but your own sketches probably would work well enough.
(published on 02/02/2012)