To remember the difference between convex and concave lenses or mirrors, always think:
Cave people lived in caves which were hollowed out of rocks. A concave surface curves inwards like the mouth of a cave (how easy is that!).
CONCAVE SURFACE CURVES INWARD
Concave surfaces curve inward and convex ones don't (convex = curve outward).
A concave lens looks like the following:
But because concave lenses actually mean thinner in the middle than on the edges, a concave lens only needs to have one surface that curves inwards. The other can be flat.
NOTE: these are called planoconcave lenses and an easy way to remember this is to think that one surface is plane and "oh!", by the way, the other is concave.
A concave lens is a lens that possesses at least one surface that curves inwards.
Concave lenses are sometimes denoted by a symbol:
This is drawn as a vertical line with inward-facing arrows to indicate the shape is thinner in the middle.