Convex lenses converge parallel rays going in and convex lenses diverge rays.
A convex lens is useful as a magnifying glass as it will produce a virtual enlarged image if the object is brought within the focal length. If the object is outside of the focal length, it will produce a real image that can be focused (burning ants of the hill!)
A concave lens is useful for people who are near-sighted. Your eye is a convex lens and near sighted people focus the light to much. A concave lens is put in place to spread the light out before entering the eye, thereby getting the light to focus further back!
With a convex lens, a virtual image is always produced!
