Difference between convexo-concave and concavo-convex lenses? What is the difference between concavo-convex and convexo-concave lenses? We dont say convexo-plane for plano-convex. Does that mean concavo-convex and convexo-concave are essentially the same?
 A: In both types, (convexo-concave or concavo-convex) the lens has one convex and one concave side. 
Convexo-concave : The concave face has a greater degree of curvature than the convex face. 
Concavo-convex : The convex face has a greater degree of curvature than the concave face. 
The images are as follows:

Now a days these lenses are referred as convex-concave or meniscus. It is this type of lens that is most commonly used in corrective lenses.
Convex-concave (meniscus) lenses can be either positive or negative, depending on the relative curvatures of the two surfaces. A negative meniscus lens has a steeper concave surface and will be thinner at the centre than at the periphery. Conversely, a positive meniscus lens has a steeper convex surface and will be thicker at the centre than at the periphery. 
A: The most important thing to remember is that a CONVEX lens (meniscus if you like) is thicker in the middle than at the edges, no quibbles, no exceptions. It accordingly causes a beam of light passing through to converge, and is said to have positive optical power.
Conversely for CONCAVE.
A plano-CONVEX lens still is a CONVEX lens, only a special kind with one side flat. But it remains conVEX, because its middle is thicker than its edge.
A concavo-CONVEX lens similarly is a special kind of CONVEX lens because its middle is thicker than its edge. The word after the hyphen is the type, whatever you put before the item is just part of its description.
A convexo-CONCAVE lens is still a concave lens, just one that has a convex surface somewhere. Being concave, it is thinner in the middle than at the edge.
And whether a lens is thicker in the middle or the edge, is the thing that make concavo-convex different from convexo-concave.
