Where is the optical centre of a Concavo convex lens? I have been taught that the Optical Centre of a lens is the point at the principal axis of a thin lens through which Ray of light passes undeviated. I was under the impression that it always passes through the Geometrical centre of the lens. However, in concavo-convex and convexo-concave lenses, this does not seem to be the case, any explanation as to why this happens would be appreciated.
 A: Let's first consider a thin convex lens. In a small region at the center of the lens, both sides of the lens are approximately symmetrical (almost parallel) so that an incident ray coming in on say the left through the center, will refract by a certain angle, and when it leaves the side on the right, it will refract by the same angle (but in the opposite direction), so that the ray leaves the lens parallel and colinear with the original ray on the left.
When light enters a medium of higher refractive index it bends toward the normal, and when it enters a medium of lower refractive index, it bends away from the normal by the same amount, if the medium on both sides of the lens has the same refractive index (air in this case, and the refractive index inside the lens is uniform) with symmetric parallel sides. So going back to our original ray entering a sufficiently thin lens on one side, it will leave as if nothing happened to it on the other side.
This will not work for a concavo-convex lens (or convex-concavo), since the center of the lens will no longer have this symmetry (the sides will not be parallel) and light entering one side will refract by an amount not equal to the ray leaving the other side.
So while we can define the optical center of a lens as the region where a light ray will pass through non-deviated, this will only be true for certain lens types. Since it will not be true for concavo-convex lenses, this may imply that these types of lenses do not have an optical center. They probably do and they are located at the same spot (center of lens) as other lenses, though we will not expect the same behavior for light rays passing through these places as we would for convex and concave lenses.
