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Your are mixing properties. Converging lens is always thicker in the centre and thinner at the edges. The other cathegory is the geometry of shape of the surfaces of the lens. Convex means that the shape is similar to the outer surbace of a sphere, concave means that the shape is similar to the iner surface of a sphere (or: convex = lower side of a spoon as we use it for sampling a soup; concave: upper (inner) shape of the spoon). A double convex lens is always a converging lens. A plano-concave lens is always a diverging (not converging) lens. A convexo-concave lens is the most usual shape of a lense used in spectacles. It can be either converging or diverging, depending on the radii of the surfaces.

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Q: Which lens is a converging lens a double-convex lens or a spherical-convex lens or a plano-concave lens or a convexo-concave lens?
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