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convex ray diagram
the middle ray won`t refract as it goes through axis

concave lens ray diagram

in a concave lens
the image will always be virtual diminished upright and on same side of lens
in a convex lens between 1f and 2f the image will be
real inverted magnified beyond 2f on other side of lens
in a convex lens at 2f the image will be
real inverted same size at 2f on other side of lens
in a convex lens nearer than f makes a image
virtual upright magnified on same side of lens