When is a real image produced by a lens the same size as the object?

Answer 1

When it's the same distance from the lens as the object. An easy way to remember this is that any ray passing through the center of the lens is not deflected; thus, for real images, a ray that passes through the lens center from a point on the object that is not on the central axis passes straight through, forming equal angles with the centerline on either side of the lens. Being equidistant and formng an image means that object distance = image diistance = focal length / 2.
See the ref.