Step 1: Think about the image a mirror produces for a distant to near real object. The size of the image relative to the object decides the magnification.
Step 2: For a convex mirror the reflected rays diverge and appear to meet behind the mirror, producing an image that is always smaller than the object. This holds for every object distance, so \(|m|\) never reaches 1.
Step 3: A plane mirror produces an image of exactly the same size, so \(|m| = 1\) (not less than 1). A concave mirror behaves like a converging mirror and can enlarge the image, so \(|m|\) can exceed 1.
Step 4: Since only the convex mirror keeps the image diminished in every case, it is the answer.
\[\boxed{\text{Convex mirror}}\]