A student investigates how the appearance of an object changes when its distance from a spherical mirror is varied. The mirror is concave with a known focal point located on the principal axis. The student places a small arrow of fixed height on the axis at three different positions: (1) far beyond the center of curvature, (2) slightly inside the center of curvature but still beyond the focal point, and (3) between the focal point and the mirror surface. No numerical measurements are provided; the student observes only relative image size, orientation, and whether the image can be projected on a screen.
(a) For each of the three object positions, describe qualitatively whether the image is upright or inverted, reduced or enlarged relative to the object, and real or virtual. Provide a brief explanation for each description based on the behavior of reflected rays.
(b) For positions (1) and (2), the student notices that the image and object heights have opposite algebraic signs, whereas for position (3) they share the same sign. Explain how the algebraic sign of the magnification connects to the orientation of the image in these cases.
(c) Discuss why the algebraic value of the magnification increases in magnitude as the object is moved from position (1) to position (3). Relate your explanation to changes in object distance along the principal axis.
(d) A plane mirror is then substituted for the concave mirror while keeping the arrow at position (2). Predict the image characteristics (orientation, size, and reality) in this new setup and justify your answer.