A physics student examines the images produced by a concave spherical mirror while keeping the mirror fixed and gradually sliding an illuminated arrow toward the mirror along the principal axis.
Initially the arrow is positioned very far from the mirror; eventually the arrow is placed well inside the mirror’s focal length.
Parts (a)–(d) ask you to interpret how the properties of the image change as the object distance passes through key regions. Assume sign conventions consistent with standard geometric-optics analysis.
(a) Describe qualitatively how the image distance, orientation, and relative size change as the object is moved from “very far” (effectively at infinity) to a distance slightly greater than twice the focal length.
(b) Explain, without performing explicit numerical calculations, why the image becomes infinitely large at the point where the object distance equals the focal length.
(c) For an object placed just inside the focal length, justify why the image switches from real to virtual and discuss how both the mirror relationship and the magnification relationship account for this change.
(d) Summarize the sequence of image characteristics (real/virtual, upright/inverted, enlarged/reduced) the observer would report while moving the object continuously from infinity to the mirror surface.