An optical bench holds a concave mirror of focal length 25 cm. A small illuminated object of height 1.5 cm slides along the principal axis such that its distance so from the mirror can vary continuously. Assume all motion remains along the axis and that the object height does not change.
(a) Derive an algebraic expression for the image height hi in terms of so, the mirror’s focal length, and the constant object height.
(b) Using your expression from part (a), evaluate the limiting value of hi as so approaches infinity. Describe the physical meaning of this limit for both image position and orientation.
(c) Determine the two distinct object distances (if any) for which the magnitude of the image height equals the object height. Indicate the orientation of the image at each of those distances.
(d) Sketch a qualitative graph of hi versus so for object distances ranging from very large values down to distances just short of the mirror surface. Label key features identified in parts (b) and (c).