Physics · Ch 6 — Optics
Lateral Magnification in Spherical Mirrors
Lateral Magnification in Spherical Mirrors
Lateral (transverse) magnification is defined as the ratio of image height to object height, . Applying the Cartesian sign convention to the similar triangles used in deriving the mirror equation gives ; combining this with the mirror equation itself, can equivalently be written as . The sign of carries direct physical meaning: negative means a real, inverted image; positive means a virtual, erect image; and the magnitude of shows whether the image is enlarged (), the same size (), or diminished (). A distinct but related idea, longitudinal magnification (for an object extended along the axis rather than perpendicular to it), is the ratio of image length to object length, and is genera …
Worked out. A thin rod of length f/3 lies along the optical axis of a concave mirror of focal length f, positioned so its own real, elongated image just touches the rod at one end -- meaning that shared end must sit exactly at the mirror's centre of curvature, u' = R = 2f, so the near end of the rod sits at u = u' + f/3 = 2f + f/3 = 7f/3 (using the sign convention, the object distance actually used is -7f/3). Applying the mirror equation to locate the image of this near end, then defining the longitudinal magnification as the ratio of image length l' to object length l (here l = f/3), and solving the resulting equation for the magnification m shows m works out to 6/(m+3) in a self-consistent form that solves to m = 3/2. This illustrates that longitudinal magnification (along the axis) is generally different in value from the lateral (transverse) magnification of the same setup, since image distance …