Problem 3
A thin converging lens in air has focal length f>0. An upright real object of height H lies on the principal axis at distance u>f from the optical center; use the convention that a real image on the opposite side has v>0. Neglect lens thickness and aberrations. (a) Establish the relation among u, v, and f. (b) Find v and identify the image as real or virtual. (c) Find signed magnification m and signed image height. Use SI units throughout and treat components as ideal exactly as specified. State sign conventions when writing equations and retain units in final results.
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Collect results in the order asked. Dimensions and physical signs provide independent checks; they do not replace the derivation but can expose algebraic errors.