A concave mirror has focal length 15 cm. An object 4.0 cm tall is placed (a) 40 cm, (b) 10 cm in front of it. Find the image position and magnification in each case, and describe the image. Sign convention: u is negative in front. f = −15 cm. Case (a): u = −40 cm. 1/v = 1/f − 1/u = −1/15 + 1/40 = (−8 + 3)/120 = −5/120 → v = −24 cm (real, in front). m = −v/u = −(−24)/(−40) = −0.60. Image: real, inverted, diminished (2.4 cm tall), between F and C. Case (b): u = −10 cm (inside F). 1/v = −1/15 + 1/10 = (−2 + 3)/30 = 1/30 → v = +30 cm (virtual, behind mirror). m = −v/u = −(30)/(−10) = +3.0. Image: virtual, upright, enlarged 3× (12 cm tall) — the shaving-mirror effect. The sign of m instantly tells upright (+) vs inverted (−).