(a) A convex lens (f = 10 cm) forms an image with v = +30 cm of an object at u = −15 cm. Find linear magnification and describe the image. (b) As a simple magnifier, what is its angular magnification with the image at the near point (D = 25 cm) and at infinity? (c) A telescope has f_o = 100 cm, f_e = 2 cm. Find M. Step 1: m = v/u = 30/(−15) = −2. Real (v > 0), inverted, twice as tall as the object. Step 2: Near point: M = 1 + D/f = 1 + 25/10 = 3.5×. Infinity: M = D/f = 2.5×. (Image at infinity is more comfortable — relaxed eye — at slight cost in magnification.) Step 3: M = −f_o/f_e = −100/2 = −50×. The minus sign means the astronomical image is inverted; terrestrial telescopes add an erecting lens. Note the telescope's angular magnification (50×) dwarfs the single lens's linear magnification (−2×) — different instruments, different magnifications.