(a) A simple microscope has f = 4 cm. Find M with the image at the near point and at infinity (D = 25 cm). (b) Where must the object be placed for each case? (c) If two such magnifiers are stacked in contact, what is the new M (image at near point)? Step 1: Near point: M = 1 + D/f = 1 + 25/4 = 7.25×. Infinity: M = D/f = 6.25×. Step 2: Image at near point: virtual image at v = −25 cm. 1/u = 1/v − 1/f = −1/25 − 1/4 = −(4+25)/100 = −29/100 → u ≈ −3.45 cm (just inside f = 4 cm ✓). Image at infinity: object exactly at f, u = −4 cm. Step 3: Two in contact: P doubles → f halves to 2 cm. M = 1 + 25/2 = 13.5×. Stacking magnifiers adds power — but aberrations also grow, which is why real loupes use doublets, not stacked singlets.