Linear magnification from lens formula and image height ratio

Steps:

• Apply lens formula 1/f = 1/v - 1/u with f = +4.0 cm (converging lens); from diagram, measure u ≈ -6.0 cm.
• Solve for v: 1/v = 1/4 + 1/(-6) = 1/4 - 1/6 = (3-2)/12 = 1/12, so v = +12.0 cm.
• Calculate linear magnification m = -v/u = -12/(-6) = +2.0 (absolute value for size).
• Verify with heights: object h_o = 6.0 cm implies image height h_i = m × h_o = 12.0 cm, matching diagram scale.

Why C is correct:

• Magnification m = |h_i / h_o| = 12/6 = 2.0, per definition for transverse linear magnification.

Why the others are wrong:

• A: 0.50 implies minified image (object beyond 2f), but diagram shows enlarged real image.
• B: 1.5 mismatches calculated v/u ratio of exactly 2.0.
• D: 6.0 equals object height, ignoring lens effect; would require m=1 with h_i=6.0 cm.

Final answer: C