Linear magnification from lens formula and ray diagram

Steps:

• Identify object distance u and image distance v from the full-scale ray diagram (e.g., u = 30 cm, v = 60 cm for f = 20 cm).
• Verify using lens formula: 1/f = 1/v - 1/u → 1/20 = 1/60 - 1/(-30), which holds true.
• Calculate linear magnification m = |v/u| = 60/30 = 2.0.
• Confirm with object height 1.5 cm; image height = m × object height = 3.0 cm (matches diagram scale).

Why A is correct:

• Magnification m = v/u gives exactly 2.0 when distances from the ray diagram satisfy the lens formula for this setup.

Why the others are wrong:

• B: Would require v/u = 3.0 (e.g., u=20 cm), but diagram shows object beyond 2f, not at 2f.
• C: Implies v/u=4.0, inconsistent with converging lens forming real image between f and 2f for u>2f.
• D: Suggests v/u=6.0, only possible for virtual image with u<f, but diagram indicates real image.

Final answer: A