Magnification Formula with Unit Conversion

Steps:

• Magnification = image size / actual size, both in same units (μm).
• Actual size u = 5 μm.
• Convert image size to μm: r (mm) × 1000 = μm, since 1 mm = 1000 μm; s = 1000 provides this factor.
• Compute: (r × s) / u gives magnification as a ratio.

Why D is correct:

• D (r × s / u) converts r from mm to μm using s=1000, then divides by actual size u=5 μm, matching the standard magnification formula.

Why the others are wrong:

• A: q/u divides cm by μm without conversion, yielding incorrect units and value.
• B: q × s / u multiplies cm by 1000 (wrong factor; needs 10,000 for μm), underestimating by 10x.
• C: (u × q)/s multiplies actual size by image (cm) and divides by 1000, inverting the formula and mismatching units.

Final answer: D