State and use the formula: magnification = image size ÷ actual size.

2.2 Size of Specimens

Learning objectives (Cambridge AO1‑AO3)

• AO1 – Knowledge: State the formula for magnification and explain that it is a dimension‑less ratio.
• AO2 – Application: Use the formula to calculate magnification, including the required conversion between millimetres (mm) and micrometres (µm).
• AO3 – Practical skills: Measure image size, convert units correctly, and record results in a clear, organised table (practical checklist below).

What is magnification?

• Magnification tells how many times larger (or smaller) an object appears on a microscope, camera screen, drawing or reticle compared with its real size.
• It is a dimension‑less ratio – the units cancel because the same unit is used for image and actual size. Never write “15 mm ×”; write simply “15×”.
• Values:
  • > 1 – enlargement (e.g. microscope image)
  • < 1 – reduction (e.g. a camera lens that makes the object appear smaller)

Key terms

Formula

Magnification = image size ÷ actual size

Unit‑conversion reminder (Supplementary material)

1 mm = 1000 µm. To convert:

• mm → µm: multiply by 1000 (e.g. 0.004 mm × 1000 = 4 µm)
• µm → mm: divide by 1000 (e.g. 250 µm ÷ 1000 = 0.25 mm)

Practical checklist (AO3)

1. Set up the microscope or camera and place the specimen on the slide.
2. Use an eyepiece reticle, scale bar on the screen, or a ruler to measure the image size. Record the value and the unit.
3. Obtain the actual size of the specimen (from a calibrated slide, literature value or direct measurement). Record the value and the unit.
4. Convert both measurements to the same unit (mm or µm) using the conversion reminder above.
5. Insert the values into the formula and calculate magnification.
6. Write the result as a pure ratio (e.g. 15×) and note whether it is an enlargement (>1) or reduction (<1).
7. Check the calculation by reversing the formula: actual size = image size ÷ magnification. The two values should agree with the measurements taken.

Worked example – enlargement

A leaf vein appears 12 mm long on a camera screen. The true length measured with a micrometer is 0.8 mm.

Worked example – reduction

A digital‑camera lens makes a 10 mm long object appear only 4 mm on the screen.

Magnification = 4 mm ÷ 10 mm = 0.4× (the image is 40 % of the real size).

Worked example – total magnification of a compound microscope

Objective power = 40×, eyepiece power = 10×.

Total magnification = 40 × 10 = 400×.

If a bacterial cell is 2 µm long, the image size on the eyepiece scale will be:

Image size = 400 × 2 µm = 800 µm = 0.8 mm.

Practice questions

1. A pollen grain measures 5 mm on the screen. Its true diameter is 0.25 mm. What is the magnification?
2. A diagram shows a plant cell that is 8 mm long on the drawing. The actual cell length is 0.4 mm. Determine the magnification used for the drawing.
3. If a microscope has a total magnification of 40× and the actual size of a bacterial cell is 2 µm, what will be the image size on the eyepiece scale?
4. A camera lens reduces the size of an object: a 12 mm long insect wing appears 7 mm on the screen. What is the magnification?

Answers to practice questions

1. Magnification = 5 ÷ 0.25 = 20×
2. Magnification = 8 ÷ 0.4 = 20×
3. Image size = 40 × 2 µm = 80 µm = 0.08 mm
4. Magnification = 7 ÷ 12 ≈ 0.58× (≈ 0.6× reduction)

Common mistakes to avoid

• Mixing units – always convert image and actual sizes to the same unit before dividing.
• Treating magnification as a unit – it is a pure ratio; write “15×”, not “15 mm ×”.
• Incorrect rearrangement – remember actual size = image size ÷ magnification, not the reverse.
• Ignoring reduced magnification – values < 1 are valid and indicate a smaller image.

Summary

• Magnification = image size ÷ actual size (dimensionless).
• Convert mm ↔ µm using 1 mm = 1000 µm before applying the formula.
• Use the practical checklist to obtain reliable measurements and to meet AO3 requirements.
• Magnification can be > 1 (enlargement) or < 1 (reduction); total microscope magnification is the product of objective and eyepiece powers.

Link to other syllabus topics (correct codes)

Understanding magnification underpins:

• 2.1 Cell structure – measuring organelles such as nuclei, chloroplasts and mitochondria.
• 3.1 Microscopy – selecting appropriate objectives, eyepieces and camera settings.
• 4.2 Transport in plants – comparing the size of xylem vessels with animal capillaries.