The big idea: Cells are tiny, so a microscope draws them bigger than life. Magnification is simply how many times bigger the image is than the real object.
It is a ratio of two lengths — image size compared with actual size — so it has no units. We write it with a , e.g. .
The one formula that runs this whole micro is:
$$M = \dfrac{\text{image size}}{\text{actual size}}$$
(both lengths measured in the same unit). Rearrange it and you can also find the real size of a cell, which is what most exam questions actually want.
- Magnification ()
- How many times larger the image is than the real object: . A ratio — no units.
- Image size
- The size you measure with a ruler on the printed micrograph or photo (often in mm).
- Actual (real) size
- The true size of the structure in real life (for cells, usually in µm).
- Scale bar
- A short line drawn on a micrograph whose label states the real distance it represents (e.g. '10 µm'). It lets you find magnification or measure real sizes without being told the magnification.
- Micrometre (µm)
- One thousandth of a millimetre: 1 mm = 1000 µm. The standard unit for cell sizes.
- Eyepiece graticule
- A tiny ruler in the microscope eyepiece, calibrated against a stage micrometer, used to measure structures while you look down the microscope.
Get the units the SAME first: Image size is usually in millimetres (you measured it with a ruler) but real cell sizes are in micrometres. Mixing them is the number-one way students get a magnification 1000× too big or too small.
Always convert to one unit before you divide:
, so to go mm → µm multiply by 1000, and to go µm → mm divide by 1000.
| Convert | Multiply by | Example |
|---|---|---|
| mm → µm | × 1000 | 0.5 mm = 500 µm |
| µm → mm | ÷ 1000 | 2500 µm = 2.5 mm |
| cm → µm | × 10 000 | 1 cm = 10 000 µm |
| m → µm | × 1 000 000 | 1 m = 1 000 000 µm |
Which way round?: Magnification is always image ÷ actual — the bigger number (the image) on top. If your answer comes out less than 1, you divided the wrong way round.
To get a real size, you instead divide the image size by the magnification (make it smaller again).
Every 5.1.3 question is one of three jobs, and they all come from the same triangle. Pick the row you need, convert units, then divide or multiply.
| What you want | Formula | In words |
|---|---|---|
| Magnification () | How many times bigger the image is than the real thing (no units — it's a ratio) | |
| Actual (real) size | Measure it on the image, then divide by the magnification | |
| Image size | The real size scaled up by the magnification |
Worked example 1 — magnification from a scale bar: A micrograph of an onion epidermal cell carries a scale bar that the label says represents 80 µm. You measure that bar with a ruler and it is 40 mm long on the page.
Step 1 — same units. Convert the image measurement to µm:
.
Step 2 — apply the formula.
.
Answer: magnification = $\times 500$ (a ratio, so no units).
Magnification from a scale bar: measure the bar on the image (40 mm = 40 000 µm), read what it represents (80 µm), then divide — magnification = ×500.
Interactive diagram
Explore the labelled diagram, charts and maps for this topic in full study mode.
Worked example 2 — real size from the magnification: On that same image, the whole cell measures 60 mm end to end with a ruler. How wide is the cell in real life?
Step 1 — same units. .
Step 2 — rearrange the formula (you want the actual size):
.
Answer: the real cell is 120 µm wide. (Sense-check: a plant cell ~100 µm is sensible — if you'd got 60 000 µm = 6 cm you'd know you forgot to divide by the magnification.)
Once you know the magnification (×500 here), the SAME formula gives a real size: actual = image ÷ magnification.
Interactive diagram
Explore the labelled diagram, charts and maps for this topic in full study mode.
The reliable 4-step routine
- Decide which size you want — magnification, or a real (actual) size — and pick the matching formula.
- Convert everything to ONE unit (µm is safest for cells): mm → µm by ×1000.
- Substitute and calculate — magnification = image ÷ actual; real size = image ÷ magnification.
- Check it makes sense + add the right unit — magnification has a and no unit; a real cell size is in µm.
When there's no scale bar: divisions & graticules: Sometimes you're given a scale instead — e.g. each small square (division) on the image represents 2.5 µm. Then a cell spanning 20 divisions is:
in real life.
To measure a real structure while you look down the microscope you use an eyepiece graticule (a scale in the eyepiece), first calibrated against a stage micrometer. If a question asks what equipment measures a cell's length accurately, the answer is the eyepiece graticule — not a plain ruler.
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How this is tested: On Paper 1B this is a 1-mark Calculate: most often 'calculate the magnification using the scale bar' or 'calculate the actual length of the cell/organelle'. The specimen Paper has a 2-mark Calculate that says 'show your working' — so always write the formula, the substitution and the answer with its unit.
Two marks are nearly always: (1) correct method/conversion, (2) correct value with the right unit (or for magnification). Forgetting the mm→µm conversion is the classic dropped mark.
IB-style question — magnification and real size from a micrograph
A light micrograph of a single human cheek (epithelial) cell carries a scale bar labelled 25 µm. On the printed image the scale bar measures 20 mm long, and the cell itself measures 56 mm across at its widest point.
(a) Calculate the magnification of the micrograph. Show your working. [2]
(b) Using your answer to (a), calculate the actual width of the cheek cell in micrometres. [2]
Worked solution
- (a) Same units first. The scale bar is on the image and represents in real life. Convert the image length: .
- (a) Apply the magnification formula. . Magnification = $\times 800$. (Mark 1: correct conversion + image ÷ actual. Mark 2: .)
- (b) Same units first. The cell measures on the image .
- (b) Rearrange for the real size. . The cheek cell is 70 µm wide. (Mark 1: image size ÷ magnification with units matched. Mark 2: with the unit.)
- Sense-check. A human cheek cell is typically ~50–70 µm across, so 70 µm is sensible. If you'd got 56 000 µm (5.6 cm) you'd know you forgot to divide by the magnification.
Final answer
(a) Scale bar 20 mm = 20 000 µm; M = 20 000 ÷ 25 = ×800. (b) Cell 56 mm = 56 000 µm; actual = 56 000 ÷ 800 = 70 µm.
✓ Why this scores full marks: It converts mm to µm before dividing, shows the formula and the substitution, gives magnification as a $\times$ with no unit, and gives the real size with µm. The sense-check guards against the wrong-way-round error.
The usual lost mark is skipping the unit conversion — dividing 20 mm by 25 µm directly gives 0.8, which is nonsense for a magnification.