Magnification = image size / actual size
The 0654 formula is , where is image size and is actual size. Rearranged: and -- decide which one you need before substituting. Magnification compares two lengths measured in the same unit, so the units cancel and it carries no unit: write it with a multiplication sign, e.g. x400, never "400 mm". A diagram is normally drawn larger than the specimen, so a correct magnification is usually greater than 1.
Image size vs actual size
Image size is the length you measure on the diagram, photograph or drawing -- use a ruler and work in millimetres (mm). Actual size is the real-life length of the specimen; it is either stated in the question or worked out from a scale bar on the diagram. Core questions keep both lengths in mm; microscopic actual sizes are usually quoted in micrometres (um). Keep the two labels straight, because swapping them inverts the formula.
(Extended) 1 mm = 1000 um
0654 Supplement requires converting between millimetres and micrometres: , so multiply by 1000 going from mm to um and divide by 1000 going the other way (). This matters because is only correct when both lengths are in the same unit, and questions routinely measure the image in mm while quoting the actual size in um. Convert one value first -- the step candidates most often skip.
Drawn from real examiner reports.
Inverting the magnification formula
Image size goes on top: , not actual/image. Dividing the wrong way round is the most repeated error on this topic. Self-check: a diagram is drawn larger than the real specimen, so the answer should come out greater than 1. A small decimal such as 0.0033 means the two numbers need swapping over.
Flagged s22 P51/P52 Q2b ii · w22 P63 Q2b iii
No x100 in the magnification formula
Asked simply to state the formula, candidates often produce a percentage-style version carrying an extra x100 term. There is no x100 anywhere in magnification: x400 means the image is 400 times bigger than the real object, not "400% bigger". Keep the x100 step for percentage-change and percentage-composition questions.
Flagged w22 P11 Q2
Decimal-point slips in a measured length
Reading a ruler or scale, candidates misplace the decimal point and record 2.6 or 260 where 26 mm was meant -- an answer out by a factor of 10 or 100. Sense-check every measurement against the diagram in front of you: a structure spanning most of the page cannot possibly be 2.6 mm long.
Flagged w22 P63 Q2b i
Answers not rounded to 2 significant figures
0654 mark schemes normally expect a calculated magnification or length to an appropriate precision -- usually 2 significant figures unless the question says otherwise. Copying the full calculator display, or over-rounding to 1 significant figure, loses the final mark even when the method and the division were both correct.
Flagged w22 P63 Q2b iii
mm and um are a factor of 1000 apart
Micrometres are a thousand times smaller than millimetres, so 5 um and 5 mm are nothing alike. Substituting a length in mm and a length in um straight into gives an answer 1000 times too big or too small. Check the unit attached to every value before you compare, convert or divide.
Units put on the wrong answer
Magnification is a ratio, so it never takes a unit -- write x300, not "300 mm". A calculated actual size or image size is a length and always needs its unit (mm or um) stated. Dropping the unit from a length, or attaching one to a magnification, is a routine and completely avoidable loss of marks.
Four steps, every time
Match the command word
"State the formula" wants the equation only -- no numbers and no x100 term. "Calculate the magnification" wants the substitution shown and a value with x in front. "Calculate the actual size" wants a length with its unit, not a magnification.
Rule one line to measure the image
Draw a single clear straight line across the full length of the structure being measured, then measure that line with a ruler in millimetres. Omitting the line, or sketching several feathery ones, loses the measurement mark even when the final number is right.
Reading a scale bar
If no actual size is given, use the scale bar: measure the bar itself on the page (its image size) and take its label, e.g. 10 um, as its actual size. That gives the magnification of the whole diagram, which then converts any other structure you measure into its real length.
Cambridge 0654 spec reference: Section B2 "Cells", sub-topic B2.2 (Core + Supplement/Extended). This leaf covers stating and using the magnification formula, calculating magnification and specimen size using millimetres (mm), and (Extended) converting measurements between millimetres and micrometres (um). Magnification () is the number of times an image is bigger than the real object.
Out of scope for B2.2 (do not use): eyepiece-graticule/stage-micrometer calibration procedure, resolution vs magnification, electron- vs light-microscope theory, nanometre-scale organelle sizes.
| Term | Mark-scheme-precise definition |
|---|---|
| Magnification () | How many times bigger an image is than the actual (real) object: . A ratio -- it has no unit |
| Image size () | The length measured on the diagram/photograph/drawing (with a ruler, usually in mm) |
| Actual size () | The true, real-life length of the specimen (often given, or found from a scale bar) |
| mm (millimetre) | The unit used to measure image size, and to state actual size for Core-level questions |
| um (micrometre) | mm; the unit typically needed for the actual size of microscopic structures (Extended) |
Unit conversions: ; to convert mm to um, multiply by 1000; to convert um to mm, divide by 1000.
How many micrometres (um) are there in 1 millimetre (mm)?
(a) State the formula that links magnification, image size and actual size. (1 mark)
(b) Explain why magnification has no unit. (1 mark)
(c) State the unit that image size is normally measured in. (1 mark)
