Magnification — image size over actual size
Magnification () tells you how many times larger an image is than the real specimen. It is a ratio of two lengths, so it carries no unit — write it as then a number, e.g. . One formula, three forms: ; ; . Picture a triangle with image size on top and beside actual size below — cover the quantity you want and read off what is left.
Image size — measure in mm, then match units
To find from a diagram or micrograph you first measure the image with a ruler, normally in millimetres, across the specimen or along the labelled line. Then read the actual size out of the question and put both lengths in the same unit before dividing. Because has no unit, the units have to cancel — and they only cancel if they match. For an actual size, divide the measured image size by the stated magnification and give the answer in mm or um.
(Extended) Micrometres — 1 mm = 1000 um
Cells are measured in micrometres (um), millionths of a metre; images and whole specimens are measured in millimetres (mm). The Extended conversion is : going mm to um multiply by 1000, going um to mm divide by 1000 — um is the smaller unit, so a length contains more of them. Check it works: an image across of a cell wide gives , not .
Drawn from real examiner reports.
Dividing mm by um without converting
Magnification has no unit, so image and actual sizes must share a unit before you divide. If they do not, the powers of ten never cancel and the answer is out by a factor of . Wrong: image , actual , "". Right: convert first, , so .
Flagged s23 P1/P2 Q4 — a comparison "proved to be demanding for most candidates": 2.5 mm had to become 2500 um before dividing
Actual size — divide, never multiply
Given the image size and the magnification, the actual size is . Many candidates multiply instead. Wrong: image at , "actual " — a cell 27 metres across. Right: . Sanity check: for the real specimen is always smaller than its image.
Flagged s23 P1/P2 Q5 — "many candidates were unable to calculate the actual size of the cell"; they needed to divide the image size by the magnification
Inverting the formula — M over image
The other rearrangement slip is writing , or dividing the magnification by the actual length, instead of . Examiner reports list the inverted formula among the standard magnification errors. Guard by writing out in full first and rearranging on paper, rather than guessing which number belongs on top.
Digest: magnification calculation — dividing magnification by actual length (inverted formula) · s23 P11/22/31 · w22 P12 Q6; P52 Q2a ii
Magnification never carries a unit
A magnification is a ratio of two lengths, so the units cancel and none survives. Write a multiplication sign and a number — — never "" or "". Quote it as a whole number as well: , not . Hanging a unit on is a presentation error that throws away a mark the working had already earned.
Flagged s23 general comments — candidates showed "some uncertainty about how to apply the magnification formula"; magnification recurs across variants
A real size always needs a unit
The mirror image of the last error. An actual size or an image size is a length, so it must carry mm or um — a bare number can lose the mark. Watch which unit the question demands: if it says "give your answer in micrometres", then is not an answer and is. Convert at the end if you did the arithmetic in mm.
Comparisons need matched units too
The unit trap is not confined to magnification. "How many times larger is cell X than cell Y" is the same ratio, so both diameters must be in one unit first: becomes , then times. If a length arrives in centimetres, convert to mm first (). Write the units next to the numbers — if they differ, stop and convert.
Digest: must convert units (mm to um x1000; cm to mm x10) · s23 P11/22/31 · w22 P12 Q6
Run FIND, CONVERT, DIVIDE, STATE
FIND the unknown, pick the rearrangement — , or . CONVERT so both lengths share a unit. DIVIDE (or multiply), showing the working. STATE the answer with its unit — or none, if it is a magnification.
Two sanity checks before you commit
An actual size must come out smaller than the image size whenever ; if yours is bigger, you multiplied where you should have divided. And a magnification below for a magnified image is impossible — it nearly always means a missed mm to um conversion.
Show the substitution, bank the method
Write the formula, substitute the numbers with their units, then compute — . That substitution line is what holds the method mark if the arithmetic slips, and lining the units up beside each other is what makes a mismatch visible before you divide.
Show the conversion as its own step
When a question mixes mm and um, put the conversion on a line of its own before the formula — "". It is often credited separately on a multi-mark item, and doing it first stops you carrying the mismatch into the division.
Magnification (): how many times larger an image (a drawing, photograph or micrograph) is than the real specimen. It is a ratio of two lengths, so it has no unit and is written as a number with a multiplication sign, e.g. .
Image size: the size of the specimen as it appears on the drawing or photograph (measure it with a ruler, normally in mm).
Actual size: the real (true) size of the specimen.
The formula and its rearrangements:
Units (Core): magnification calculations at Core are usually done in millimetres (mm). Image size and actual size must be in the same unit before dividing.
(Extended) micrometre (um): the unit for cell-sized objects; . Convert so both measurements share a unit before you calculate.
Define magnification, and state its unit.
(a) State the formula that links magnification, image size and actual size.
(b) State the unit of magnification.
(c) State how you would rearrange the formula to calculate the actual size of a specimen.
