Calculating Magnification
Magnification is calculated as image size divided by actual size. Both measurements must be in the same unit before dividing, and the answer has no unit since it is a ratio.
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The magnification formula
Magnification describes how many times larger an image appears compared with the real, actual size of the object. The formula is: magnification = image size ÷ actual size.
Rearranged, this also gives actual size = image size ÷ magnification, and image size = actual size × magnification. Magnification has no unit because it is a ratio between two lengths.
Unit conversion before calculating
- 1 centimetre (cm) = 10 millimetres (mm)
- 1 millimetre (mm) = 1000 micrometres (μm)
- 1 centimetre (cm) = 10,000 micrometres (μm)
- Always convert the image size and actual size into the same unit before dividing.
Worked example
A diagram of a cell has an image size (length) of 40 mm. The actual size of the cell is 200 μm. Find the magnification of the diagram.
Step 1: Convert both measurements to the same unit. Convert 40 mm to μm: 40 mm × 1000 = 40,000 μm.
Step 2: Apply the formula. Magnification = image size ÷ actual size = 40,000 μm ÷ 200 μm = 200.
The diagram is magnified 200 times, written as x200.
How it is examined
Paper 3 and structured questions often give a scale bar, a stated magnification, or a measured length on a diagram and ask you to calculate the actual size of a structure, or to calculate the magnification when both sizes are given. You may also be asked to measure a length on a printed diagram using a ruler before substituting it into the formula.
Common mistakes
Rearranging the formula to find actual size
The same formula answers three kinds of question, depending on which two values are given. To find the actual size of a structure, rearrange it to actual size = image size ÷ magnification; to find how large a drawing should be, use image size = actual size × magnification.
Worked example: an electron micrograph is labelled ×5000, and a mitochondrion on it measures 15 mm across. Actual size = image size ÷ magnification = 15 mm ÷ 5000 = 0.003 mm. Converting to micrometres, 0.003 mm × 1000 = 3 μm, a realistic width for a mitochondrion.
Reading and using a scale bar
Micrographs often carry a scale bar instead of a stated magnification. A scale bar is a short line labelled with the real length it represents, such as 10 μm.
To find the magnification of the whole image, measure the printed length of the scale bar with a ruler, convert both lengths to the same unit, then divide the measured length by the length the bar represents.
Worked example: a scale bar is printed 20 mm long and labelled 10 μm. Convert 20 mm to micrometres: 20 × 1000 = 20,000 μm.
Magnification = measured length ÷ actual length = 20,000 μm ÷ 10 μm = ×2000. Once the magnification is known, the actual size of any structure in the same image can be found by measuring it and dividing by 2000.
Reference calculations
| Given | Formula to use | Worked substitution | Answer |
|---|---|---|---|
| Image 40 mm, actual 200 μm | magnification = image ÷ actual | 40,000 μm ÷ 200 μm | ×200 |
| Magnification ×5000, image 15 mm | actual = image ÷ magnification | 15 mm ÷ 5000 | 0.003 mm (3 μm) |
| Actual 50 μm, magnification ×100 | image = actual × magnification | 50 μm × 100 | 5000 μm (5 mm) |
| Scale bar 20 mm = 10 μm | magnification = bar ÷ value | 20,000 μm ÷ 10 μm | ×2000 |
Paper 3-style questions
Question 1 (measuring and using numbers). A photomicrograph of a cheek cell is printed with a scale bar 25 mm long, labelled 50 μm. The cell measures 60 mm across on the print.
(a) Calculate the magnification of the photomicrograph. (b) Calculate the actual width of the cheek cell in micrometres.
Model answer. (a) Convert the bar length: 25 mm = 25,000 μm; magnification = measured length ÷ actual length = 25,000 μm ÷ 50 μm = ×500. (b) Actual width = image size ÷ magnification = 60 mm ÷ 500 = 0.12 mm = 120 μm after converting mm to μm.
Question 2 (interpreting data). A student measures the same specimen twice and calculates magnifications of ×198 and ×202. Suggest why the two values differ, and state how to obtain a more reliable value.
Model answer. The difference comes from small errors in measuring the image length with the ruler, such as parallax or reading only to the nearest millimetre. Taking repeated measurements and finding the mean, and measuring along the longest clear axis, gives a more reliable magnification.
Question 3 (defining operationally). Explain, in terms of the formula, why magnification has no unit while actual size does.
Model answer. Magnification = image size ÷ actual size; both are lengths measured in the same unit, so the units cancel and the answer is a pure ratio with no unit. Actual size is a single measured length, so it keeps its unit, such as μm or mm.
Source:SRC-DSKP-EN
Frequently asked questions
What is the formula for magnification?
Why does magnification have no unit?
How do you convert millimetres to micrometres?
How do you use a scale bar to find actual size?
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