Calculate magnification from image and actual size
Use a ratio with both lengths in millimetres.
Section B2.2 · Size of specimens
Mapped to the named 0654 section using teaching from the corresponding single-science course. A 0654-specific review of every Core and Supplement objective is still in progress. Written practice is self-checked; it does not demonstrate supervised laboratory competence or award an official Cambridge grade.
Before you begin
- Recall the distinction between plant, animal and bacterial cells. Read the supplied evidence before drawing a conclusion.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
Which quantity is measured on the drawing?
What you will learn
- State the magnification formula.
- Calculate a dimensionless ratio from matching lengths.
Compare the same dimension
Magnification = image size ÷ actual size. Image size is the measured length in the drawing or displayed image; actual size is the corresponding length in the specimen. Measure the same dimension in both: do not divide image length by actual width.
When both lengths are in millimetres, the units cancel and magnification has no length unit. An image length of 36 mm and actual length 0.09 mm give 36 ÷ 0.09 = 400, written ×400. It is not 400 mm.
Check the direction of the ratio
An enlarged image has a greater length than the actual specimen, so its magnification exceeds one. Reversing the division would give 0.0025 in the example, which is inconsistent with enlargement. An image can also be reduced, with magnification below one; the formula still applies.
The lengths supplied in this lesson are fixed numerical data. A responsive drawing on a phone is not physically 36 mm long unless calibrated. Use the stated measurements, not an uncalibrated screen ruler or the SVG pixel width.
Sources for this lesson
Pause and explain
A 36 mm image represents 0.09 mm actual length. Which result is valid?
Worked example
An image is 36 mm long and the corresponding specimen is 0.09 mm long. Calculate magnification.
Show the worked solution
- Both lengths are in mm.
- Use 36 ÷ 0.09.
- Units cancel.
Answer ×400.
Try a topic test
Choose Easy, Normal or Difficult. Save your answers and open worked review after finishing.
Test this topic →From guided practice to a new situation
Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
An image is 24 mm long; actual length is 0.06 mm. Find magnification.
Give me a hint
Divide the larger image length by actual length.
Compare my reasoning
- 24 ÷ 0.06 = 400.
- Cancel mm units.
×400.
Look for these in your work
- Correct division.
- No length unit.
An image is 54 mm wide; actual width is 0.18 mm. Find magnification.
Give me a hint
Use corresponding widths.
Compare my reasoning
- 54 ÷ 0.18 = 300.
- State the ratio.
×300.
Look for these in your work
- Matching widths.
- No mm on the answer.
A student divides an image length of 20 mm by actual width 0.04 mm and gets 500. Why is the calculation not justified even though arithmetic is correct?
Give me a hint
Matching units are necessary but not sufficient.
Compare my reasoning
- Length and width are different dimensions.
- Need actual length corresponding to the image length.
It compares non-corresponding dimensions; obtain actual length first.
Look for these in your work
- Identify mismatch.
- Specify the missing measurement.
Common mistakes
- Divide image size by actual size, not the reverse.
- Magnification has no mm unit.
What can you explain now?
What is the formula for magnification?
Compare with the explanation
Image size divided by actual size.
Use matching dimensions and matching units.
After trying it yourself, choose your next review. This is your self-assessment.
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Make it stick
Write the ratio, explain the unit cancellation and check its direction.
If you needed the solution, close it and solve the problem again from a blank page. A correct answer is stronger when you can explain the reason for each step.