Magnifying Instruments and Biological Drawings
Senior 1 · Biology
Magnifying Instruments and Biological Drawings
Lesson 3 of 4
25 min
In a textbook, a drawing of a human cheek cell is 4 cm across: about the size of a large coin. Yet about 17 real cheek cells would fit side by side across a single millimetre. A drawing, a photograph or a microscope image is useless for measuring unless you know how much it has been magnified. This lesson shows how to calculate magnification, and how to work back from an image to the real size.
Definition
Magnification: the number of times larger an image is than the actual object. It has no unit; write it as, for example, ×400.
Image size: the size of the drawing, photograph or view, measured with a ruler. Actual size: the real size of the object.
Micrometre (symbol µm): one thousandth of a millimetre, the usual unit for cells.
Total magnification of a light microscope: the magnification of the eyepiece multiplied by the magnification of the objective in use.
Rearranged, the same relationship gives the other two quantities:
For a microscope:
And the units you need:
Figure 1: The magnification triangle and the unit ladder. Always convert both sizes to the same unit before dividing.
| Eyepiece | Objective | Total magnification |
|---|---|---|
| ×10 | ×4 (low power) | ×40 |
| ×10 | ×10 (medium power) | ×100 |
| ×10 | ×40 (high power) | ×400 |
| ×10 | ×100 (oil immersion) | ×1000 |
Worked example 1: magnification of a drawing
A bean seed is 15 mm long. Keza's drawing of it is 60 mm long. What is the magnification of her drawing?
Answer: ×4. She writes "×4" under the title of the drawing.
Worked example 2: actual size from a photograph
A photograph of Elodea leaf cells was taken at ×400. On the photograph, one cell is 36 mm long. What is its actual length in micrometres?
Convert to micrometres (multiply by 1000):
Answer: the cell is 90 µm long.
Worked example 3: when the units are different
A cheek cell is 60 µm across. In a drawing it is 24 mm across. Find the magnification.
Answer: ×400. Dividing 24 by 60 without converting would give 0.4, which is obviously wrong: a drawing of a cell cannot be smaller than the cell.
Worked example 4: using a scale bar
Many micrographs carry a scale bar instead of a magnification. A scale bar labelled 50 µm measures 20 mm on the page. What is the magnification of the photograph?
Answer: ×400. The scale bar works as a built-in ruler: it is an image of a known actual length.
Warning
Common mistakes. (1) Dividing sizes in different units: always convert first. (2) Writing magnification with a unit, such as "×400 mm": magnification has no unit. (3) Measuring the image carelessly: measure in millimetres with a ruler, from edge to edge of the structure itself. (4) Putting the numbers the wrong way up: the image size goes on top. A magnification smaller than 1 for a cell is a warning sign.
Size is evidence. A laboratory technician identifying a parasite in a blood smear compares its size with the red blood cells around it, about 7–8 µm across; researchers checking a mosquito larva or a grain of pollen do the same. Whenever a scientific photograph is published, it carries either a magnification or a scale bar, so that anyone can work out the real size with the formulas in this lesson.
How to calculate magnification (Science Sauce). Follow the I-A-M triangle and watch how the units are converted before dividing.
Tip
Memory hook: "I Am Magnificent": I on top, Actual size and Magnification underneath. And "mm to µm, times a thousand."
Practice: magnification
Key points
Sources and credits
Figure 1, the table, the worked examples and the practice questions are written by Ganzaa.
