Magnification, size and scale
Magnification is how many times larger an image is than the real thing. It has no units — it is one length divided by another — and it is written with a multiplication sign in front of it, as in ×400.
Total magnification
A light microscope magnifies twice, once at each lens, so the two magnifications multiply.
total magnification = eyepiece magnification × objective magnification
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Eyepiece magnification — printed on the eyepiece, almost always ×10.
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Objective magnification — printed on the side of each objective lens, commonly ×4, ×10 and ×40.
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A ×10 eyepiece with the ×4 objective gives ×40.
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The same eyepiece with the ×40 objective gives ×400.
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Read the objective, do not assume it. Turning the nosepiece changes the total magnification, and a drawing labelled with the wrong one is wrong.
Working out the real size of a cell
You can get a real size from the field of view — the diameter of the circle you can see down the eyepiece.
- Measure the field of view on the lowest power by laying a clear ruler on the stage and reading the diameter in millimetres.
- Count how many cells fit end to end across that diameter.
- Divide: the diameter divided by the number of cells is the length of one cell.
- Convert if the answer is small. 1 mm = 1000 μm, and a plant cell is usually easier to talk about in micrometres (μm).
Field of view changes with magnification. Going from ×40 to ×400 is ten times the magnification, so the field of view is a tenth of the width. If it was 4.5 mm across at ×40, it is 0.45 mm across at ×400.
The magnification of your drawing
The magnification you write on a drawing is the magnification you viewed it at, so a specimen drawn under the ×40 objective with a ×10 eyepiece is labelled ×400.
If you are asked for the magnification of the drawing itself, that is a different calculation:
magnification of drawing = size of drawing ÷ actual size
- Both lengths must be in the same unit before you divide, or the answer is out by a factor of a thousand.
- The answer has no unit, because the units cancel.
Worked ExampleFinding the real size of a cell, and the magnification of a drawing
A student views onion epidermis with a ×10 eyepiece and the ×4 objective. Laying a ruler on the stage, the field of view measures 4.5 mm across. Six cells fit end to end across the diameter. The student's drawing of one cell is 60 mm long.
Find (a) the total magnification used, (b) the real length of one cell in μm, and (c) the magnification of the drawing.
Step 1 — (a) Total magnification
The two lenses multiply, so multiply the eyepiece by the objective.
total magnification = 10 × 4 = ×40
Step 2 — (b) Real length of one cell
Six cells span the whole field of view, so one cell is a sixth of the field's diameter. Divide the diameter by the number of cells.
length of one cell = 4.5 ÷ 6 = 0.75 mm
Now convert to micrometres, since 1 mm = 1000 μm.
0.75 × 1000 = 750 μm
Step 3 — (c) Magnification of the drawing
Magnification of a drawing is the drawing's size divided by the real size — but only once both are in the same unit. The drawing is 60 mm and the cell is 0.75 mm, so millimetres will do for both.
magnification = 60 ÷ 0.75 = 80
There is no unit, because millimetres divided by millimetres cancel.
Step 4 — Check the answer is sensible
The drawing is much bigger than the cell but much smaller than the ×400 view, so a value of ×80 sits where it should. An answer of ×0.08 or ×80 000 would mean the units were mixed up.