Making something bigger is easy: a photocopier can enlarge a blurred photo as much as you like, but it stays blurred. What decides how much detail you can see is not magnification but resolution. Cell biology only took off once microscopes with better resolution arrived, because organelles such as ribosomes are far too small to resolve with light.
Explained simply
Magnification means how many times larger the image is than the real object. Resolution (resolving power) means the smallest distance between two points that can still be seen as two separate points. If two points are closer than the resolution, they blur into one, however much you magnify.
Resolution is limited by the wavelength of the radiation used. Visible light has wavelengths of about 400–700 nm, and a light microscope cannot resolve points closer than about half the wavelength, roughly 200 nm (0.2 µm). Electrons behave like waves with a wavelength thousands of times shorter, so an electron microscope can resolve about 0.5 nm. That is why it can show the internal structure of mitochondria, ribosomes and membranes.
Light microscope
Transmission electron microscope (TEM)
Scanning electron microscope (SEM)
Radiation
light
electrons pass through the specimen
electrons bounce off the surface
Resolution
about 200 nm
about 0.5 nm
about 3–10 nm
Useful magnification
up to about ×1500
up to about ×500 000
up to about ×100 000
Image
colour, living or dead specimens
2D slice showing internal detail
3D-looking surface view
Specimen
can be alive
dead, in a vacuum, very thin sections
dead, in a vacuum, coated in metal
Electron images are black and white; colours you see in textbooks are added afterwards ("false colour").
Logarithmic size scale from 0.1 nm to 1 mm: a ribosome (25 nm) and a virus (100 nm) are below the 200 nm resolution of the light microscope, a bacterium (2 µm) and an animal cell (20 µm) are above it, and the electron microscope resolves down to about 0.5 nm
Units. Cells are measured in micrometres and organelles often in nanometres:
1mm=1000μm1μm=1000nm
The magnification equation. If I is the size of the image, A the actual size of the object and M the magnification:
M=AIA=MII=A×M
M has no units because it is a ratio, so I and Amust be in the same unit before you divide. Measure the image with a ruler in mm, then convert to µm by multiplying by 1000.
Worked example
Question 1: An electron micrograph of a mitochondrion has magnification ×12 000. The image of the mitochondrion is 36 mm long. Calculate its actual length in µm. [2 marks]
Step 1 — convert the image length to µm.36mm×1000=36000μm
Step 2 — rearrange and substitute.A=MI=1200036000μm=3μm
Answer: 3 µm. A sensible size: mitochondria are usually 1–5 µm long.
Question 2: A micrograph has a scale bar 20 mm long labelled 5 µm. A cell in the same image is 60 mm across. Find (a) the magnification and (b) the actual width of the cell. [3 marks]
Step 1 — use the scale bar to find M. The bar's image is 20 mm = 20 000 µm and its actual size is 5 µm, so
M=AI=5μm20000μm=×4000
Step 2 — find the cell's actual size.60mm=60000μm, so
A=400060000μm=15μm
Answer: (a) ×4000; (b) 15 µm.
Common mistakes
Mixing units. Dividing a length in mm by a length in µm gives a magnification 1000 times wrong. Convert first.
Saying a higher magnification shows more detail. Detail depends on resolution; extra magnification beyond the resolution only gives a bigger blur ("empty magnification").
Giving magnification units. Write ×4000, not 4000 µm.
Measuring the scale bar label instead of the bar. Measure the bar's length with a ruler; the label tells you its actual size.
Thinking electron microscopes can look at living cells. The specimen is in a vacuum, so it must be dead.
Where you see this in real life
Hospital pathology labs use light microscopes to look at stained tissue biopsies within minutes, because colour stains and speed matter more than nanometre detail. When the SARS-CoV-2 virus was first identified in 2020, researchers used electron microscopes to see its crown of spike proteins, a structure about 100 nm across that no light microscope could resolve.