Biology › Cells, microscopy and biological organisation › Microscopy: magnification, resolution and what you can trust
Microscopy: magnification, resolution and what you can trust
Magnification makes an image bigger. Resolution decides whether making it bigger tells you anything new. The two are separate quantities set by separate things, and the wavelength of whatever you are looking with sets the second one — which is the whole reason electron microscopes exist.
Before this Cell ultrastructure and the organelles · Standard form and SI prefixes
Before you start
A microscope that magnifies more shows you more. That is how the word is used in a shop, and in biology it is wrong in a way that costs marks. Take a photograph through a light microscope and enlarge it until a mitochondrion is the size of your hand, and the mitochondrion will be a grey smudge the size of your hand. Nothing new appears, because the light that formed the image could never separate two points closer than about 0.2 µm in the first place. Magnification is how much bigger. Resolution is how much detail is there to make bigger.
What you should be able to do
- Define magnification and resolution and explain why they are not the same thing.
- Explain why an electron microscope resolves finer detail than a light microscope.
- Compare a light microscope, a TEM and an SEM by beam, resolution, specimen and the kind of image each produces.
- Rearrange and use magnification = image size ÷ actual size, converting units correctly.
- Describe how an eyepiece graticule is calibrated with a stage micrometer, and explain why artefacts appear in electron micrographs.
Two words that sound alike and are not
Magnification is the number of times larger the image is than the object. It is a ratio, so it has no units, and it can be pushed as high as you like — a projector will happily throw a blurred image onto a wall at ×10 000.
Resolution is the shortest distance between two points that can still be seen as two points rather than one. It is a length, so it does have units, and the smaller the number the better the instrument. That last part catches people out. A resolution of 0.1 nm is far better than a resolution of 200 nm, even though 0.1 is the smaller number.
Magnification beyond what the resolution supports is called empty magnification, and it is exactly as useless as it sounds. Resolution is the ceiling; magnification only decides how close you stand to it.
What sets the ceiling is wavelength. Two points closer together than roughly half a wavelength of whatever is illuminating them cannot be told apart, because the waves spread and overlap. Visible light runs from about 400 to 700 nm, which lands the best light microscope at around 0.2 µm — 200 nm. A beam of electrons behaves as a wave too, and at the accelerating voltages a transmission electron microscope uses, that wavelength comes out at about 0.004 nm: something like a hundred thousand times shorter than visible light, not merely a thousand. Shorter wavelength, finer detail — that is the sentence the mark scheme wants, and it is why a TEM resolves about 0.1 nm where light stops at 200 nm.
Notice that the half-wavelength rule promises far more than 0.1 nm and does not deliver it. A wave 0.004 nm long ought to separate points a few thousandths of a nanometre apart, and no transmission electron microscope of this kind comes close. The wavelength is not the thing holding it back: the lenses are. Electrons are focused by magnetic fields, which are far cruder instruments than a shaped piece of glass, and the aberrations they introduce blur the image long before the wavelength would. The wavelength is why an electron microscope can do this at all; the lenses are why it does not do better still.
- Magnification
- How many times larger the image is than the actual object. A ratio, with no units.
- Resolution
- The minimum distance between two points at which they can still be distinguished as separate. A length, and smaller is better.
- Empty magnification
- Enlarging an image beyond the detail its resolution contains, so nothing further becomes visible.
Three instruments, three compromises
The light microscope is the one on the bench. It uses visible light and glass lenses, magnifies usefully to about ×1500 and resolves to about 0.2 µm. Its real advantage is that nothing has to die: you can watch a live protoctist swimming, in colour, in a drop of pond water. Nothing else here can do that.
The transmission electron microscope fires a beam of electrons through a very thin section of specimen. Electrons that pass straight through land on a screen or detector below; parts of the specimen stained with heavy metals scatter electrons and come out dark. The result is a flat, two-dimensional section at resolutions down to about 0.1 nm and magnifications of half a million times. It is where almost every ultrastructure image you have ever seen came from.
The scanning electron microscope sweeps a beam across the surface of a whole specimen coated in a thin film of metal, and collects the electrons knocked off that surface with detectors placed above it. Because the signal comes from the surface and depends on its shape, the image looks three-dimensional. The price is resolution: an SEM typically manages a few nanometres, worse than a TEM, though still far beyond anything light can do.
| Light | TEM | SEM | |
|---|---|---|---|
| Radiation | Visible light | Beam of electrons | Beam of electrons |
| Focused by | Glass lenses | Electromagnets | Electromagnets |
| Resolution | ≈ 0.2 µm | ≈ 0.1 nm | ≈ 3–10 nm |
| Useful magnification | ×1500 | ×500 000 | ×100 000 |
| Specimen | Whole or sectioned, may be alive | Ultrathin section, dead | Whole, coated in metal, dead |
| Image | Colour, two-dimensional | Two-dimensional section | Three-dimensional surface |
Both electron microscopes have to work in a vacuum, because air molecules deflect electrons and the beam would scatter before it reached anything. A vacuum removes the water from a living cell instantly, so the specimen must be dead, fixed and dehydrated before it goes in. Every electron micrograph you will ever see is of something that was killed to be photographed, and every colour on one was added afterwards.
Doing the sum
One relationship carries this whole topic, and questions on it are worth easy marks provided the units are handled properly.
magnification = image size ÷ actual sizerearranged: actual size = image size ÷ magnification
Some people like the triangle; the algebra is simple enough without it. What actually goes wrong is the units. The image size is something you measured with a ruler, so it is in millimetres. The actual size is a cell or an organelle, so it wants to be in micrometres or nanometres. Convert one to match the other before you divide, never after, and remember that magnification itself has no units at all.
1 mm = 1000 µm 1 µm = 1000 nm 1 mm = 1 000 000 nmlearn these three; almost every mistake in this topic is one of them
From a micrograph to a real length
A mitochondrion on an electron micrograph measures 42 mm from end to end. The micrograph is labelled ×15 000. Calculate the actual length of the mitochondrion in micrometres.
Convert first. 42 mm × 1000 = 42 000 µm, so the image is 42 000 µm long in the units the answer wants.
Now divide: actual = image ÷ magnification = 42 000 ÷ 15 000 = 2.8 µm.
Check it against something you know. Mitochondria run from about 1 to 10 µm, so 2.8 µm is exactly the right size and the answer is believable. An answer of 2800 µm should have stopped you — that is nearly three millimetres, and you could have seen it without a microscope at all.
TRY IT — The same equation the other way up
A chloroplast is 5 µm long. On a printed micrograph it measures 60 mm. Calculate the magnification of the micrograph.
Check your answer
×12 000.
Convert to a common unit first: the image is 60 mm, and 60 × 1000 = 60 000 µm.
Then magnification = image ÷ actual = 60 000 ÷ 5 = 12 000.
Write it as ×12 000 with no units after it. Adding 'µm' to a magnification is a common slip and it will be marked wrong, because a ratio of two lengths cannot have a length as its unit.
Measuring things with the microscope you actually have
A micrograph comes with its magnification printed on it. A microscope on the bench does not, so before you can measure anything you have to work out what the scale in the eyepiece is worth.
There are two scales involved. The eyepiece graticule is a transparent disc with a ruled scale, sitting in the eyepiece. Its divisions are arbitrary — they stay the same apparent size whichever objective lens you use, because they are not part of the image of the specimen. The stage micrometer is a slide with a scale of known length: usually 1 mm ruled into 100 parts, so each division is 10 µm. It goes on the stage, where the objective magnifies it along with everything else.
The procedure is short. Put the stage micrometer on the stage, focus, and turn the eyepiece until the two scales lie parallel. Count how many eyepiece divisions cover a measured number of stage divisions. Divide the known length by the number of eyepiece divisions to get the value of one division. Then take the micrometer away, put your specimen on, and measure it in eyepiece divisions.
The trap is at the end. Change the objective lens and the calibration is void, because the objective magnifies the stage micrometer but not the graticule. Switch from ×10 to ×40 and each eyepiece division is worth a quarter of what it was. Calibrate for every lens you intend to use.
Reading a cell off the graticule
A student calibrates an eyepiece graticule against a stage micrometer and finds that 40 eyepiece divisions cover 10 stage divisions. The stage micrometer is 1 mm divided into 100 parts. An onion epidermis cell then measures 34 eyepiece divisions long. Calculate its length in micrometres.
Start with the stage micrometer, because it is the only thing here with real units. 1 mm ÷ 100 = 0.01 mm per division, which is 10 µm. Ten of those divisions is 100 µm.
That length is covered by 40 eyepiece divisions, so one eyepiece division = 100 ÷ 40 = 2.5 µm.
The cell is 34 divisions long, so 34 × 2.5 = 85 µm.
Onion epidermis cells are typically tens of micrometres across, so 85 µm is sensible. Had the arithmetic given 850 µm you would be claiming a cell you could see with the naked eye.
Artefacts, and the pictures you should not fully believe
Preparing a specimen for an electron microscope is violent. It is fixed in chemicals, dehydrated through a series of solvents, embedded in resin, cut into sections tens of nanometres thick and stained with salts of heavy metals such as lead or osmium. Any of those steps can change what you are looking at.
An artefact is a structure visible in the image that was not present in the living cell. Air bubbles trapped under a coverslip, creases and tears in a section, precipitated stain, and organelles pulled out of shape by dehydration are all artefacts, and early electron microscopists spent years arguing about which structures were real. The mesosome — an infolding of membrane once drawn in every bacterium in every textbook — turned out to be one, produced by the fixing chemicals.
The way scientists settled such arguments is worth knowing, because questions ask about it. If a structure shows up after several different preparation methods, and in more than one type of microscope, it is probably real. If it appears only when one particular technique is used, it probably is not.
- Artefact
- A structure seen in a prepared specimen that was not present in the living cell, produced by the preparation or imaging process.
- Eyepiece graticule
- A ruled scale in the eyepiece whose divisions have no fixed length until it is calibrated.
- Stage micrometer
- A slide bearing a scale of known length, used to calibrate an eyepiece graticule for one particular objective lens.
There is a second reason electron micrographs mislead, and it has nothing to do with damage. A TEM image is one thin slice through a three-dimensional object. A mitochondrion sliced across its width appears as a small circle; the same mitochondrion sliced along its length appears as a long sausage; and one that happens to be bent can be caught by the knife twice over, so a single organelle turns up in the image as two separate profiles with cytoplasm between them. All three are the same organelle. When a micrograph seems to show organelles of wildly different sizes, or more of them than the cell can plausibly hold, the plane of the section is usually the explanation.
In the exam
- Define both words if a question asks for the difference. Magnification is how many times larger, with no units; resolution is the smallest separation still seen as two points, with units. Answers that say resolution is 'how clear the image is' score nothing.
- The reason electron microscopes resolve better is the shorter wavelength of an electron beam. That is the mark. 'Electrons are smaller' is not the same statement and does not earn it.
- Convert units before dividing, and quote the answer in the unit the question asked for. Show the conversion as a line of working — if the final number is wrong you can still be given credit for the method.
- Never put a unit on a magnification. It is a ratio, so ×12 000 is the whole answer.
- Questions about why electron microscopes cannot show living cells want the vacuum: electrons are deflected by air, so the specimen must be in a vacuum, which no living thing survives.
- If asked to evaluate an image, remember that the section is one plane through a three-dimensional object, and that preparation can create artefacts.
Check yourself
A student photographs a cell through a light microscope, then enlarges the photograph on a computer until the whole image is a metre wide. She says she has now magnified the cell about ×20 000, so she should be able to see its ribosomes. Explain why she will not.
Answer
Her arithmetic is fine and her conclusion is wrong, because magnification and resolution are different quantities and only one of them has changed.
Enlarging the photograph raises the magnification but cannot add detail that the original image never contained. The detail was fixed at the moment the light microscope formed the image.
That limit comes from the wavelength of visible light, roughly 400 to 700 nm. Two points closer than about 0.2 µm cannot be resolved, so they merge into one. A ribosome is around 25 nm across — some eight times smaller than the limit — so it was never separately recorded.
All the enlargement does is make the same blur bigger, which is what empty magnification means. To see ribosomes she needs a shorter wavelength, and that means an electron microscope.
Questions
Question 14 marks
An eyepiece graticule is calibrated against a stage micrometer whose divisions are each 10 µm long. 25 eyepiece divisions are found to cover 4 stage micrometer divisions. A cell then measures 15 eyepiece divisions across. Calculate the diameter of that cell in micrometres.
Mark scheme
- M1 4 stage micrometer divisions correspond to 4 × 10 = 40 µm
- M1 one eyepiece division is worth 40 divided by 25
- M1 = 1.6 µm per eyepiece division, then multiplied by the 15 divisions the cell covers
- A1 a final answer of 24 µm
Question 24 marks
Explain why a transmission electron microscope resolves finer detail than a light microscope, and explain why it cannot be used to look at a living cell.
Mark scheme
- B1 resolution is limited by the wavelength of the radiation used to illuminate the specimen
- B1 a beam of electrons has a far shorter wavelength than visible light, so points much closer together can still be seen as separate
- B1 the electron beam has to travel through a vacuum, because air molecules deflect electrons and scatter the beam
- B1 a vacuum removes the water from a cell, so the specimen must be dead, fixed and dehydrated before it is put in
Question 34 marks
Compare a transmission electron microscope with a scanning electron microscope, referring to the specimen used, the electrons detected, the image produced and the resolution achieved.
Mark scheme
- B1 a transmission instrument needs an ultrathin section, whereas a scanning instrument takes a whole specimen coated in a thin film of metal
- B1 a transmission instrument detects electrons that have passed through the specimen, whereas a scanning instrument detects electrons knocked off its surface
- B1 a transmission instrument gives a two-dimensional image of a section, whereas a scanning instrument gives a three-dimensional image of a surface
- B1 a transmission instrument resolves to about 0.1 nm, which is better than the few nanometres a scanning instrument manages
Question 43 marks
A ribosome measures 5 mm across on an electron micrograph labelled as being at a magnification of 200 000 times. Calculate the actual diameter of the ribosome, giving your answer in nanometres.
Mark scheme
- M1 actual size = image size divided by magnification
- M1 converts 5 mm to 5 000 000 nm before dividing, or works consistently in another single unit
- A1 an answer of 25 nm, which is the expected size for a ribosome
Question 53 marks
A student examining an electron micrograph counts what appear to be forty separate mitochondria, of widely differing sizes and shapes, in one small cell. Suggest two reasons why this count and these shapes may be misleading.
Mark scheme
- B1 the micrograph is one thin section through a three-dimensional cell, so each organelle is seen only where the knife happened to cut it
- B1 a mitochondrion cut across appears as a small circle and one cut along its length as a long sausage, so the same organelle gives different profiles
- B1 a bent organelle can be caught by the knife twice, so one mitochondrion appears as two separate profiles and the number is overcounted
Question 62 marks
State what is meant by the magnification of an image, and state what is meant by the resolution of a microscope.
Mark scheme
- B1 magnification is how many times larger the image is than the actual object, and is a ratio with no units
- B1 resolution is the minimum distance between two points at which they can still be distinguished as separate
Worth remembering
- Magnification = image ÷ actual. No units on the answer.
- Resolution is a distance, and smaller is better: 0.1 nm beats 0.2 µm.
- Shorter wavelength, better resolution — which is why electrons beat light.
- TEM: thin section, electrons through, flat image. SEM: whole surface, electrons off, three-dimensional image.
- Recalibrate the eyepiece graticule every time you change objective lens.