Cell theory, scale and the microscope
By the end of this lesson you will be able to
- State the three parts of cell theory: all living things are made of cells; the cell is the basic unit of life; all cells come from pre-existing cells.
- Label the parts of a light microscope and describe how to use and care for it so that a slide comes into focus without damage.
- Calculate total magnification (eyepiece × objective) and convert between millimetres, micrometres and nanometres.
- Estimate the size of a cell from the width of the field of view and the number of cells counted across it.
- Make a temporary slide of onion epidermis and explain why it is stained.
The puzzle
You are built from about 30 trillion tiny compartments, each with a copy of the instructions for building all of you. A mopane tree is built the same way. So is the yeast in bread and the bacterium in yoghurt. Nobody had any idea this was true until a man looked at a slice of cork through a lens in 1665 and saw rows of little boxes. Why did it take so long — and how do we know that a thing too small to see is really there?
A grain of salt is about 0.3 mm across. Which of these do you think are smaller than a grain of salt, and by how much: a human skin cell, a bacterium, a red blood cell, a virus, a full stop on this page? Write your guesses in order of size before reading on.
Compare your answer
From largest to smallest: full stop (about 0.5 mm — bigger than the salt grain), skin cell (about 0.03 mm, ten times smaller than the salt), red blood cell (0.008 mm, nearly forty times smaller), bacterium (0.001–0.005 mm, a hundred times smaller), virus (0.0001 mm and less — a thousand times smaller than the salt and invisible in any light microscope). Most people guess cells are bigger than they are. Almost everything in this unit is smaller than the smallest thing you have ever seen with your eyes, which is why the whole subject had to wait for the microscope.
The science — structured notes
1.1 Cell theory — three sentences that took two centuries
A cell is the smallest unit of a living thing that can carry out the seven life processes on its own. Every organism you classified in Unit 4 — bacterium, fungus, plant, animal — is made of cells. The modern cell theory says:
A student says: “A rock crystal grows in a cave, so it must be made of cells.”
Sentence 1 works in one direction only: every living thing is made of cells, not every thing that grows. A crystal grows by adding atoms to its outside; it does not respire, feed, sense or reproduce (Lesson 4.1).
Sentence 3 rules it out too: a crystal is not produced by an existing cell dividing. Growth by itself is not evidence of cells; the evidence is to look with a microscope — a crystal shows flat faces and no compartments, while a slice of any plant shows boxes with nuclei.
Use cell theory to answer each.
(a) A baobab tree has been alive for 1500 years. Explain why every one of its cells came from another cell.
(b) A pot of yoghurt left in a warm kitchen goes sour faster. Which sentence of cell theory explains why the bacteria increase in number, and how?
(c) A virus is a coat of protein around a strand of genetic material and can only multiply inside a cell. Explain why viruses are the awkward case for cell theory.
Reveal answer
(a) The tree began as a single fertilised cell inside a seed; every cell in the trunk, leaves and roots was produced by the division of an existing cell (sentence 3). New cells are added each year by division in the growing layers; none appeared from non-living sap or soil.
(b) Sentence 3 — cells come from cells. Each bacterium divides into two; in the warmth they divide faster, so the population doubles again and again and more acid is produced. They are not created by the milk.
(c) A virus is not a cell (no cytoplasm, no membrane of its own, no respiration), yet it carries genetic instructions and reproduces — by making a cell copy it. It fails sentence 1 (not made of cells) but obeys sentence 3 in a twisted way (it needs a cell). Most biologists call it a non-living particle that becomes active only inside a host cell.
1.2 The light microscope — parts, use and care
The instrument that made this unit possible is the compound light microscope: two sets of lenses that magnify one after the other, with light shone up through a thin specimen.
| Part | What it does | Rule for using it |
|---|---|---|
| Eyepiece (ocular) lens | The lens you look through; usually ×10 | Keep both eyes open to avoid strain; never touch the glass |
| Objective lenses | Three or four lenses on a turret: ×4, ×10, ×40 (sometimes ×100) | Always start on the lowest power; click the turret round, never push the lenses |
| Stage and clips | Flat platform that holds the slide over the light | Clip the slide; move it by the stage controls, not your fingers |
| Coarse focus | Moves the stage or tube a long way | Use only on low power; on high power it can drive the lens into the slide |
| Fine focus | Moves a tiny distance for a sharp image | The only focus knob you touch on ×40 |
| Lamp or mirror and diaphragm | Lights the specimen from below; the diaphragm controls how much | Less light usually shows more detail in a pale specimen |
| Arm and base | The frame | Carry with one hand under the base, one on the arm |
Turn to the ×4 objective. Clip the slide on the stage with the specimen over the hole.
Looking from the side (not through the eyepiece), use the coarse focus to bring the stage close to the lens without touching.
Look through the eyepiece and turn the coarse focus slowly the other way — away from the slide — until the image appears. Sharpen with the fine focus.
Move the part you want into the centre, then click to ×10 and refocus with the fine knob only. Repeat for ×40. Adjust the diaphragm until the detail shows.
Afterwards: return to ×4, remove the slide, switch off the lamp, cover the microscope.
“The best way to find a small object on a slide is to start on the ×40 objective, because it is the most powerful.”
Reveal answer
False. At ×40 the field of view is less than half a millimetre across, so you would be searching a slide 25 mm wide through a keyhole — and with the coarse focus in use, risking the lens. Start at ×4 where the field is about 4.5 mm, find and centre the object, then step up. Higher magnification always means a smaller field and a shallower depth of focus.
1.3 Magnification and units
Total magnification = eyepiece magnification × objective magnification. With a ×10 eyepiece: ×4 objective gives ×40; ×10 gives ×100; ×40 gives ×400. Magnification tells you how many times bigger the image is than the object; it does not tell you the object’s size.
To state sizes you need units smaller than the millimetre:
| Unit | Symbol | Relation | Typical thing |
|---|---|---|---|
| millimetre | mm | 1 mm = 1/1000 m | Grain of salt (0.3 mm); onion cell (0.3 mm); human egg cell (0.1 mm — just visible) |
| micrometre (micron) | μm | 1 mm = 1000 μm | Cheek cell (60 μm); red blood cell (8 μm); bacterium (1–5 μm) |
| nanometre | nm | 1 μm = 1000 nm | Virus (20–300 nm); cell membrane thickness (about 8 nm); a water molecule (0.3 nm) |
A red blood cell is 0.008 mm across. Give this in μm. A virus is 100 nm across; give this in μm and in mm.
0.008 mm × 1000 = 8 μm.
100 nm ÷ 1000 = 0.1 μm; 0.1 μm ÷ 1000 = 0.0001 mm. The red blood cell is 80 times wider than the virus.
Check the direction: converting to a smaller unit gives a bigger number. Examiner reports on Criterion C say unit conversion is one of the most common lost marks — write the working.
1.4 Measuring a cell: field of view and counting
The circle you see through the eyepiece is the field of view. Its real width is known for each objective (on a typical school microscope: 4.5 mm at ×40, 1.8 mm at ×100, 0.45 mm at ×400 — measure yours with a clear ruler on the stage at ×40). Count how many cells fit across the middle of the field; then:
size of one cell = width of field of view ÷ number of cells across it
At ×100 the field is 1.8 mm wide and a student counts 6 onion cells across it.
1.8 mm ÷ 6 = 0.3 mm = 300 μm per cell.
At ×400 the field is 0.45 mm and the count is 2 (only 1½ cells actually fit, rounded). 0.45 ÷ 2 = 0.23 mm — a rougher answer, because a count of 2 could really be anywhere from 1.5 to 2.5. Low counts give poor precision; choose the magnification that gives ten or more cells across if you can.
Sanity check: the answer is the same order of size at both magnifications, which it must be — the cell has not changed, only the view.
More precisely, a slide with a printed scale (a stage micrometer) or an eyepiece scale (a graticule) lets you measure directly — that is the method used in Years 4 and 5. For now, counting across the field is the estimate the examiners accept, provided you state the field width and show the division.
A student counts 30 cheek cells across the ×400 field (0.45 mm) and 3 across the ×40 field (4.5 mm) of the same slide.
(a) Calculate the cell size from each count, in μm.
(b) Explain why the two answers disagree so much, and which is more trustworthy.
Reveal answer
(a) ×400: 0.45 mm ÷ 30 = 0.015 mm = 15 μm. ×40: 4.5 mm ÷ 3 = 1.5 mm = 1500 μm.
(b) At ×40 the cheek cells are almost invisible and the student has probably counted clumps, not cells — and a count of “3” could be 2 or 4, a ± 33 % uncertainty. At ×400 thirty separate cells are visible and a count error of one changes the answer by only 3 %. The ×400 value is far more trustworthy; the typical size of a cheek cell is 50–80 μm, so the student may also have counted overlapping cells at ×400 and should check across a second field.
1.5 Making a slide — onion epidermis
A specimen for a light microscope must be thin (one cell thick, so light passes through) and usually stained (most cell contents are transparent). The classic first slide:
Try it — the microscope
Look at onion epidermis under the ×4, ×10 and ×40 objectives and count the cells across the field each time. Record three counts per objective and calculate the cell size from each — do the three lenses agree? Then switch the specimen to cheek cells and to yeast: which objective do you need before you can count them at all? Finally switch the stain off and see what a nucleus looks like unstained.
Suppose your onion counts were: ×4 objective (field 4.5 mm) → 15; ×10 (1.8 mm) → 6; ×40 (0.45 mm) → 2.
(a) Calculate the cell length from each, in mm and μm.
(b) Describe the pattern in the counts and explain it.
(c) Explain why the ×40 answer is the least reliable, and suggest how to improve the estimate without changing the microscope.
Reveal answer
(a) ×4: 4.5 ÷ 15 = 0.30 mm = 300 μm. ×10: 1.8 ÷ 6 = 0.30 mm = 300 μm. ×40: 0.45 ÷ 2 = 0.225 mm = 225 μm.
(b) Each time the magnification rises ten-fold in area (×4 → ×40 objective is ×10 in width), the count falls from 15 to 6 to 2 — roughly in proportion to the field width, because the cells stay the same real size while the field shrinks.
(c) With only two cells across, a count cannot be closer than one whole cell, so the uncertainty is about ± 50 %; the true count is nearer 1.5. Use the lens that shows the most cells (×4 or ×10), count across several different fields and take a mean, or count across the diameter in two directions and average.
Common mistakes to avoid
- “Magnification ×400 means the cell is 400 μm” — magnification is a ratio, not a size. Size comes from the field of view or a scale.
- Forgetting the eyepiece — total magnification is eyepiece × objective, so a ×40 objective gives ×400, not ×40.
- Units the wrong way round — 1 mm = 1000 μm, so 0.3 mm = 300 μm, not 0.0003 μm.
- Coarse focus on high power — broken slide, scratched lens, lost marks in the practical.
- Drawing air bubbles as cells — bubbles are perfect circles with a thick dark rim and nothing inside.
- “Cells are the building blocks of life” as an explanation — a slogan is not an explanation; quote the three sentences and apply the right one.
How we found out — a slice of cork and a bead of glass
In 1665 Robert Hooke, curator of experiments at the Royal Society in London, published Micrographia, a book of drawings of what he saw through a microscope he had built himself: a flea the size of a page, the point of a needle looking like a blunt stump, and a thin slice of cork. The cork was full of tiny empty boxes, which reminded him of the small rooms — cellae — that monks slept in. He called them cells. He was looking at the dead walls of plant cells; the living contents had long gone, but the name stuck.
A few years later, in the Dutch town of Delft, a cloth merchant named Antonie van Leeuwenhoek ground tiny glass beads into single lenses so good that they magnified nearly 300 times — better than Hooke’s compound instrument. In 1674 he looked at a drop of lake water and saw it teeming with “animalcules”; in 1676 he described bacteria from his own teeth; he saw red blood cells, sperm cells, yeast. The Royal Society did not believe him until Hooke repeated the observations. Leeuwenhoek kept his lens-grinding secret to his death, and for a century afterwards nobody could see as much as he had.
It took until 1838–39 for two Germans, Matthias Schleiden (plants) and Theodor Schwann (animals), to state that every organism they had examined was made of cells; and until 1855 for the physician Rudolf Virchow to add the third sentence, omnis cellula e cellula — every cell from a cell — after studying diseased tissue and finding that tumours grew from the patient’s own cells dividing. Two hundred years from the first drawing to the theory: because a theory needs thousands of observations, better instruments and the willingness to say that what everyone believed (life from mud) was wrong.
Why did the Royal Society ask Hooke to repeat Leeuwenhoek’s observations before accepting them, and what does this tell you about how science treats a surprising claim?
Reveal answer
Leeuwenhoek was an unknown tradesman claiming to see living things nobody else had ever seen, using an instrument nobody else could copy. A claim is accepted only when it can be reproduced by someone else with their own equipment — the same rule as repeating trials in your own experiments. Hooke’s confirmation turned a story into evidence. Surprising claims need stronger evidence, not weaker, and the burden of showing it lies with the person making the claim.
Where it is used now
- Clinics. Across Botswana, tuberculosis is still confirmed in many clinics by a laboratory technician looking at a stained sputum smear under a light microscope at ×1000 and counting the red rod-shaped bacteria; malaria in the northern districts is confirmed the same way from a drop of blood. The skills in this lesson — focusing, staining, counting across a field — are done thousands of times a day.
- Water and food safety. Water-treatment plants count microorganisms in samples; dairies check milk for bacteria; brewers count yeast cells with a counting chamber to decide how much to add.
- Farming. Plant pathologists identify fungal spores on a crop leaf under a microscope before choosing a treatment; a wrong identification wastes a season’s spray.
- Forensics. Hairs, fibres, pollen and soil grains on clothing are compared under microscopes to link a person to a place.
- Everywhere there is a phone. Clip-on lenses and folded-paper microscopes costing a few pula turn a phone camera into a ×100 instrument, and are used in schools and field clinics that have never had a laboratory.
Science now — and the scientist you need to be
What is happening in 2026
The microscope is being reinvented from both ends. At the expensive end, cryo-electron microscopes freeze cells so fast that water cannot form crystals and then image individual protein molecules inside them; a technique called expansion microscopy does the opposite — it swells the specimen itself, evenly, several times over, so that an ordinary light microscope can see detail that used to need an electron beam. At the cheap end, a smartphone camera plus a printed lens is now a field microscope, and machine-learning software trained on millions of labelled images will scan a blood smear or a sputum slide and flag the fields a technician should look at first. In countries with few laboratory staff — including much of southern Africa — that combination is being trialled to speed up diagnosis of malaria and tuberculosis. The software does not replace the person who prepares the slide, checks the focus and takes responsibility for the result; it changes what one trained person can get through in a day.
None of it changes the arithmetic of this lesson. Whoever is looking — a technician, a student, a program — a measurement is a field width divided by a count, with the uncertainty that the count carries.
The mindshift
What you need to be able to do
Every biology practical from now to the eAssessment involves a microscope, and Criterion C questions regularly give you a magnification or a scale bar and ask for a size — with the marks lost on units. The habit to build: write the field width, write the count, divide, state the unit, convert if asked, and say how sure you are. That last part — “the count could be one out, so the size is between 0.26 and 0.36 mm” — is what separates a level 5–6 answer from a level 7–8 one.
See an example
Page: 100 pages = 8 mm, so one page = 0.08 mm = 80 μm; more precise with 200 pages. Hair: 20 turns covered 1.5 mm, so one hair = 0.075 mm = 75 μm — could be improved by winding 50 turns. Sugar: 10 grains = 5 mm, so 0.5 mm = 500 μm each, but the grains varied from 0.3 to 0.8 mm, so I would sieve them or measure 30. The AI gave “a human hair is about 70 μm” with no range; mine came out close, but I know why.
Key terms
| Cell | The smallest unit of a living thing that can carry out the life processes; all organisms are made of one or more. |
| Cell theory | All living things are made of cells; the cell is the basic unit of life; all cells come from pre-existing cells. |
| Unicellular / multicellular | Made of one cell (bacteria, yeast, amoeba) / made of many cells (plants, animals, most fungi). |
| Magnification | How many times larger the image is than the object; total = eyepiece × objective. |
| Field of view | The circle of specimen visible through the eyepiece; it shrinks as magnification rises. |
| Micrometre (μm) | One thousandth of a millimetre; the unit for cells. 1 mm = 1000 μm; 1 μm = 1000 nm. |
| Stain | A dye (iodine, methylene blue) that colours transparent cell parts so they can be seen. |
| Epidermis | The outer layer of cells of a plant part, one cell thick — easy to peel and view. |
| Coverslip | The thin glass square laid over a specimen to flatten it and protect the lens. |
Think like a scientist
Criterion C A student measured the width of the field of view at ×40 total magnification by placing a clear plastic ruler on the stage: 4.5 mm. She then viewed a slide of cheek cells and counted the cells across the field at three magnifications, three fields each.
| Total magnification | Field width / mm | Count 1 | Count 2 | Count 3 |
|---|---|---|---|---|
| ×40 | 4.5 | 70 | 60 | 65 |
| ×100 | 1.8 | 28 | 31 | 30 |
| ×400 | 0.45 | 7 | 8 | 15 |
(a) Identify the anomalous count and suggest a cause.
(b) Calculate the mean count at each magnification (exclude the anomaly) and the cell size from each mean, in μm.
(c) Explain why the field width at ×100 and ×400 could be calculated rather than measured with the ruler.
(d) Evaluate which magnification gave the most reliable cell size, using the data.
(e) Suggest one improvement to the method that would reduce the uncertainty in the count.
Model answer
(a) Count 3 at ×400 (15) — it is nearly double the other two (7, 8). Likely causes: a different field was counted where cells overlapped in a clump, or the student counted cells touching the edge on both sides, or counted across a diameter that passed through a fold.
(b) ×40: (70 + 60 + 65) ÷ 3 = 65; 4.5 mm ÷ 65 = 0.069 mm = 69 μm. ×100: (28 + 31 + 30) ÷ 3 = 29.7 ≈ 30; 1.8 ÷ 30 = 0.060 mm = 60 μm. ×400: (7 + 8) ÷ 2 = 7.5; 0.45 ÷ 7.5 = 0.060 mm = 60 μm. (Means of whole-number counts are rounded to one decimal place at most; the sizes agree to about 10 %.)
(c) The ruler’s millimetre marks cannot be seen at ×100 (only part of one millimetre fills the field) or at ×400. But magnification is proportional: going from ×40 to ×100 makes the field 2.5 times narrower (4.5 ÷ 2.5 = 1.8 mm), and ×400 makes it ten times narrower (0.45 mm). Measuring once at low power and calculating is standard practice.
(d) At ×100 the three counts are within ± 1.5 of the mean (about 5 %), the cells are large enough to see individually, and 30 cells across gives a small uncertainty per cell. At ×40 the counts spread from 60 to 70 (± 8 %) because the cells are too small to separate reliably; at ×400 a count of 7 or 8 is one cell out either way (± 13 %) and one field gave an anomaly. ×100 is the most reliable here — the highest magnification is not automatically the best.
(e) Count across five or more fields, always along the same diameter, with a rule for cells cut by the edge (count only the ones on the left edge); or use an eyepiece graticule calibrated against a stage micrometer so that the cell is measured directly rather than counted.
Probe deeper — exam-style questions
Attempt every question before opening the answer. Marks in brackets show what a full answer is worth.
State the three statements of cell theory.
Reveal answer
All living things are made of one or more cells [1]; the cell is the basic unit of structure and function in living things [1]; all cells come from pre-existing cells [1].
A microscope has a ×10 eyepiece and objectives of ×4, ×10 and ×40. Calculate the total magnification available, and state the field of view at the highest power if it is 4.5 mm at the lowest.
Reveal answer
×40, ×100 and ×400 [1]; the field shrinks in proportion, so at ×400 it is 4.5 ÷ 10 = 0.45 mm [1].
A student writes: “At ×400 I counted 5 cells across the 0.45 mm field, so each cell is 400 ÷ 5 = 80 μm.” Identify two errors and give the correct answer.
Reveal answer
The magnification (400) was used instead of the field width (0.45 mm) [1]; the unit was simply written as μm without converting [1]; correct: 0.45 mm ÷ 5 = 0.09 mm = 90 μm [1].
Describe how to make a temporary slide of onion epidermis, including the purpose of the stain and how to avoid air bubbles.
Reveal answer
Peel a one-cell-thick layer of epidermis from the inside of an onion scale and lay it flat in a drop of water on a slide [1]; add iodine solution to stain the nucleus and cytoplasm, which are otherwise transparent [1]; lower the coverslip from one edge at an angle with a mounted needle so that air is pushed out rather than trapped [1].
True or false, with a reason: “A bacterium 2 μm long could be seen clearly with a ×40 objective.”
Reveal answer
False as a clear image — at ×400 total magnification a 2 μm bacterium appears 0.8 mm across, a dot with no visible detail [1]; bacteria are usually viewed with a ×100 oil-immersion objective (×1000) and stained, and even then only their shape is visible [1].
Explain why Hooke’s cork cells appeared empty, why Leeuwenhoek’s claims were doubted, and what finally turned “cells” into a theory.
Reveal answer
Cork is dead bark: only the cell walls remain, the living contents having gone [1]; Leeuwenhoek’s single-lens microscopes were better than anyone else’s and he kept the method secret, so nobody could reproduce his observations until Hooke did [1]; Schleiden and Schwann (1838–39) showed that every plant and animal examined was made of cells, and Virchow (1855) showed that cells arise only by division — general observations plus the origin of cells made it a theory [1].
Summary
- Cell theory: all organisms are made of cells; the cell is the basic unit of life; all cells come from pre-existing cells.
- Use the microscope from low power up, coarse focus only on low power, fine focus on high; carry it by arm and base; keep lenses dry.
- Total magnification = eyepiece × objective. 1 mm = 1000 μm; 1 μm = 1000 nm. Light microscopes cannot show anything much below 200 nm.
- Cell size = field of view width ÷ number of cells across; the more cells you count, the smaller the uncertainty.
- A slide must be thin and usually stained; lower the coverslip at an angle to avoid bubbles.
Next time → Inside the cell: what an animal cell and a plant cell contain, what each part is for, and how to draw what you see so that an examiner can read it.