Microscopy and Magnification

Cells are far too small for the naked eye, so every discovery in cell biology has depended on the microscope. This lesson covers the two main kinds of microscope (light and electron), the all-important magnification equation and how to rearrange it, how to convert between millimetres and micrometres, and the required practical of using a light microscope to look at cells. The magnification calculation is one of the most dependable sources of marks in the biology part of your combined-science course — and also one where a careless unit slip throws the answer out by a factor of a thousand — so we will take it step by step.

By the end of this lesson you should be able to compare light and electron microscopes, use and rearrange $\text{magnification} = \dfrac{\text{image size}}{\text{actual size}}$magnification=actual sizeimage size​, convert between units, and describe how to prepare and view a slide.

This lesson builds AO1 (understanding of microscopy and the two microscope types) and AO2 (applying the magnification equation, including the maths of rearranging it and converting units).

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What a Microscope Does: Magnification and Resolution

Two separate ideas describe the job a microscope does:

• Magnification — how many times bigger the image is than the real object.
• Resolution (resolving power) — the smallest distance between two points that can still be seen as two separate points. Higher resolution means a sharper image showing more detail.

A good microscope needs both. Magnifying a blurry image only gives you a bigger blurry image; it is high resolution that lets you actually see fine detail.

Light vs Electron Microscopes

Feature	Light (optical) microscope	Electron microscope
Uses	A beam of light and glass lenses	A beam of electrons
Maximum magnification	About $\times 1500$×1500 to $\times 2000$×2000	Over $\times 1\,000\,000$×1000000
Resolution	About $200 \text{ nm}$200 nm	About $0.2 \text{ nm}$0.2 nm (much better)
Specimens	Living or dead; in colour	Dead only (in a vacuum); images are black and white
Cost and size	Cheap, small, portable	Very expensive, large
What you can see	Cells, nuclei, chloroplasts	Internal detail of organelles, ribosomes, membranes

It is the electron microscope's much higher resolution that transformed our understanding of cells. When it was invented, it revealed sub-cellular detail — such as the internal structure of mitochondria and the existence of ribosomes — that a light microscope simply cannot resolve.

Exam Tip: If a question asks why an electron microscope shows more detail, the key word is resolution, not just "higher magnification". Electrons have a much shorter wavelength than light, which gives them far higher resolving power.

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The Magnification Equation

This is the equation you must know and be able to rearrange in both directions:

$\text{magnification} = \frac{\text{image size}}{\text{actual size}}$magnification=actual sizeimage size​

Magnification has no units — it is just a "number of times" (for example $\times 100$×100). The image size and the actual size must be in the same unit before you divide. A formula triangle makes rearranging easy:

Cover the quantity you want to find:

• Cover I (image size) and you are left with $M \times A$M×A, so $\text{image} = \text{magnification} \times \text{actual}$image=magnification×actual.
• Cover A (actual size) and you are left with $\dfrac{I}{M}$MI​, so $\text{actual} = \dfrac{\text{image}}{\text{magnification}}$actual=magnificationimage​.
• Cover M (magnification) and you are left with $\dfrac{I}{A}$AI​, the original equation.

Units: millimetres, micrometres and nanometres

Cell measurements jump between units, so you must be able to convert quickly and confidently:

$1 \text{ mm} = 1000 \text{ }\mu\text{m} \qquad 1 \text{ }\mu\text{m} = 1000 \text{ nm}$1 mm=1000 μm1 μm=1000 nm

To go from mm to µm, multiply by $1000$1000. To go from µm to mm, divide by $1000$1000.

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Worked Examples

Worked Example 1 — Finding magnification

A cell has an actual diameter of $50 \text{ }\mu\text{m}$50 μm. In a drawing it measures $100 \text{ mm}$100 mm across. What is the magnification?

Step 1 — get both sizes into the same unit. Change the image size to micrometres: $100 \text{ mm} = 100 \times 1000 = 100\,000 \text{ }\mu\text{m}$100 mm=100×1000=100000 μm.

Step 2 — apply the equation:

$\text{magnification} = \frac{\text{image size}}{\text{actual size}} = \frac{100\,000 \text{ }\mu\text{m}}{50 \text{ }\mu\text{m}} = 2000$magnification=actual sizeimage size​=50 μm100000 μm​=2000

Answer: $\times 2000$×2000.

Common error: dividing $100 \text{ mm}$100 mm by $50 \text{ }\mu\text{m}$50 μm without converting — that gives $2$2, which is a hundred-thousandth of the right answer. Convert first, every single time.

Worked Example 2 — Finding actual size

A photograph of a cell at a magnification of $\times 4000$×4000 shows the cell as $20 \text{ mm}$20 mm wide. What is the real width of the cell, in micrometres?

Step 1 — rearrange for actual size:

$\text{actual size} = \frac{\text{image size}}{\text{magnification}} = \frac{20 \text{ mm}}{4000} = 0.005 \text{ mm}$actual size=magnificationimage size​=400020 mm​=0.005 mm

Step 2 — convert mm to µm: $0.005 \text{ mm} \times 1000 = 5 \text{ }\mu\text{m}$0.005 mm×1000=5 μm.

Answer: $5 \text{ }\mu\text{m}$5 μm.

Common error: leaving the answer as $0.005 \text{ mm}$0.005 mm when the question asks for micrometres. Always check which unit the question actually wants.

Worked Example 3 — Finding image size

A bacterium is $2 \text{ }\mu\text{m}$2 μm long. It is drawn at a magnification of $\times 5000$×5000. How long is the drawing, in millimetres?

Step 1 — rearrange for image size:

$\text{image size} = \text{magnification} \times \text{actual size} = 5000 \times 2 \text{ }\mu\text{m} = 10\,000 \text{ }\mu\text{m}$image size=magnification×actual size=5000×2 μm=10000 μm

Step 2 — convert µm to mm: $10\,000 \div 1000 = 10 \text{ mm}$10000÷1000=10 mm.

Answer: $10 \text{ mm}$10 mm.

Exam Tip: Set your working out in three lines — equation, substitution, answer with unit — and write the unit at every stage. Examiners award method marks even when the final arithmetic slips, but only if your working is there to see.

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Total Magnification of a Light Microscope

A light microscope has two lenses in a line, so its total magnification is the two multiplied together:

$\text{total magnification} = \text{eyepiece magnification} \times \text{objective magnification}$total magnification=eyepiece magnification×objective magnification

Worked Example 4

A microscope has a $\times 10$×10 eyepiece lens and a $\times 40$×40 objective lens. What is the total magnification?

$\text{total magnification} = 10 \times 40 = 400$total magnification=10×40=400

Answer: $\times 400$×400.

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Required Practical: Using a Light Microscope

A core practical of this topic is using a light microscope to observe and draw cells — commonly onion epidermal cells or cheek cells. The method runs like this:

flowchart TD
  A["Add a drop of water to a clean slide"] --> B["Place a thin piece of tissue<br/>(e.g. onion epidermis) in the water"]
  B --> C["Add a stain such as iodine<br/>to make structures visible"]
  C --> D["Lower a coverslip slowly with a mounted needle<br/>to avoid trapping air bubbles"]
  D --> E["Clip the slide on the stage;<br/>start with the lowest-power objective"]
  E --> F["Use the coarse focus to bring cells into view,<br/>then the fine focus to sharpen"]
  F --> G["Switch to a higher-power objective and refocus;<br/>draw what you see"]

The points the exam rewards are:

• A stain (such as iodine or methylene blue) is added so that colourless structures like the nucleus become visible.
• The coverslip is lowered slowly with a mounted needle to avoid trapping air bubbles (which look like dark-edged circles and hide the cells).
• Always start on the lowest-power objective so the specimen is easy to find, then increase the magnification.
• A scientific drawing should use clear, unbroken lines, no shading, and should include a scale or the magnification used.

Exam Tip: If asked why iodine is added, the answer is to stain the cells so structures (especially the nucleus and cell wall) show up/become visible under the microscope. If asked about bubbles, the mark is for lowering the coverslip slowly to avoid trapping them.

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Estimating Size Using a Scale Bar

Many micrographs come with a scale bar — a short line labelled with the real distance it represents (for example a $10 \text{ }\mu\text{m}$10 μm bar). You can use it to estimate the size of a cell.

Worked Example 5

On a micrograph, a scale bar labelled "$10 \text{ }\mu\text{m}$10 μm" measures $5 \text{ mm}$5 mm long with a ruler. A cell next to it measures $20 \text{ mm}$20 mm across. Estimate the actual width of the cell.

The scale bar tells you that $5 \text{ mm}$5 mm on the image represents $10 \text{ }\mu\text{m}$10 μm in real life, so each millimetre on the image represents $\dfrac{10}{5} = 2 \text{ }\mu\text{m}$510​=2 μm.

The cell measures $20 \text{ mm}$20 mm across, so its real width is:

$20 \text{ mm} \times 2 \text{ }\mu\text{m per mm} = 40 \text{ }\mu\text{m}$20 mm×2 μm per mm=40 μm

Answer: about $40 \text{ }\mu\text{m}$40 μm.

Worked Example 6 — Number of cells across a field of view

A student views onion cells under a microscope. Eight cells fit end to end across the field of view, which is $1.6 \text{ mm}$1.6 mm wide. Estimate the average length of one cell, in micrometres.

Step 1 — find the length of one cell in millimetres by dividing the field width by the number of cells:

$\frac{1.6 \text{ mm}}{8} = 0.2 \text{ mm}$81.6 mm​=0.2 mm

Step 2 — convert to micrometres ($\times 1000$×1000): $0.2 \text{ mm} \times 1000 = 200 \text{ }\mu\text{m}$0.2 mm×1000=200 μm.