Microscopy and Magnification

Cells are far too small to see with the naked eye, so the whole of cell biology depends on the microscope. This lesson covers the two main types of microscope (light and electron), the all-important magnification equation, how to rearrange it, how to convert between millimetres and micrometres, and the required practical of using a light microscope to observe cells. The magnification calculation is one of the most reliable sources of marks in Topic B1 of OCR Gateway Science A — and one where careless unit errors lose marks — so we will work through it carefully.

By the end 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.

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Why We Need Microscopes: Magnification and Resolution

Two ideas describe what 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, more detailed image.

A good microscope needs both. Magnifying a blurry image just gives a bigger blurry image; high resolution is what reveals 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

The electron microscope's far higher resolution is why scientists' understanding of cell structure jumped forward when it was invented — it revealed sub-cellular detail (such as the internal structure of mitochondria and the existence of ribosomes) that light microscopes simply cannot resolve.

Exam Tip: If asked why electron microscopes show more detail, the key word is resolution (not just "higher magnification"). Electrons have a much shorter wavelength than light, giving far higher resolving power.

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The Magnification Equation

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

$\text{magnification} = \frac{\text{image size}}{\text{actual size}}$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 handy triangle helps you rearrange it:

Cover the quantity you want:

• 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 convert 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 — convert to 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 — this gives $2$2, which is a hundred-thousandth of the right answer. Convert first, every 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 the unit the question 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: Lay your working out in three lines — equation, substitution, answer with unit — and state the unit at every stage. Examiners award method marks even if the final arithmetic slips, but only if your working is visible.

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Total Magnification of a Light Microscope

A light microscope has two lenses in series, so its total magnification is the product of the two:

$\text{total magnification} = \text{eyepiece magnification} \times \text{objective magnification}$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 Topic B1 is using a light microscope to observe and draw cells (commonly onion epidermal cells or cheek cells). The method:

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"]

Key points the exam rewards:

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

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Estimating Size Using a Scale Bar