Biology 9700/12 — October/November 2021

Background Concept

Magnification describes how many times larger an image is than the real object it depicts. The CIE definition is:

$$\text{Magnification} = \frac{\text{image size}}{\text{actual size}}$$

Both sizes MUST be expressed in the same unit before dividing — otherwise the number carries no meaning. The most common units in microscopy are:

• $1 \text{ m} = 10^{2} \text{ cm} = 10^{3} \text{ mm} = 10^{6} \text{ µm} = 10^{9} \text{ nm}$

Electron micrographs of cell ultrastructure are typically printed at magnifications of $\times 10\,000$ to $\times 100\,000$ or more, because the structures being shown (ribosomes, membranes, organelles) are sub-micrometre in size.

Understanding the Question

The question gives you a scale bar — a printed line on the micrograph that tells you what real-world distance it represents. Here:

• The printed scale bar measures $2 \text{ cm}$ on the page.
• That printed length corresponds to an actual specimen length of $1 \text{ µm}$.

You are asked to calculate the magnification of the whole micrograph. Both pieces of information are needed; the scale bar is essentially a worked example of the magnification.

The four options differ by a factor of 10 each, so the most common trap is a unit-conversion slip (e.g. forgetting that $1 \text{ cm} = 10^{4} \text{ µm}$, not $10^{2}$ µm).

Approach

1. Apply the magnification formula: $\text{M} = \text{image size} / \text{actual size}$.
2. Convert the image size ($2 \text{ cm}$) into the same units as the actual size ($µ\text{m}$).
3. Divide and pick the matching option.

Step-by-Step Reasoning

Step 1 — State the formula.

$$\text{Magnification} = \frac{\text{image size}}{\text{actual size}}$$

Step 2 — Convert the image size to micrometres. $1 \text{ cm} = 10\,000 \text{ µm} = 10^{4} \text{ µm}$, so:

$$2 \text{ cm} = 2 \times 10^{4} \text{ µm} = 20\,000 \text{ µm}$$

Step 3 — Substitute into the formula. The actual size is $1 \text{ µm}$:

$$\text{Magnification} = \frac{20\,000 \text{ µm}}{1 \text{ µm}} = \times 20\,000$$

Step 4 — Match to the options. The result $\times 20\,000$ is option C.

Key Takeaways

• Magnification is a ratio — both sides must be in the SAME unit.
• Memorise the metric ladder, especially $1 \text{ cm} = 10^{4} \text{ µm} = 10^{7} \text{ nm}$ — these conversions come up in almost every microscopy question.
• A scale bar is a shortcut: the printed length / actual length it represents IS the magnification of the image at that point.
• The CIE accepts answers left as a power of 10 in working, but the final mark usually requires the number in its ordinary form with the correct prefix (e.g. $\times 20\,000$, not $2 \times 10^{4}$).

Common Mistakes

• Dividing without converting units: $2 / 1 = 2$ is wrong because the units are different. Candidates who do this often pick option A ($\times 200$) thinking they have "divided by 0.01".
• Using the wrong conversion: treating $1 \text{ cm}$ as $10\,\text{mm} = 10^{4} \text{ µm}$ is correct; treating it as $100 \text{ µm}$ (i.e. using the mm conversion by mistake) gives $\times 2$ — clearly nonsense.
• Confusing actual and image size: the printed scale bar is the IMAGE size; the real specimen length it represents is the ACTUAL size. Swapping them gives a magnification of $\times 5 \times 10^{-5}$, which isn't even an option but illustrates the error.

Things to Be Careful About

• Show the unit conversion step explicitly in your working — it is where most candidates lose the mark, and writing it down protects you if the final arithmetic slips.
• Watch the SI prefixes: $µ\text{m}$ is micrometre ($10^{-6} \text{ m}$), NOT millimetre. A single letter changes the answer by a factor of $1000$.
• The options differ by a factor of 10, so the only "trap" options here are unit-conversion errors. If you obtain a value that does not match an option exactly, redo the conversion rather than rounding.
• Magnification has no units — it is written with a multiplication sign in front ($\times 20\,000$), not with a slash or the word "times".