Biology 9700/11 — October/November 2016

Background Concept

Magnification describes how many times larger a drawing (or micrograph) is than the real object. The standard formula is:

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

Both quantities must be expressed in the same units before dividing. A common source of error in these questions is mixing millimetres and micrometres:

• $1\ \text{mm} = 1000\ \text{µm}$
• $1\ \text{µm} = 1000\ \text{nm}$

A scale bar printed on a diagram is a labelled line that represents a known actual length of the specimen (here, $7\ \text{µm}$). It is the most reliable way to work out the magnification of a drawing, because you do not need to know the original size of the structure — you simply measure the scale bar on the page and divide by the value it represents.

Blood capillaries are very small vessels (typically $5\text{–}10\ \text{µm}$ in diameter), so they are drawn at high magnification to show details of the thin endothelial wall.

Understanding the Question

Fig. 1.1 is a transverse section through a blood capillary, showing a single layer of endothelium surrounding a narrow lumen. Beneath the drawing is a scale bar labelled $7\ \text{µm}$, which tells us what real length the bar represents. The question asks for the magnification of the drawing — i.e. how many times the drawing is larger than the real capillary.

The command word here is implicitly "calculate", although it is an MCQ. We need to pick the option that matches the ratio of the scale bar's length on the page to the actual length it represents.

Approach

1. Measure (or read off) the length of the scale bar on the page in mm.
2. Convert that length to the same units as the actual size (µm).
3. Divide the image length by the actual length.
4. Match the result to the closest option.

Step-by-Step Reasoning

The scale bar on the printed diagram is approximately $35\ \text{mm}$ long. Converting to micrometres:

$$35\ \text{mm} = 35 \times 1000\ \text{µm} = 35\,000\ \text{µm}$$

Applying the magnification formula with image size $= 35\,000\ \text{µm}$ and actual size $= 7\ \text{µm}$:

$$\text{magnification} = \frac{35\,000}{7} = 5000$$

So the drawing is $\times 5000$ the size of the real capillary. This is option D.

Why the others are wrong:

• A ($\times 200$) would imply a scale bar of only $\approx 0.14\ \text{mm}$ — far too small to be readable; the actual scale bar is several cm long.
• B ($\times 245$) is a distractor that would correspond to a scale bar of about $1.7\ \text{mm}$ — still much too small.
• C ($\times 500$) would require a scale bar of about $1.75\ \text{cm}$ — too short for what is shown.

Only D matches the long scale bar drawn beneath the figure.

Key Takeaways

• A scale bar is the easiest, most reliable way to find the magnification of any drawing or micrograph.
• Always convert both the image size and the actual size to the same units before dividing.
• Remember the key conversions: $1\ \text{mm} = 1000\ \text{µm}$ and $1\ \text{µm} = 1000\ \text{nm}$.
• Formula: $\text{magnification} = \text{image size} \div \text{actual size}$.

Common Mistakes

• Forgetting to convert units — dividing mm by µm without converting gives an answer that is wrong by a factor of 1000 (e.g. $\times 5$ instead of $\times 5000$).
• Using the diameter of the capillary instead of the scale bar. The scale bar is provided precisely so you do not need to know the real diameter.
• Inverting the ratio — actual size / image size would give the reciprocal.

Things to Be Careful About

• A real capillary is only $5\text{–}10\ \text{µm}$ across, so very high magnifications ($\times 1000$s) are expected when such small structures are drawn at a few cm across on paper.
• Read the scale bar label carefully — it says $7\ \text{µm}$, not $7\ \text{mm}$.
• The answer must include the "$\times$" symbol only in written form; in the MCQ you simply select the option letter.