Biology 9700/13 — May/June 2022

Background Concept

Magnification describes how many times larger a drawing (or micrograph) is than the actual specimen. It is calculated as:

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

Whenever image size and actual size are compared, they MUST be in the same units. Common conversions to remember: $1\,\text{mm} = 1000\,\mu\text{m}$ and $1\,\text{cm} = 10\,000\,\mu\text{m}$. A printed scale bar (the line drawn next to a figure and labelled with its real length) is the easiest way to work out magnification because the actual size is given to you — you only have to measure the line on the page.

The tissue in the figure is ciliated columnar epithelium of the type lining the trachea and large bronchi. Tall columnar cells bear apical cilia that beat mucus upwards; the flask-shaped cell with vesicles is a goblet cell that secretes mucus. Recognising the tissue is not required to answer this question, but it confirms the cells are real, micrometre-scale objects rather than nanometre-scale.

Understanding the Question

You are given a diagram of ciliated epithelium with a scale bar labelled $80\,\mu\text{m}$. The task is to find the magnification of the diagram. There is no other way to obtain a number here — the only actual size stated is the scale bar, so the answer must come from measuring the bar on the page and dividing by $80\,\mu\text{m}$.

Approach

1. Use a ruler to measure the length of the scale bar in millimetres.
2. Convert that measurement into the same units as the scale bar label (micrometres).
3. Apply $\text{magnification} = \text{image size} / \text{actual size}$.
4. Match the result to the closest option.

Step-by-Step Reasoning

• The scale bar in the printed diagram measures approximately $28\,\text{mm}$ on the page.
• Converting: $28\,\text{mm} = 28 \times 1000\,\mu\text{m} = 28\,000\,\mu\text{m}$.
• Substituting into the magnification equation:
  $\text{magnification} = \frac{28\,000\,\mu\text{m}}{80\,\mu\text{m}} = 350$
• The magnification is $\times 350$, which corresponds to option B.

You can sanity-check this: an epithelial cell is typically about $20\,\mu\text{m}$ wide, and in the diagram each cell is roughly $7\,\text{mm}$ across. $7000/20 = 350$, consistent with the scale-bar calculation.

Key Takeaways

• Magnification is image size divided by actual size; both must be in the same unit.
• A labelled scale bar on a diagram lets you calculate magnification without knowing the object's real size.
• For paper-based measurements, convert mm to µm ($\times 1000$) before dividing.

Common Mistakes

• Forgetting to convert units. Dividing $28\,\text{mm}$ by $80\,\mu\text{m}$ directly gives $0.35$ — a tempting trap that points to option A ($\times 35$). Always convert first.
• Using the wrong end of the scale bar. Some figures have a scale with major divisions; make sure you measure the full length indicated by the label, not just one subdivision.
• Confusing magnification with resolution. Magnification is a ratio (no units); resolution is the smallest distance two points can be distinguished (a real distance, in nm or µm). They are not interchangeable.

Things to Be Careful About

• The scale bar label is $80\,\mu\text{m}$ (micrometres), NOT $80\,\text{nm}$ or $80\,\text{mm}$. A nanometre-scale bar would be unrealistic for a light micrograph of whole cells.
• Significant figures: a measurement taken with a millimetre ruler is only reliable to about $\pm 1\,\text{mm}$, so a quoted magnification of $\times 350$ is appropriate; do not write $\times 347$ or similar over-precise figures.
• Diagrams of light-micrograph tissue typically sit in the $\times 100$–$\times 1000$ range; $\times 35$ is too low (it would not show cell detail) and $\times 35\,000$ belongs to electron micrographs, not this kind of line drawing.