Biology 9700/12 — May/June 2011

Background Concept

Microscopes do not directly give you the real size of a specimen. The eyepiece graticule is a tiny scale (usually 100 divisions) etched onto a glass disc that sits inside the eyepiece lens; when you look down the microscope you see the graticule scale superimposed on the specimen. Each division has no fixed real-world size — the value of one graticule unit depends on the magnification of the objective lens being used. That is why a stage micrometer is needed. A stage micrometer is a slide with a precisely known scale (e.g. $0.01\ \text{mm}$ per division). By lining up the graticule against the stage micrometer at a given magnification, you can work out what one graticule unit represents in real units. Once calibrated, you can swap the stage micrometer for your specimen slide and simply count the graticule units across the structure of interest, then multiply by the calibration.

The standard conversions you must know:

• $1\ \text{mm} = 1000\ \mu\text{m}$
• $1\ \mu\text{m} = 1000\ \text{nm}$
• So $1\ \text{mm} = 10^{6}\ \text{nm}$

Most cells sit comfortably in the $\mu\text{m}$ range, so converting to $\mu\text{m}$ at the end is normal practice.

Understanding the Question

The question has already done the calibration step for you and tells you that one eyepiece graticule unit equals $0.005\ \text{mm}$ at the magnification being used. The diameter of a spongy mesophyll cell spans 3.5 of those units on the graticule. The command word "estimate" signals that a single multiplication (with a sensible unit conversion) is all that is required; you do not need to think about uncertainty, calibration curves or anything else.

Approach

Multiply the number of graticule units by the real length of one unit, then convert the answer from millimetres to micrometres so the magnitude sits in a familiar range for cell dimensions.

Step-by-Step Reasoning

1. Multiply graticule units by the calibration: $$3.5 \times 0.005\ \text{mm} = 0.0175\ \text{mm}$$
2. Convert mm to μm using $1\ \text{mm} = 1000\ \mu\text{m}$: $$0.0175\ \text{mm} \times \frac{1000\ \mu\text{m}}{1\ \text{mm}} = 17.5\ \mu\text{m}$$
3. Match to the options. $17.5\ \mu\text{m}$ rounds to $18.0\ \mu\text{m}$ — option C.

The distractors are the classic place-marking traps: option A is three orders of magnitude too small (forgot to convert mm to μm and treated $0.0175$ as the final answer in μm), B is one order of magnitude too small (forgot one of the unit conversions), and D is one order of magnitude too large (moved the decimal the wrong way).

Key Takeaways

• A graticule reading is meaningless without first calibrating it against a stage micrometer at the same magnification.
• One graticule unit is some number of mm; multiply by the count and always convert to a sensible unit (μm for cells, nm for organelles/viruses, mm for larger structures).
• Order-of-magnitude errors are the most common trap here — always sanity-check against what you know about typical cell sizes (eukaryotic cells ≈ $10$–$100\ \mu\text{m}$).

Common Mistakes

• Forgetting to convert mm to μm and reporting $0.0175$ as the answer, or worse treating it as $0.0175\ \mu\text{m}$ (option A).
• Moving the decimal in the wrong direction during the $\times 1000$ conversion, giving $180$ instead of $18$ (option D) or $1.8$ (option B).
• Adding instead of multiplying the graticule units with the calibration value.
• Using the wrong end of the stage micrometer scale during the original calibration — make sure you align the two scales at both ends before averaging, because objectives are not perfectly parfocal between slides.

Things to Be Careful About

• State units at every step; CIE examiners reward a correct unit on a numerical answer.
• The answer should be given to the same number of significant figures as the data supports (3.5 units × 0.005 mm → answer to ~2 sig figs, so $18\ \mu\text{m}$ or $17.5\ \mu\text{m}$ are both acceptable forms).
• This is a recall/application of a practical skill — there is no penalty for showing the working, and on later, longer questions the working is what carries the marks.