Biology 9700/13 — May/June 2018

Background Concept

A light microscope carries two measuring devices: a stage micrometer (a slide with a precisely engraved scale, usually 1 mm divided into 0.01 mm or 0.1 mm divisions) and an eyepiece graticule (a small scale — typically 100 arbitrary units — etched onto a disc that sits inside the eyepiece). The graticule has no fixed real length; the same graticule unit corresponds to a different real length at each objective lens because the magnification of the objective changes how big the graticule's image appears. To turn "graticule units" into micrometres you must calibrate the graticule at each objective, by lining the two scales up on a stage micrometer and reading how many graticule units span a known stage-micrometer distance. Once calibrated, the value ($\mu\text{m}$ per graticule unit) is fixed for that objective until the microscope is changed.

To measure a specimen: count the graticule units it spans, then multiply by the calibration for the objective in use. The result is the actual (real) size of the specimen, not the magnified image. Magnification is the ratio image size / actual size, so actual size = image size / magnification — equivalent to multiplying the graticule reading (the image size in calibrated units) by the calibration factor.

Understanding the Question

The question asks which of the four listed steps are actually required to find the actual width of a xylem vessel viewed under the $\times 10$ objective. The candidate has to decide, for each step, whether it is correct, unnecessary, or actively wrong. Two steps are correct, two contain a deliberate error, and only one combination of the four options matches the correct pair.

Approach

Test each statement in turn against the standard procedure and the unit relationships:

1. Check the unit conversion factor in step 1.
2. Check whether the calibration in step 2 uses the correct objective.
3. Check that step 3 is the correct way to obtain a measurement.
4. Check that step 4 correctly converts the graticule reading into an actual length.

Then select the option that contains exactly the correct steps.

Step-by-Step Reasoning

Step 1 — Convert mm to μm by multiplying by $10^{-3}$.
Since $1\text{ mm} = 10^{3}\text{ μm} = 1000\text{ μm}$, converting a length from mm to μm requires multiplication by $10^{3}$, not $10^{-3}$. Multiplying by $10^{-3}$ would give the value in metres. The step is wrong, and in any case a stage micrometer's divisions are already small enough that no further $\text{mm} \rightarrow \mu\text{m}$ conversion is needed if you use the micrometer's stated units correctly.

Step 2 — Calibrate using the stage micrometer on the $\times 4$ objective.
Each objective magnifies the graticule image by a different amount, so the calibration ($\mu\text{m}$ per graticule division) is different at $\times 4$ and at $\times 10$. The calibration must be carried out on the same objective that will be used for the measurement — here $\times 10$. A calibration done at $\times 4$ is invalid for the $\times 10$ measurement, so this step is wrong.

Step 3 — Measure the width using the eyepiece graticule.
This is exactly the correct method: while looking at the specimen through the $\times 10$ objective, count the number of graticule units the xylem vessel spans from one wall to the other. ✓

Step 4 — Multiply the graticule units by the calibration.
The calibration is expressed in $\mu\text{m}$ (or sometimes $\text{mm}$) per graticule division at the relevant objective. Multiplying the graticule reading (divisions) by the calibration ($\mu\text{m}$ per division) gives a real length in $\mu\text{m}$ — the actual width of the vessel. ✓

Only steps 3 and 4 are correct, so the answer is D (3 and 4 only).

Key Takeaways

• The eyepiece graticule is a unitless scale; it must be calibrated against a stage micrometer at each objective lens before it can give a real length.
• Calibration is always done on the same objective used for the measurement — a calibration at one magnification does not transfer to another.
• Actual size of a specimen (in $\mu\text{m}$) = (number of graticule divisions) × (calibration at the chosen objective, in $\mu\text{m}$ per division).
• $1\text{ mm} = 10^{3}\text{ μm}$ and $1\text{ μm} = 10^{3}\text{ nm}$; converting up the scale multiplies by $10^{3}$, converting down divides by $10^{3}$ (or multiplies by $10^{-3}$).

Common Mistakes

• Wrong conversion direction: writing "multiply by $10^{-3}$ to go from mm to μm" — you are going from a larger unit to a smaller unit, so the number must increase, not decrease.
• Cross-objective calibration: assuming one calibration applies to every objective on the microscope. The graticule is in the eyepiece, but the objective determines the magnification of everything visible, including the graticule image.
• Confusing the role of the graticule: thinking the graticule itself measures micrometres, rather than an arbitrary count that has to be converted using the calibration.
• Forgetting the calibration step entirely: measuring with the graticule but not multiplying by the calibration, so the "answer" is left in meaningless graticule units.

Things to Be Careful About

• Quote the calibration in the same unit as the answer you want; if calibration is in mm per division, convert the result to μm ($\times 10^{3}$) before giving the final answer.
• Always re-calibrate if the microscope, the eyepiece, or the objective is changed — calibrations are not transferable between instruments.
• A stage micrometer is used only for calibration; never for measuring the specimen itself.
• Use the correct power of ten for unit conversions — this is the most commonly failed point in this style of MCQ.