Biology 9700/13 — October/November 2021

Background Concept

A photomicrograph is an enlarged photograph taken down a microscope. The magnification of the photograph tells you how many times larger the image is than the real specimen. It is calculated using the formula:

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

A scale bar is a short line printed on the micrograph with a label giving the real (actual) length that the line represents. In this question, the scale bar represents $2\ \text{µm}$ of real specimen. So if the scale bar is $L$ millimetres long on the printed image, then $L\ \text{mm}$ of image corresponds to $2\ \text{µm}$ of actual specimen.

Because the magnification compares like-with-like, both the image size and the actual size must be in the same units. This is why the millimetre measurement has to be converted to micrometres (multiply by 1000) before the division.

Understanding the Question

The student has a photomicrograph of a cell with a scale bar labelled $2\ \text{µm}$ and must decide which of four manipulations of the scale bar length will give the magnification of the cell. The command word is implicit but clear: choose the correct method.

Approach

Use the magnification formula on the scale bar itself. The image size of the scale bar (measured in mm on the page) divided by the actual size it represents (2 µm) gives the magnification. Convert the mm measurement to µm so that the two quantities in the formula share units, then divide by 2.

Step-by-Step Reasoning

1. State the formula. Magnification = image size / actual size.
2. Identify image and actual sizes for the scale bar. Image size = measured length of scale bar on the page (mm). Actual size = 2 µm (printed next to the bar).
3. Convert units. Convert the image size from mm to µm by multiplying by 1000.
4. Divide by the actual size. Divide the converted image size by 2 (the actual size in µm).
5. Check option C. "Measure the length of the scale bar in millimetres, convert to micrometres and divide by 2" matches the procedure exactly.
6. Eliminate the others:
   • A divides the cell's image size by the scale bar's image size. Both are in image units, so this gives a dimensionless ratio of two lengths on the page — not the magnification.
   • B has the wrong structure: it multiplies the cell's image size by 2000 and divides by the scale bar's image size. This combines a conversion factor and a ratio in a way that does not produce a magnification.
   • D multiplies by 2 instead of dividing by 2, which inverts the result and gives an answer 4× too large.

Key Takeaways

• Magnification = image size / actual size, with both quantities in the same units.
• A scale bar is a direct way of finding the magnification of the whole photograph: measure the bar on the page, convert to the same units as the printed actual length, then divide.
• Always check the units — a mm/µm mix-up is the most common error.

Common Mistakes

• Treating the scale bar as if it gives the cell's magnification directly, rather than the image's overall magnification.
• Forgetting to convert mm to µm and so dividing, say, 10 by 2 and writing "5" as the magnification, when the real answer is 5000×.
• Multiplying by 2 instead of dividing by 2 (option D) — the scale bar represents 2 µm, so the actual size in the denominator is 2, not the multiplier.
• Dividing the cell's image size by the scale bar's image size (option A) — this gives a relative size, not a magnification.

Things to Be Careful About

• The magnification found from the scale bar applies to the whole photograph, not just the cell. It can then be used to find any structure's actual size: actual size = image size / magnification.
• Always state the magnification with an "×" (e.g. ×5000) so it is not confused with an absolute size.
• Use proper unit notation: mm, µm, nm — note the Greek mu (µ) in micrometres, not the English 'u'.