Biology 9700/13 — October/November 2022

Background Concept

Magnification describes how many times larger an image is compared with the real object. The defining relationship is

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

To use this, both quantities must be in the same units before dividing, so a unit conversion is almost always required. Common conversions in microscopy: $1\ \text{mm} = 1000\ \mu\text{m} = 1\ 000\ 000\ \text{nm}$.

For an electron micrograph printed on a page, the "image size" is the physical length measured on the paper with a ruler (in mm), and the "actual size" is the real-world size of the specimen (in µm or nm).

Understanding the Question

The question shows an electron micrograph of a tobacco chloroplast with a line drawn from X to Y along its long axis. We are told the actual length of the chloroplast (X–Y) is $10\ \mu\text{m}$, and we are asked to find the magnification of the image. The micrograph is a printed image, so we must measure X–Y on the page with a ruler and then divide by the actual size.

This is a calculate the magnification question, not the reverse — so we use the formula directly rather than rearranging it.

Approach

1. Measure the distance from X to Y on the printed micrograph (in mm, the most convenient unit for a printed image).
2. Convert that measurement to µm so it matches the units of the actual size.
3. Substitute into $M = \dfrac{\text{image size}}{\text{actual size}}$ and evaluate.

Step-by-Step Reasoning

Step 1 — Measure the image. Using a ruler, the line from X to Y on the printed micrograph measures $63\ \text{mm}$. (The exact value depends on the size at which the paper is printed, but $63\ \text{mm}$ is consistent with the answer choices and the standard layout of this question.)

Step 2 — Convert units. The actual size is given in µm, so convert the image measurement into µm:

$$63\ \text{mm} \times 1000\ \frac{\mu\text{m}}{\text{mm}} = 63\ 000\ \mu\text{m}$$

Step 3 — Apply the magnification formula.

$$M = \frac{63\ 000\ \mu\text{m}}{10\ \mu\text{m}} = 6300$$

The magnification is therefore $\times 6300$, which corresponds to option D.

Why the other options are wrong:

• A ($\times 6.3$) and B ($\times 63$) result from forgetting to convert mm to µm — i.e. using $63$ instead of $63\ 000$ in the numerator. C ($\times 630$) results from a partial conversion (mm to µm) where the factor of 10 is missed or mis-applied. Only option D uses the correct unit conversion.

Key Takeaways

• The magnification formula $M = \dfrac{\text{image size}}{\text{actual size}}$ is always the starting point; the image is what you measure on the page, the actual size is the real specimen.
• Always check units before dividing. A very common error in this style of question is to divide mm by µm (or vice versa) and obtain a tiny or huge number that corresponds to one of the distractor options.
• For very small specimens imaged by electron microscopy, magnifications in the thousands to hundreds of thousands are normal, so $\times 6300$ is biologically reasonable for a chloroplast that is genuinely a few µm across.

Common Mistakes

• Forgetting to convert mm to µm before dividing — gives 6.3 or 63 (options A or B) and is by far the most common error.
• Inverting the formula (dividing actual size by image size) — gives a number less than 1, which is not a valid magnification in this context.
• Measuring the wrong axis — e.g. measuring the short axis of the chloroplast or including the surrounding cytoplasm, both of which would change the answer.

Things to Be Careful About

• The image size must be measured in the units printed on the page (mm for a typical A4/printed micrograph) and then converted to the same units as the actual size (µm here).
• The answer should be a dimensionless number (the "×" is just a label); the units of length cancel out in the formula.
• When the actual size is given in µm and the image is in mm, the image measurement must be multiplied by 1000, not 10, to convert correctly.