The microscope in cell studies

1. Overview

Cells are far too small to see with the unaided eye, so biologists use microscopes to study them. A light microscope uses visible light and glass lenses, while an electron microscope uses a beam of electrons. To make sense of what we see we must be able to prepare specimens, draw them accurately, and turn the size of an image into the actual size of the specimen. The two ideas that run through everything in this topic are magnification (how many times bigger the image is) and resolution (how much detail can be seen). These are different properties, and electron microscopes are powerful mainly because of their far higher resolution, not just higher magnification.

Key Definitions

• Magnification: how many times larger an image of a specimen is compared with the actual (real) size of the specimen.
• Resolution: the smallest distance between two points that can still be seen as two separate points rather than as one blurred point.
• Photomicrograph: a photograph of a specimen taken through a light microscope.
• Electron micrograph: an image of a specimen produced by an electron microscope (scanning or transmission).
• Eyepiece graticule: a small transparent scale fitted into the microscope eyepiece, used to measure the size of a specimen in eyepiece units.
• Stage micrometer: an accurate scale on a microscope slide, used to calibrate (find the real value of) the eyepiece graticule divisions at each magnification.
• Temporary preparation: a slide of fresh cellular material made quickly for immediate viewing, not preserved for long-term storage.
• Scale bar: a labelled line on a micrograph or drawing showing the real length that the line represents on the specimen.

Content

Making a temporary preparation

A temporary preparation is a slide made quickly from fresh material so it can be viewed straight away. A common example is a slice of onion epidermis or a smear of cheek cells. The usual steps are:

• Place a small, thin piece of the specimen onto a clean glass slide. The material must be thin so light can pass through it.
• Add a drop of liquid — often water, or a stain such as iodine or methylene blue. A stain adds contrast so structures like the nucleus and cell wall become visible.
• Lower a cover slip gently at an angle, often using a mounting needle, so that air bubbles are not trapped underneath (a bubble has a dark edge and can be mistaken for a cell).
• Press out any excess liquid with filter paper and view first on low power, then switch to higher power once the specimen is in focus.

Drawing cells from slides and photomicrographs

Biological drawings have their own conventions, and following them gains marks:

• Use a sharp pencil and draw clear, continuous lines — no sketchy or overlapping lines.
• Do not add shading or colour.
• Draw only what you can actually see; keep the proportions of the structures correct.
• For a plan (low-power) drawing of a tissue, show only the boundaries between tissues — do not draw individual cells inside them.
• For a high-power drawing, show the structure of a few representative cells in detail.
• Add a title, label lines (drawn with a ruler, not crossing each other), and where possible a magnification or scale bar.

Magnification calculations

Magnification is found from:

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

Picture these three quantities as a triangle — image size on top, with actual size and magnification side by side below it — so you can read off the other two arrangements:

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

The single most important step is to make sure the image size and actual size are in the same units before dividing. The unit conversions you must know are:

• 1 mm = 1000 µm
• 1 µm = 1000 nm
• 1 mm = 1 000 000 nm

A magnification has no units because it is a ratio of two lengths.

Worked example

Exam-style question: A student photographs a plant cell through a light microscope. On the photomicrograph the cell measures 36 mm long. The magnification of the photomicrograph is ×400. Calculate the actual length of the cell in micrometres. [3]

Model answer:

• Convert the image size to micrometres: 36 mm × 1000 = 36 000 µm.
• Rearrange the equation: actual size = image size ÷ magnification = 36 000 ÷ 400.
• Actual length = 90 µm (1 mark for conversion, 1 for correct working, 1 for the answer with the correct unit).

Working from electron micrographs and scale bars

The same equation applies to electron micrographs, including both scanning electron microscope (SEM) images (which show 3-D surface detail) and transmission electron microscope (TEM) images (which show thin internal sections). Many micrographs do not state a magnification directly; instead they carry a scale bar. To use one:

• Measure the printed length of the scale bar with a ruler.
• Read the real length it represents (e.g. a bar labelled "2 µm").
• The magnification of the whole image equals the measured bar length divided by the real length it represents (in the same units).

A quicker route avoids working out the magnification at all: just scale the structure directly against the bar. If a bar labelled "2 µm" measures 20 mm on the print and a mitochondrion measures 30 mm, its actual length is $\frac{30}{20} \times 2 = 3\ \mu\text{m}$ — that is, the measured structure length divided by the measured bar length, times the real value of the bar.

Using an eyepiece graticule and stage micrometer

An eyepiece graticule is a scale inside the eyepiece, but its divisions are arbitrary "eyepiece units" — they only mean a real length once they have been calibrated. Calibration uses a stage micrometer, an accurately ruled scale on a slide (each small division is usually 0.01 mm = 10 µm). The whole process has three stages:

1. Calibrate. Line up the eyepiece graticule against the stage micrometer at the magnification you will use. Count how many stage-micrometer divisions match a known number of eyepiece divisions, then work out the real length of one eyepiece division.
2. Recalibrate for each objective. Changing the objective changes the apparent size, so the value of one eyepiece division is different at every magnification. A calibration done on low power cannot be reused on high power — you must redo step 1 whenever you change objective.
3. Measure your specimen. Remove the stage micrometer, view your specimen, count the eyepiece divisions it covers, and multiply by the value of one division to get its real size.

A quick way to find the real length of one eyepiece division is:

$$\text{1 eyepiece division} = \frac{\text{number of stage divisions} \times \text{length of one stage division}}{\text{number of eyepiece divisions}}$$

Always choose the right unit for the structure — mm for tissues, µm for cells and many organelles, and nm for very small structures such as membranes.

Worked example

Exam-style question: A student lines up an eyepiece graticule against a stage micrometer and finds that 100 eyepiece divisions exactly match 25 stage-micrometer divisions. Each stage-micrometer division is 0.01 mm. The student then removes the micrometer and measures a single cell that spans 40 eyepiece divisions. Calculate the actual length of the cell in micrometres. [3]

Model answer:

• Find the real length covered by 25 stage divisions: 25 × 0.01 mm = 0.25 mm = 250 µm.
• So 100 eyepiece divisions = 250 µm, meaning 1 eyepiece division = 250 ÷ 100 = 2.5 µm.
• The cell spans 40 eyepiece divisions, so actual length = 40 × 2.5 = 100 µm (1 mark for the calibration of one division, 1 for correct working, 1 for the answer with the correct unit).

Resolution versus magnification

Magnification makes an image bigger; resolution is how much detail that image contains. The two are independent: enlarging an image beyond a certain point ("empty magnification") just makes a blur larger without revealing anything new.

Resolution is limited by the wavelength of the radiation used. Visible light has a long wavelength, so a light microscope cannot separate very close points; a beam of electrons behaves as a wave with a far shorter wavelength, which is why the electron microscope resolves much finer detail. The key figures to learn are summarised below:

Property	Light microscope	Electron microscope
Radiation used	visible light (≈ 400–700 nm)	beam of electrons (much shorter wavelength)
Approximate resolution	about 200 nm	about 0.2 nm
Maximum useful magnification	around ×1500	around ×500 000

The electron microscope's resolution is roughly a thousand times better (200 nm ÷ 0.2 nm = 1000). This is why it can reveal small organelles such as ribosomes and the detail of membranes, while a light microscope cannot.

Key Equations

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

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

$$\text{1 eyepiece division} = \frac{\text{number of stage divisions} \times \text{length of one stage division}}{\text{number of eyepiece divisions}}$$

Useful conversions: 1 mm = 1000 µm; 1 µm = 1000 nm; 1 mm = 1 000 000 nm.

Common Mistakes to Avoid

• Muddling unit conversions in a calculation. The commonest error is mixing millimetres and micrometres. Convert both lengths to the same unit first, remembering that 1 mm = 1000 µm, before you divide.
• Giving magnification a unit. Magnification is a ratio of two lengths, so it is just a number (e.g. ×400) with no units — only the actual size carries a unit.
• Calling the double membrane round the nucleus the "nuclear membrane". When labelling an electron micrograph, use the precise term nuclear envelope for the double membrane surrounding the nucleus.
• Adding shading or drawing cells in a plan drawing. A plan (low-power) drawing shows only the boundaries between tissues — clear continuous pencil lines, with no shading and no individual cells.
• Putting units inside a results table. Place units only in the column headings, separated by a forward slash (for example "Length / µm"), and keep the body of the table for numbers only.
• Treating magnification and resolution as the same thing. Magnification enlarges the image; resolution is the detail it can show. Saying an electron microscope "magnifies more" misses the point — its real advantage is far higher resolution.
• Forgetting to recalibrate the graticule. The value of one eyepiece division changes with each objective, so a calibration done on low power cannot be reused on high power.

Exam Tips

• In any size calculation, show your working line by line and write the unit at every stage — method marks are given even if the final number slips.
• Memorise the triangle — image size on top, actual size and magnification below — so you can rearrange the equation instantly to find any one of the three.
• For graticule questions, calibrate one eyepiece division first, then multiply by the number of divisions the specimen covers — do not try to do it in a single step.
• When a micrograph has a scale bar, measure it with your ruler first; this is usually the intended route to the magnification.
• Quote the right unit for the scale of the structure: mm for tissues, µm for cells and most organelles, nm for membranes and very fine detail.
• For "explain the difference between resolution and magnification" questions, define both terms and link the higher resolution of electron microscopes to the shorter wavelength of electrons.
• Use precise terms in drawings and answers — nuclear envelope, photomicrograph versus electron micrograph — to pick up vocabulary marks.