The microscope in cell studies

Magnification is simply how many times larger the image is than the real object. It is a dimensionless ratio calculated from

$M = \dfrac{I}{A}$

where $I$ is the image size (measured from the photograph or drawing) and $A$ is the actual size of the specimen. You can magnify any image arbitrarily by photographing it or zooming in on a screen.

Resolution, by contrast, is the minimum distance between two points at which they can still be told apart. Below the resolution limit, two distinct points merge into a single blur and no amount of further magnification can recover the information. Resolution is set by the wavelength of the radiation used to form the image: the minimum resolvable distance is approximately $\lambda / 2$.

Visible light has wavelengths of about 400–700 nm, so a light microscope cannot resolve detail finer than approximately 200 nm — about the diameter of a small mitochondrion. Pushing the magnification past ×1500 produces an image that is larger and blurrier but no more detailed — a phenomenon called empty magnification.

To see finer structures the radiation has to have a shorter wavelength. Accelerated electrons have a de Broglie wavelength of approximately 0.005 nm, which (after lens-aberration limits are accounted for) allows the transmission electron microscope to resolve detail down to about 0.5 nm — fine enough to see individual ribosomes and the bilayer of a membrane.

Cells and their components span six orders of magnitude in size, so 9700 routinely uses three units:

Unit	Symbol	Size in metres	Typical use
millimetre	mm	$10^{-3}$ m	Whole organs, scale bars
micrometre	μm	$10^{-6}$ m	Cells, large organelles
nanometre	nm	$10^{-9}$ m	Membranes, ribosomes, viruses

The conversions to memorise:

$1 \text{ mm} = 10^3 \text{ μm} = 10^6 \text{ nm}$

When you apply $M = I/A$, always convert image size and actual size to the same unit first. If the question gives a scale bar in mm and a structure size in μm, choose one unit and convert before substituting. Cambridge mark schemes deduct marks for forgetting to convert.

Typical sizes to recognise:

• Bacterium: 1–5 μm.
• Animal cell: 10–30 μm; plant cell: 30–100 μm.
• Mitochondrion: 0.5–2 μm long.
• Chloroplast: 5–10 μm.
• Ribosome: ~20 nm.
• Cell membrane bilayer: ~7 nm thick.
• Virus: 20–300 nm.

A light microscope (sometimes called an optical or compound microscope) uses a beam of visible light from below, focused through a series of glass lenses — typically a condenser, an objective and an eyepiece (ocular) lens. The total magnification is the product of the objective and eyepiece magnifications: a ×40 objective with a ×10 eyepiece gives ×400 total.

Advantages.

• Specimens can be living. This is the only way to observe processes such as cytoplasmic streaming or mitosis in real time.
• Colour images are possible — natural pigment colours are preserved, and a wide range of coloured stains (methylene blue, eosin, iodine) provide contrast.
• Cheap, portable and easy to operate. Used in schools, clinics and research labs.

Limitations.

• Resolution is limited to approximately 200 nm by the wavelength of visible light, so individual ribosomes (~20 nm), the bilayer of a membrane (~7 nm) and most viruses cannot be resolved.
• Useful magnification stops at around ×1500. Beyond this is empty magnification.

Specimen preparation. Tissue is fixed (e.g. formaldehyde) to preserve structure, dehydrated, embedded in wax, sectioned with a microtome (typically 5–20 μm thick), mounted on a slide, stained and covered with a coverslip. Living specimens such as protoctists or onion epidermis can be mounted directly in water.

In a TEM, a beam of accelerated electrons (typically 100–300 kV) is fired through an ultra-thin section of specimen held in a high vacuum. Electromagnetic lenses focus the beam onto a fluorescent screen or detector. Regions of the specimen that contain more heavy-metal stain absorb more electrons and appear darker on the final image.

Specimen preparation is extensive and destructive:

1. Tissue is fixed (usually with glutaraldehyde and then osmium tetroxide).
2. Dehydrated through an alcohol series.
3. Embedded in epoxy resin.
4. Cut into ultra-thin sections (50–100 nm thick) using an ultramicrotome with a glass or diamond knife.
5. Sections are placed on a copper grid and stained with heavy-metal salts (uranyl acetate, lead citrate) that scatter electrons.

Because the column is held in a vacuum, living specimens cannot be imaged — they would explode as their water vaporises.

Image. Monochrome (black-and-white) two-dimensional projection of the section. Reveals internal ultrastructure: cristae of mitochondria, thylakoids of chloroplasts, ribosomes on rER, the trilaminar appearance of the cell-surface membrane (dark-light-dark).

Resolution and magnification. Resolution ~0.5 nm; useful magnification up to ~×500 000.

Limitations. Specimens must be dead and ultra-thin; the preparation may introduce artefacts; the equipment is expensive, large and requires a vibration- and field-free environment.

In an SEM, a focused electron beam is scanned across the surface of a metal-coated specimen in a raster pattern. As the primary beam strikes the surface, secondary electrons are knocked out of the specimen and collected by a detector positioned at an angle. The intensity of the secondary-electron signal at each point of the scan is used to build up the image.

Because the image is built from surface emissions, the SEM produces an image with apparent three-dimensional depth — surface features such as the spines on a pollen grain, the surface of a leaf, or the microvilli of an epithelial cell appear with topographic relief.

Specimen preparation. Specimens are fixed, dehydrated and sputter-coated with a thin film of a heavy metal (typically gold or platinum) to provide a good source of secondary electrons.

Resolution and magnification. Resolution ~3–10 nm; useful magnification up to ~×100 000.

When to choose SEM over TEM.

• Use SEM if you want to study the SURFACE of an intact specimen — e.g. the texture of cell-surface microvilli, the shape of viruses on a host cell, the surface of a biofilm.
• Use TEM if you want to study the INTERNAL ultrastructure of a thin section — e.g. mitochondrial cristae, ribosomes on the rER.

Feature	Light microscope (LM)	TEM	SEM
Source	Visible light, λ 400–700 nm	Electron beam, λ ≈ 0.005 nm	Electron beam, λ ≈ 0.005 nm
Lenses	Glass	Electromagnetic	Electromagnetic
Resolution	~200 nm	~0.5 nm	~3–10 nm
Maximum useful magnification	~×1500	~×500 000	~×100 000
Specimen	Living or dead	Dead, ultra-thin (50–100 nm)	Dead, surface-coated
Stain	Coloured dyes (methylene blue, eosin)	Heavy-metal salts (uranyl acetate, lead citrate)	Sputter coat (gold/platinum)
Image	Coloured, 2-D, real-time	Monochrome, 2-D internal ultrastructure	Monochrome, 3-D surface topography
Vacuum required?	No	Yes (high vacuum)	Yes (high vacuum)
Cost / size	Cheap, portable	Expensive, large	Expensive, large

How to use this table in an exam. When asked to ‘compare’, give the SAME row for BOTH (or all three) instruments — e.g. ‘LM resolution ~200 nm whereas TEM resolution ~0.5 nm’. Saying only ‘TEM has higher resolution’ scores half a mark.

An eyepiece graticule is a transparent disc engraved with a numbered scale (typically 0–100). It is inserted into the eyepiece of a light microscope so that the scale appears superimposed on the specimen image. The eyepiece graticule has the same number of divisions at every magnification — but each division corresponds to a different real-world length at each magnification.

A stage micrometer is a microscope slide carrying an accurately engraved scale — usually 1 mm divided into 100 divisions of 10 μm each.

Calibration procedure (e.g. at ×400):

1. Place the stage micrometer on the stage and focus.
2. Rotate the eyepiece so its scale is parallel to the stage micrometer scale.
3. Align the zero marks of both scales.
4. Count how many eyepiece divisions (epd) span a known number of stage micrometer divisions.
5. Convert. For example, if 50 epd span 100 stage divisions (= 1000 μm), then 1 epd = 20 μm at ×400.

Using the calibrated graticule. Remove the stage micrometer and place the actual specimen on the stage at the SAME magnification. Measure structures by counting eyepiece divisions and multiplying by the calibration value.

Re-calibrate every time you change objective lens — calibration values are unique to each magnification.

Every magnification calculation in 9700 reduces to four steps.

Step 1 — Identify $I$ and $A$. The image size ($I$) is what you measure on the photograph or drawing. The actual size ($A$) is provided in the question or read from a scale bar.

Step 2 — Convert. Express both $I$ and $A$ in the SAME unit. Use $1 \text{ mm} = 10^3 \text{ μm} = 10^6 \text{ nm}$.

Step 3 — Substitute into

$M = \dfrac{I}{A}$

(or, if the question gives $M$ and $I$ and asks for $A$, rearrange to $A = I/M$).

Step 4 — Quote the answer. Magnification has no units (write ‘×500’ or just ‘500’). Actual sizes should be quoted in an appropriate unit — μm for whole cells / organelles, nm for membranes / ribosomes / viruses.

Sanity check against expected sizes (see the at-a-glance section). An ‘actual mitochondrion’ of 8 mm or a ‘ribosome’ of 0.001 nm means you have made a unit-conversion error.