Microscopy

Magnification is how many times larger the image is than the actual (real) size of the object — it is the size of the image divided by the size of the object, $M = I/A$.

It has no units because it is a ratio of two lengths (image size and actual size): when one length is divided by another the units cancel, leaving a pure number such as ×400.

Most cell structures are transparent and colourless, so they have very little contrast with the background and with each other and are difficult to see.

A stain is a coloured chemical that binds to particular structures and absorbs light, making those structures appear darker and more visible — this increases the contrast.

Because different stains bind to (have an affinity for) different structures, more than one stain can be used to distinguish components from one another (for example colouring the nucleus differently from the cytoplasm). This is differential staining.

A light microscope uses a beam of light passing through the specimen, so the specimen does not need to be in a vacuum and can be alive and moving — exactly what is needed to watch living protoctists swim.

An electron microscope requires the specimen to be placed in a vacuum, so the organisms would be dead (and dehydrated), and they could not be observed alive or moving.

In addition, a light microscope shows specimens in their natural colour, is cheap and portable, and the resolution (~200 nm) is more than enough to see whole single-celled organisms.

The amount of detail a microscope can show depends on its resolution — the shortest distance between two points that can still be seen as two separate points. The higher the resolution, the more detail is visible.

Resolution is limited by the wavelength of the radiation used to view the specimen: a microscope cannot resolve two points closer together than about half that wavelength.

A light microscope uses light, which has a relatively long wavelength (about 400–700 nm). This limits its resolution to about 200 nm, so structures closer than this merge into one and cannot be seen.

An electron microscope uses a beam of electrons, which behave as waves with a much shorter wavelength than light. This gives a far higher resolution (about 0.1–0.5 nm).

Because its resolution is around a thousand times better, the electron microscope can distinguish much smaller structures — such as ribosomes and the internal membranes of organelles — that a light microscope cannot resolve, so it shows much more detail.

How the image is formed. In a TEM, a beam of electrons is transmitted through an extremely thin section of the specimen; denser regions absorb more electrons and appear darker. In an SEM, the electron beam is scanned across the surface of a whole specimen and the electrons that are reflected (bounced off) the surface are detected to build the image.

Type of image. Because the electrons pass through a thin slice, the TEM produces a highly detailed two-dimensional image of the internal structure of the cell, showing organelles and membranes. Because the SEM detects electrons reflected from the surface, it produces a three-dimensional image of the surface of the specimen.

Resolution. The TEM has the higher resolution (about 0.5 nm), so it shows finer internal detail; the SEM has a lower resolution (a few nm), but its advantage is the 3-D surface view.

Similarities. Both use electromagnets as lenses, both require the specimen to be dead and held in a vacuum, both produce black-and-white images (false colour may be added later), and both can introduce artefacts during preparation. Overall, a TEM is chosen for detailed internal structure and an SEM for 3-D surface appearance.

(a) Use the magnification equation rearranged for actual size:

$A = \frac{I}{M} = \frac{48\ \text{mm}}{8000} = 0.006\ \text{mm}$

Convert to micrometres: $0.006\ \text{mm} \times 1000 = 6\ \text{µm}$.

So the actual diameter of the nucleus is 6 µm (a realistic value for a nucleus), quoted to 1 significant figure to match the precision of the data.

(b) A scale bar representing a real length of 2 µm, drawn at ×5000, has an image length of:

$I = M \times A = 5000 \times 2\ \text{µm} = 10\,000\ \text{µm} = 10\ \text{mm}$

So the scale bar would be drawn 10 mm long.

First the student must calibrate the eyepiece graticule, because one graticule division does not correspond to a fixed real length and changes with the objective lens.

She places the stage micrometer — a slide with an accurately engraved scale of known real length (e.g. divisions of 0.01 mm = 10 µm) — on the microscope stage and focuses on it.

She then lines up the eyepiece graticule scale against the stage micrometer scale and counts how many eyepiece divisions correspond to a known real distance on the stage micrometer.

She calculates the real length of one eyepiece division by dividing the known stage-micrometer distance by the number of eyepiece divisions it covers (for example, if 50 eyepiece divisions cover 100 µm, one division = 2 µm).

She then removes the stage micrometer and places the slide of plant cells under the same objective lens. She measures the diameter of the cell in eyepiece divisions.

Finally she multiplies the number of eyepiece divisions across the cell by the calibrated value of one division to obtain the real diameter in µm. She must recalibrate if she changes the objective lens, and should measure several cells and take a mean to improve reliability.

Describe the relationship. As the best resolution value decreases (from 200 nm for the light microscope, to 5 nm for the SEM, to 0.5 nm for the TEM), the smallest structure that can be clearly seen also gets smaller (from a mitochondrion of ~1000 nm, to a virus surface of ~100 nm, to a ribosome of ~25 nm). A smaller resolution value therefore means more detail can be seen — note that a lower number means a better resolving power.

Explain the trend. Resolution is the shortest distance between two points that can still be seen as separate, and it is limited by the wavelength of the radiation used. The light microscope uses a long wavelength (500 nm), so its resolution is poor (200 nm) and it cannot separate structures closer than this — it sees down to a mitochondrion but no further.

The electron microscopes use electrons with a far shorter wavelength (0.005 nm), giving a much smaller (better) resolution value. The TEM, with the best resolution of 0.5 nm, can distinguish the smallest structures of all, such as ribosomes, because it can separate points only 0.5 nm apart.

The SEM has the same wavelength but a poorer resolution (5 nm) than the TEM because it detects reflected surface electrons rather than transmitted ones; it can still resolve structures far smaller than the light microscope can.

(a) First find the mean actual length of one cell by dividing the total real length of the row by the number of cells:

$\text{mean cell length} = \frac{0.6\ \text{mm}}{8} = 0.075\ \text{mm}$

Convert this to micrometres by multiplying by 1000 (1 mm = 1000 µm):

$0.075\ \text{mm} \times 1000 = 75\ \text{µm}$

So the mean actual length of one cell is 75 µm — a realistic value for an onion epidermal cell.

(b) The image length on the drawing is found by rearranging $M = I/A$ to make image size the subject, $I = M \times A$. Using the actual cell length of 75 µm (or 0.075 mm) and a magnification of ×500:

$I = M \times A = 500 \times 0.075\ \text{mm} = 37.5\ \text{mm}$

So one cell would appear 37.5 mm long on the ×500 drawing.

Reasons the structures might be genuine. It is entirely expected that a structure could appear in a TEM but not in a light micrograph: the TEM has a far higher resolution (~0.5 nm) than the light microscope (~200 nm), because electrons have a much shorter wavelength than light. Small organelles such as ribosomes are below the light microscope's resolution limit and so are invisible with light but visible with a TEM. The fact that the structures are only seen with the higher-resolution instrument is therefore consistent with their being real but very small.

Reasons for caution — artefacts. However, the claim is not yet justified. To be viewed in a TEM, the specimen must be killed, dehydrated, embedded, cut into ultra-thin sections, treated with heavy-metal stains and placed in a vacuum. Each of these harsh preparation steps can distort or damage the cell or precipitate the stain, creating an artefact — a structure that appears in the image but was not present in the living cell. The dark circular "structures" could be such artefacts (for example clumps of stain), which would explain why they never appear in light micrographs of living, unprocessed cells.

Evaluating the evidence. Because the structures are seen only in TEM images and never with the light microscope, two explanations are possible — a genuine sub-resolution organelle, or a preparation artefact — and the data given cannot distinguish between them. The claim of a "new organelle" is therefore premature.

Precautions and further work. To decide, the researcher should: prepare the specimens by different fixation/staining methods and check whether the structures persist (artefacts often vary with the method); examine many cells and several specimens to show the structures are consistent and not random; compare with published electron micrographs; and, if possible, use complementary techniques (such as a different type of microscopy or biochemical isolation) to confirm the structures exist in living cells. Only if the structures reliably appear regardless of preparation method is the claim of a new organelle supported.

Conclusion. The higher resolution of the TEM makes it plausible that a small real structure is being seen, but because electron-microscope preparation readily produces artefacts and the structures appear in only one technique, the claim is not yet justified without further controls.