Cambridge International A-Level Biology

Units of length

Cells and their contents are measured in three units, each a thousand times smaller than the one before.

A typical animal cell is tens of micrometres across, a bacterium is one to five micrometres, a ribosome is around 25 nanometres and a virus is tens to hundreds of nanometres. Choosing the unit that gives a number between about 1 and 1000 keeps calculations manageable, and converting between units is the commonest place to lose a factor of a thousand.

Magnification and resolution

Magnification is how many times larger an image is than the real object. Resolution is the smallest distance between two points at which they can still be seen as separate. A microscope that magnifies without resolving more detail only makes a blurred image larger, which is why the two ideas are kept apart: magnification can be increased without limit on paper, but resolution is set by the wavelength of the radiation used.

A light microscope uses visible light, whose wavelengths (roughly 400 to 700 nm) limit resolution to about 200 nm (0.2 µm). Two structures closer together than that merge into one blob, however high the magnification. Useful magnification therefore stops at about ×1500. Electron microscopes use a beam of electrons, whose wavelength is far shorter, so they resolve structures much less than a nanometre apart in the best transmission instruments and a few nanometres apart in scanning instruments.

Light and electron microscopes compared

Electron microscopes work in a vacuum, because air would scatter the electrons, and this is why their specimens cannot be alive. The preparation (fixing, dehydrating, staining or coating) can produce artefacts, which are structures in the image that were not present in the living cell, so an electron micrograph is interpreted with that in mind.

Preparing a temporary slide

A temporary preparation of plant or animal tissue is made to be looked at straight away and thrown away afterwards.

1. Cut or peel a very thin piece of tissue, such as onion epidermis or a slice of a leaf, so that light can pass through a single layer of cells.
2. Place it on a clean slide in a drop of water, or in a drop of stain. Iodine in potassium iodide solution stains starch grains blue-black and makes plant nuclei easier to see; methylene blue stains the nuclei of cheek cells.
3. Lower a coverslip onto the specimen at an angle, using a mounted needle, so that air bubbles are not trapped. Air bubbles look like dark rings and hide the cells.
4. Blot away any liquid at the edge, then view under low power first and move up to a higher power.

Drawing what is seen

A drawing of cells from a slide is made with clear single pencil lines, with no shading and no colouring. It is large enough to show the detail, it shows only what is seen (not what a textbook says should be there), and each label line touches the structure it names without crossing other lines. A plan diagram, used for tissues, shows the outlines and distribution of tissues and draws no individual cells.

Measuring with an eyepiece graticule

An eyepiece graticule is a small scale in the eyepiece lens, marked in arbitrary divisions. Its divisions have no fixed size, because the image it is laid over changes with the objective lens in use. It is calibrated against a stage micrometer, a slide with a scale of known length, usually divided into 10 µm intervals.

1. Put the stage micrometer on the stage and focus on it with the objective lens that will be used.
2. Rotate the eyepiece so that the two scales lie side by side, and line up the zero marks.
3. Find a place further along where the two scales line up exactly again, and count the divisions of each.
4. Work out the length of one eyepiece division.

For example, if 50 eyepiece divisions line up with 20 stage divisions of 10 µm each, then 50 eyepiece divisions equal 200 µm, so

A cell that spans 12.5 eyepiece divisions is $12.5 \times 4 = 50\ \mu\text{m}$ long. The calibration belongs to one objective lens, so it is repeated whenever the lens is changed. Measuring several cells and taking a mean reduces the effect of variation between cells.

Calculating magnification and actual size

The relationship between the three quantities is

and it is rearranged to find whichever quantity is missing. The image and the object must be in the same unit before dividing, and since actual sizes are usually in micrometres, the measured image length in millimetres is converted to micrometres first.

Worked example: magnification from a drawing

A student draws a cell and measures the drawing as 54 mm long. The cell is known to be 18 µm long.

Worked example: actual size from a micrograph

An electron micrograph of a mitochondrion has magnification ×14 000. The mitochondrion measures 63 mm on the printed image.

Using a scale bar

Many micrographs carry a scale bar instead of a stated magnification. The bar is measured with a ruler, and its length on the page is divided by the length it is labelled with. If a bar labelled 2 µm measures 30 mm, then

and any other structure in the same image is then measured in the same way and divided by 15 000 to give its real size. A scale bar stays correct if the picture is copied at a different size, whereas a stated magnification does not.