Microscopy and Magnification

Most cells are far too small to see with the naked eye. A typical animal cell is about 0.02 mm across — roughly the width of a fine hair split into many strands — so studying cells means magnifying them.

Two measurements describe how good a microscope is, and they are not the same thing:

• Magnification — how many times bigger the image is than the real object.
• Resolution (resolving power) — the smallest distance between two points that can still be seen as two separate points, rather than blurring into one.

A microscope that magnifies hugely but has poor resolution just gives you a bigger blur. To see fine detail you need both: high magnification and high resolution.

Resolution is the ability to distinguish two close objects as separate. It sets the real limit on how much useful detail you can see.

This is the idea the whole topic rests on, so be clear on the difference before moving to the equation.

The relationship between magnification, the image size you measure, and the real size of the object is a single equation you must be able to use in both directions.

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

Magnification has no units — it is a ratio of two lengths, so it is written as a number with a "×", such as 400×. The image size and the actual size must be in the same unit before you divide.

Worked example — find the magnification

An image of a cell measures 50 mm across. The real cell is 0.05 mm across. Find the magnification.

Step	Working
Write the equation	magnification = image size ÷ actual size
Substitute (same units)	magnification = 50 mm ÷ 0.05 mm
Calculate	magnification = 1000×

Check: 0.05 mm × 1000 = 50 mm, which matches the image. The answer is correct.

The same equation rearranges two ways. A formula triangle makes the rearrangement reliable: cover the quantity you want, and what is left tells you whether to multiply or divide.

Worked example — find the actual size

A cell is viewed at a magnification of 400×. Its image measures 24 mm across. Find the real size of the cell.

Step	Working
Rearrange	actual size = image size ÷ magnification
Substitute	actual size = 24 mm ÷ 400
Calculate	actual size = 0.06 mm
Convert to µm	0.06 mm × 1000 = 60 µm

Check: 60 µm = 0.06 mm, and 0.06 mm × 400 = 24 mm, which matches the image. The answer is correct.

Decide what the question is asking for before you start: the magnification (a number), or a real length (which needs a sensible unit such as µm or nm).

Cells are measured in millimetres (mm), micrometres (µm) and nanometres (nm). Getting the prefixes and conversions right is where most marks are lost, so learn this ladder.

Prefix	Symbol	Metres	Relationship
centi	cm	$10^{-2}$ m	1 cm = 10 mm
milli	mm	$10^{-3}$ m	1 mm = 1000 µm
micro	µm	$10^{-6}$ m	1 µm = 1000 nm
nano	nm	$10^{-9}$ m	1 nm = $10^{-9}$ m

The key chain to memorise:

$1\text{mm}=1000\text{µm}=1,000,000\text{nm}$

Worked example — convert a small length

An organelle measures 0.0007 mm. Express this in micrometres and in nanometres.

Step	Working
mm → µm (× 1000)	0.0007 mm × 1000 = 0.7 µm
µm → nm (× 1000)	0.7 µm × 1000 = 700 nm

To go from a larger unit to a smaller one you multiply (the number gets bigger); going the other way you divide. Here 0.0007 mm and 700 nm are the same length written two ways.

Cell sizes often come out as awkward decimals like 0.0007 mm. Writing them in standard form — a number between 1 and 10 multiplied by a power of 10 — keeps them tidy and avoids miscounting zeros. The 8461 specification asks you to express answers in standard form where appropriate.

$a\times 10^n,\text{where }1\le a<10$

For a small number the power of 10 is negative; the power tells you how many places the decimal point moves.

Worked example — write a size in standard form

Express 0.0007 mm in standard form.

Step	Working
Move the decimal to get 1 ≤ a < 10	0.0007 → 7.0
Count the places moved (right)	4 places
Negative power for a small number	$7\times 10^{-4}$ mm

So 0.0007 mm = $7\times 10^{-4}$ mm. A bacterium about 0.002 mm long is $2\times 10^{-3}$ mm, and a 60 µm cell is $6\times 10^{-5}$ m. Orders of magnitude compare sizes by powers of ten: an object that is $10\times$ longer than another is one order of magnitude bigger, and a cell at $\sim 10^{-5}$ m is about three orders of magnitude larger than an organelle at $\sim 10^{-8}$ m.

(Higher Tier note — Foundation candidates handle standard form too, but more demanding standard-form manipulation and order-of-magnitude comparisons are most likely to appear on Higher papers.)

A light microscope focuses visible light through glass lenses. An electron microscope fires a beam of electrons instead of light. Because electrons have a far shorter wavelength than light, an electron microscope resolves much finer detail — so it has both much higher magnification and much higher resolving power. That higher resolution is the reason it can reveal sub-cellular structures a light microscope cannot.

Feature	Light microscope	Electron microscope
Magnification	up to about 1500–2000×	up to about 1,000,000× or more
Resolution	about 200 nm	about 0.2 nm
Detail visible	nucleus, cell wall, chloroplasts, larger structures	internal detail of organelles and sub-cellular structures
Specimens	living or dead	dead only (samples are in a vacuum)
Cost / size	cheap, portable, used in schools	very expensive, large, specialist labs

The development of the electron microscope let biologists see and understand many more sub-cellular structures, because of its higher magnification and resolving power. That single point — better resolution reveals more detail — is the spec's headline for this topic.

The trade-off: a light microscope can show living cells, but only an electron microscope reveals the finest internal detail.

Required practical 1 uses a light microscope to observe, draw and label plant and animal cells. You need to know the method and the drawing conventions, and a magnification scale must be included.

Slide preparation (e.g. onion epidermis or cheek cells):

• Peel a thin, single-cell-thick layer of tissue and place it on a clean glass slide.
• Add a drop of stain (such as iodine for plant cells or methylene blue for cheek cells) to make structures show up clearly.
• Lower a coverslip at an angle with a mounting needle to avoid trapping air bubbles.

Focusing — start on low power:

• Begin with the lowest-power objective lens, then move up to higher powers once the cells are in view.
• Focus using the coarse adjustment first, then the fine adjustment for a sharp image.

Drawing conventions:

• Use a sharp pencil with clear, continuous lines — no shading or colouring in.
• Draw what you actually see, not a textbook diagram.
• Use straight label lines that touch the structure, with labels written horizontally.
• State the magnification used, and include a magnification scale.

Total magnification = eyepiece magnification × objective magnification. A ×10 eyepiece with a ×40 objective gives 10 × 40 = 400×.

1. Confusing magnification with resolution

These are different. Magnification is how many times bigger the image is; resolution is the smallest detail you can still tell apart. Electron microscopes beat light microscopes on both, and it is the higher resolution that lets us see more sub-cellular detail.

2. Not converting to the same unit before dividing

The magnification equation only works if image size and actual size share a unit. Convert first (for example 0.05 mm stays in mm, or change everything to µm), then divide.

3. Forgetting the formula triangle direction

Magnification = image ÷ actual. To find the real size, divide the image by the magnification; to find the image size, multiply the magnification by the actual size. Cover the quantity you want in the triangle to check.

4. Getting the power of ten the wrong way round

Small lengths (less than 1) use a negative power in standard form, such as $7\times 10^{-4}$ mm. Large numbers use a positive power. Count the decimal places carefully — a single miscounted zero loses the mark.

5. Shading or colouring biological drawings

In Required practical 1 drawings, use clean pencil lines only, with straight label lines and the magnification stated. Shading and colouring lose marks and are not part of the scientific drawing convention.