Microscopy, Magnification and Resolution

AS · 16 min

Almost everything you will learn about cells was discovered by looking down a microscope, so this note is the foundation of the whole course. It covers the units used to measure cells, the magnification equation, how to measure with an eyepiece graticule and stage micrometer, and the difference between magnification and resolution. Magnification calculations appear on almost every Paper 1, Paper 2 and Paper 3, and they are some of the easiest marks to secure if you are systematic about units.

Units for measuring cells

Cells and organelles are far too small for millimetres to be convenient, so biologists use two smaller units. Each step down is a factor of 1000.

Key result

Unit	Symbol	In metres	Relationship
millimetre	mm	$10^{-3}\ \text{m}$	$1\ \text{mm} = 1000\ \mu\text{m}$
micrometre	µm	$10^{-6}\ \text{m}$	$1\ \mu\text{m} = 1000\ \text{nm}$
nanometre	nm	$10^{-9}\ \text{m}$	$1\ \text{mm} = 1\,000\,000\ \text{nm}$

To go to a smaller unit, multiply by 1000. To go to a larger unit, divide by 1000.

It helps to have a feel for the sizes involved, because the examiners often ask whether a structure can be seen with a light microscope, and because an answer that is out by a factor of 1000 should look wrong to you.

Structure	Typical size
Plant cell (e.g. palisade mesophyll)	40–100 µm long
Animal cell (e.g. cheek cell)	20–40 µm across; red blood cell about 7–8 µm
Nucleus	about 10 µm across (5–20 µm)
Chloroplast	about 3–10 µm long
Mitochondrion	about 0.5–1 µm wide, 1–10 µm long
Bacterium	generally 1–5 µm
Lysosome	about 0.1–0.5 µm
Ribosome	about 20–30 nm (80S); 70S slightly smaller
Virus	about 20–300 nm
Cell surface membrane (thickness)	about 7–10 nm

Magnification

Magnification tells you how many times bigger the image is than the real object. If a cell that is really 20 µm across appears 40 mm across in a drawing, the drawing is 2000 times bigger than the cell.

Definition

Magnification is the number of times larger an image is than the actual size of the object, calculated as image size divided by actual size.

Key result

\text{magnification} = \frac{\text{image size}}{\text{actual size}} \qquad\qquad M = \frac{I}{A}

Rearranged: $A = \dfrac{I}{M}$ and $I = A \times M$ .

Both sizes must be in the same unit before you divide. Magnification has no units: write $\times 2000$ , never "2000 µm".

A useful memory aid is the triangle with $I$ on top and $A$ and $M$ underneath: cover the quantity you want and the other two show you whether to multiply or divide.

Any magnification calculation

Write the equation you are using, $M = I / A$ or a rearrangement.
Measure the image with a ruler in millimetres (measure the longest dimension unless told otherwise).
Convert so both lengths are in the same unit. Converting the image to micrometres (multiply mm by 1000) is usually easiest.
Substitute and calculate.
Give the answer with the correct unit (or none for magnification) and a sensible number of significant figures, usually 2 or 3.

Magnification of a microscope

The total magnification of a light microscope is the eyepiece magnification multiplied by the objective magnification. With the standard Paper 3 microscope, a $\times 10$ eyepiece with the $\times 10$ low-power objective gives $\times 100$ , and with the $\times 40$ high-power objective gives $\times 400$ .

Scale bars

Many photomicrographs and electron micrographs carry a scale bar, a line labelled with the actual length it represents. A scale bar lets you find the magnification without being told it, because the bar is itself an image of known actual size.

Using a scale bar

Measure the scale bar with a ruler in mm and convert to the unit on its label.
Magnification $=$ length of scale bar (measured) $\div$ length written on the bar.
Measure the structure of interest and divide by that magnification to get its actual size.

Alternatively, work by proportion: if a 20 mm bar represents 5 µm, a 60 mm structure is $3 \times 5 = 15$ µm.

Actual size from a given magnification (routine)

An electron micrograph of a mitochondrion has a magnification of $\times 12\,000$ . The image of the mitochondrion is 36 mm long. Calculate the actual length of the mitochondrion in µm.

Solution

A = \frac{I}{M}

Convert the image length: $36\ \text{mm} = 36 \times 1000 = 36\,000\ \mu\text{m}$ .

A = \frac{36\,000\ \mu\text{m}}{12\,000} = 3.0\ \mu\text{m}

This is a sensible size for a mitochondrion (1–10 µm long), which is a useful check.

Magnification from a scale bar

A photomicrograph has a scale bar 25 mm long labelled 5 µm. A cell on the photomicrograph measures 80 mm across.

(a) Calculate the magnification of the photomicrograph. (b) Calculate the actual width of the cell.

Solution

(a) Convert the bar to µm: $25\ \text{mm} = 25\,000\ \mu\text{m}$ .

M = \frac{I}{A} = \frac{25\,000\ \mu\text{m}}{5\ \mu\text{m}} = \times 5000

(b) Convert the cell image: $80\ \text{mm} = 80\,000\ \mu\text{m}$ .

A = \frac{80\,000\ \mu\text{m}}{5000} = 16\ \mu\text{m}

Check by proportion: the cell is $80/25 = 3.2$ scale bars wide, and $3.2 \times 5 = 16$ µm.

Magnification of your own drawing

A student draws a cell that is actually 60 µm long. The drawing is 120 mm long. Calculate the magnification of the drawing.

Solution

M = \frac{I}{A} = \frac{120 \times 1000\ \mu\text{m}}{60\ \mu\text{m}} = \frac{120\,000}{60} = \times 2000

The magnification of a drawing depends on how big you drew it, not on which objective lens you used. A drawing made at $\times 400$ can have a magnification of $\times 2000$ on paper.

Watch out

The most common error in this topic is failing to convert units. Dividing 36 (mm) by 12 000 gives 0.003, which is in mm, not µm. Always write the unit next to every number in your working so that a mismatch is obvious.

Measuring with an eyepiece graticule and stage micrometer

To measure a real specimen down a microscope you need a scale you can see at the same time as the specimen. That is the job of the eyepiece graticule, a small glass disc in the eyepiece with a scale engraved on it, usually 100 divisions. Because it sits in the eyepiece, the graticule appears the same size at every magnification, while the specimen appears bigger as you change to a higher-power objective. So an eyepiece unit has no fixed size: it must be calibrated separately for each objective lens.

Calibration uses a stage micrometer, a microscope slide with a scale of known length engraved on it, commonly 1 mm divided into 100 divisions, so each stage micrometer division is $0.01\ \text{mm} = 10\ \mu\text{m}$ .

Calibration at one magnification: 40 eyepiece units line up exactly with 10 stage micrometer divisions (100 µm), so one eyepiece unit represents 2.5 µm.

Calibrating an eyepiece graticule

Place the stage micrometer on the stage and focus on its scale using the objective you will measure with.
Rotate the eyepiece so the graticule scale lies alongside and parallel to the micrometer scale.
Line up the zero of the graticule with a line on the micrometer.
Find a point further along where a graticule line coincides exactly with a micrometer line. Use as long a stretch as possible to reduce the percentage error.
Calculate: length of one eyepiece unit $=$ (number of stage divisions $\times$ length of one stage division) $\div$ number of eyepiece units.
Remove the micrometer, place the specimen on the stage without changing the objective, and measure the specimen in eyepiece units.
Actual size $=$ number of eyepiece units $\times$ calibrated length of one eyepiece unit.
Repeat the calibration for each objective lens.

Calibrating and measuring at high power

At $\times 400$ , 40 eyepiece units are exactly equal to 10 stage micrometer divisions. Each stage micrometer division is 0.01 mm. A cheek cell spans 24 eyepiece units.

(a) Calculate the length of one eyepiece unit in µm. (b) Calculate the width of the cell. (c) How many eyepiece units would the same cell span using the $\times 10$ objective (total magnification $\times 100$ )?

Solution

(a) One stage division $= 0.01\ \text{mm} = 10\ \mu\text{m}$ , so 10 divisions $= 100\ \mu\text{m}$ .

1\ \text{eyepiece unit} = \frac{100\ \mu\text{m}}{40} = 2.5\ \mu\text{m}

(b) Width $= 24 \times 2.5 = 60\ \mu\text{m}$ .

(c) Changing from the $\times 40$ to the $\times 10$ objective reduces the magnification of the specimen by a factor of 4, but the graticule does not change size. So each eyepiece unit now covers four times as much specimen: $1\ \text{eyepiece unit} = 4 \times 2.5 = 10\ \mu\text{m}$ . The cell spans $60 / 10 = 6$ eyepiece units.

Watch out

Two errors cost marks every year. First, stating that one eyepiece unit "is" a fixed length: it depends on the objective, so it must be recalibrated. Second, saying the stage micrometer is used to measure the specimen: it is only used for calibration and is removed before the specimen is viewed.

Resolution

Magnification on its own does not reveal detail. You can enlarge a blurred photograph as much as you like, but two dots that were merged into one blob stay merged. What matters is resolution.

Definition

Resolution is the ability to distinguish between two separate points that are close together; the resolution of a microscope is the smallest distance between two points that can still be seen as separate.

The resolution of any microscope is limited by the wavelength of the radiation it uses. Two objects can only be distinguished if they are separated by more than about half the wavelength. Visible light has wavelengths of about 400–700 nm, so the best resolution of a light microscope is about 200 nm ( $0.2\ \mu\text{m}$ ). Anything smaller than about 200 nm, or any two structures closer together than this, cannot be resolved however much you magnify the image.

Electrons can behave as waves with an extremely short wavelength (far less than 1 nm), so electron microscopes have much better resolution: about 0.5 nm for a transmission electron microscope with biological specimens.

Key result

Increasing magnification beyond the limit set by resolution gives a bigger image but no more detail. This is why a light microscope's useful magnification stops at about $\times 1500$ : beyond that the image just gets larger and blurrier.

Better resolution comes from shorter wavelength radiation.

Why some organelles are only visible with an electron microscope

A ribosome is about 25 nm across, a cell surface membrane about 7–10 nm thick, and a microtubule about 25 nm in diameter. These are all far below 200 nm, so they cannot be seen with a light microscope at all. Structures larger than 200 nm, such as the nucleus, chloroplasts, and (just) mitochondria, can be seen with a light microscope, but their internal detail (cristae, thylakoids, nuclear pores) needs an electron microscope. The cell surface membrane is often described as "visible" in light micrographs, but what you see is the boundary of the cell, not the membrane's structure.

Light and electron microscopes compared

There are two types of electron microscope. In a transmission electron microscope (TEM) a beam of electrons passes through a very thin section of the specimen; denser regions (stained with heavy metals) scatter more electrons and appear darker. The result is a flat, two-dimensional image of a slice, showing internal structure. In a scanning electron microscope (SEM) the electron beam is scanned across the surface of a specimen coated in a thin layer of metal; electrons bouncing off the surface are detected to build up a three-dimensional-looking image of the surface. The SEM has lower resolution than the TEM.

Feature	Light microscope	Transmission EM	Scanning EM
Radiation	visible light (400–700 nm)	electrons	electrons
Focused by	glass lenses	electromagnets	electromagnets
Best resolution	about 200 nm	about 0.5 nm	several nm (worse than TEM)
Useful magnification	up to about $\times 1500$	up to about $\times 500\,000$	up to about $\times 100\,000$
Image	colour (stained), 2-D section	black and white, 2-D section	black and white, 3-D surface view
Specimen	living or dead	dead only	dead only
Conditions	air	vacuum	vacuum
Preparation	simple, quick	complex: fixing, very thin sections, heavy-metal stains	complex: fixing, metal coating
Artefacts	few	common	common
Cost and size	cheap, portable	very expensive, large	very expensive, large

Electron micrographs are black and white because electrons have no colour. "False-colour" electron micrographs have had colour added afterwards by computer to highlight structures. An artefact is a structure seen in a preparation that was not present in the living cell, produced by the preparation process.

Exam tip

"Explain the differences between magnification and resolution" is a favourite question. A full answer:

defines magnification (how many times larger the image is than the object);
defines resolution (the ability to distinguish two points close together as separate);
states that resolution is limited by wavelength, light microscope about 200 nm, electron microscope about 0.5 nm;
explains that electrons have a much shorter wavelength than light, so electron microscopes have higher resolution;
notes that increasing magnification without increasing resolution does not reveal more detail.

Say "higher resolution" or "better resolution", not "bigger resolution". A smaller resolution distance is a better resolution, so phrase it as "can distinguish points closer together".

Can it be seen? (describe and explain)

Explain why ribosomes can be seen in an electron micrograph but not with a light microscope, even at the highest magnification.

Solution

Marking points:

Ribosomes are about 25 nm in diameter (accept 20–30 nm).
The resolution of a light microscope is about 200 nm (0.2 µm) ...
... because resolution is limited by the wavelength of light (400–700 nm).
Objects smaller than the resolution limit cannot be distinguished, so increasing magnification only enlarges a blurred image.
Electrons have a much shorter wavelength, giving a resolution of about 0.5 nm, so ribosomes can be resolved.

Exam-hard: working from a scale bar on an unfamiliar organism

An electron micrograph shows a chloroplast. The image of the chloroplast is 48 mm long. The scale bar on the micrograph is 30 mm long and is labelled 3.75 µm.

(a) Calculate the magnification of the micrograph. (b) Calculate the actual length of the chloroplast. (c) A student said a ribosome 25 nm across would appear 1.0 mm across at this magnification. Is the student correct?

Solution

(a) Scale bar: $30\ \text{mm} = 30\,000\ \mu\text{m}$ .

M = \frac{30\,000\ \mu\text{m}}{3.75\ \mu\text{m}} = \times 8000

(b) $48\ \text{mm} = 48\,000\ \mu\text{m}$ .

A = \frac{48\,000\ \mu\text{m}}{8000} = 6.0\ \mu\text{m}

(c) $I = A \times M = 25\ \text{nm} \times 8000 = 200\,000\ \text{nm} = 200\ \mu\text{m} = 0.2\ \text{mm}$ . The student is not correct: the ribosome would appear 0.2 mm across. (A ribosome would appear 1.0 mm across at $\times 40\,000$ .)

Making temporary preparations

The syllabus expects you to be able to make a temporary preparation (a slide that is not permanently sealed) of cellular material. The usual examples are onion epidermis stained with iodine solution and cheek cells or other animal tissue stained with methylene blue. The full method, drawing rules and the sampling of cells in a field of view are in Microscopy and biological drawing.

In outline:

Place a drop of water or stain on a clean slide.
Add a thin layer of tissue, one cell thick (for example, a piece of onion epidermis peeled with forceps), keeping it flat.
Lower a coverslip at an angle with a mounted needle so that air bubbles are not trapped.
Blot away excess liquid with paper towel.
View with the low-power objective first, focus with the coarse focus, then move to high power and use only the fine focus.

Stains make transparent structures visible by binding to particular components: iodine stains starch grains blue-black and makes the nucleus and cell walls of onion cells visible; methylene blue stains the nuclei of animal cells.

Practical skills

Using the microscope in Paper 3

Start on low power ( $\times 100$ total) to find the specimen, then move to high power ( $\times 400$ ) to measure or draw detail.
Focus with the coarse focus only on low power; on high power use the fine focus only, to avoid crashing the objective into the slide.
Calibrate the graticule separately for each objective you use.
When measuring, take several measurements (for example, of several cells) and calculate a mean, because cells vary.
Sources of error: graticule lines are thick relative to small structures; the edges of cells are hard to judge; cells may be cut at different angles in a section, so they appear different sizes.

Summary

$1\ \text{mm} = 1000\ \mu\text{m}$ and $1\ \mu\text{m} = 1000\ \text{nm}$ .
Magnification $=$ image size $\div$ actual size, with both in the same unit. Magnification has no units.
A scale bar gives magnification as measured bar length $\div$ labelled length.
An eyepiece graticule must be calibrated against a stage micrometer for every objective lens.
Resolution is the ability to distinguish two close points as separate. It is limited by wavelength.
Light microscope: resolution about 200 nm, useful magnification about $\times 1500$ . TEM: about 0.5 nm.
TEM gives 2-D sections showing internal structure; SEM gives 3-D surface views with lower resolution.
Ribosomes (about 25 nm), membranes (7–10 nm) and microtubules are too small to be seen with a light microscope.

Practice questions

Question

Convert (a) 0.045 mm to µm, (b) 2.5 µm to nm, (c) 750 nm to µm.
A bacterium is 2.5 µm long. Its image in a micrograph is 50 mm long. Calculate the magnification.
A nucleus in a photomicrograph at $\times 2500$ is 35 mm in diameter. Calculate its actual diameter.
A scale bar 18 mm long represents 2 µm. An organelle on the same micrograph is 63 mm long. Calculate (a) the magnification and (b) the actual length of the organelle.
State two reasons why the light microscope is still used in schools and hospitals even though electron microscopes have much better resolution.
Describe the difference between the images produced by a transmission electron microscope and a scanning electron microscope.
Using the $\times 40$ objective, one stage micrometer division (10 µm) is equal to 2.5 eyepiece units. A root hair cell spans 17 eyepiece units. Calculate the width of the root hair cell and state what you would need to do before measuring at a different magnification.
Explain why increasing the magnification of a light microscope above about $\times 1500$ does not allow more detail to be seen. (3 marks)
A student measured the lengths of 10 palisade cells with a calibrated graticule and found a mean of 26 eyepiece units at $\times 100$ , where 1 eyepiece unit $= 10\ \mu\text{m}$ . She then drew one cell 130 mm long. (a) Calculate the mean actual length of the cells. (b) Calculate the magnification of her drawing if the cell she drew was of average length. (c) Suggest why she measured ten cells rather than one.
A student claims that a structure 150 nm across will become visible with a light microscope if he uses a $\times 100$ objective with a $\times 20$ eyepiece. Evaluate this claim. (4 marks)

Answers

(a) $0.045 \times 1000 = 45\ \mu\text{m}$ . (b) $2.5 \times 1000 = 2500\ \text{nm}$ . (c) $750 \div 1000 = 0.75\ \mu\text{m}$ .
$M = 50\,000\ \mu\text{m} \div 2.5\ \mu\text{m} = \times 20\,000$ .
$A = 35\,000\ \mu\text{m} \div 2500 = 14\ \mu\text{m}$ .
(a) $M = 18\,000\ \mu\text{m} \div 2\ \mu\text{m} = \times 9000$ . (b) $A = 63\,000 \div 9000 = 7.0\ \mu\text{m}$ (or by proportion: $63/18 = 3.5$ bars, $3.5 \times 2 = 7\ \mu\text{m}$ ).
Any two: living specimens can be viewed (movement, cell division); colour is seen; it is cheap and portable; preparation is quick and simple; there is no vacuum; fewer artefacts.
TEM: electrons pass through a thin section; the image is a 2-D section showing internal structures (organelles); higher resolution. SEM: electrons are reflected from the metal-coated surface; the image shows the 3-D surface of the specimen; lower resolution than TEM.
One eyepiece unit $= 10 \div 2.5 = 4\ \mu\text{m}$ . Width $= 17 \times 4 = 68\ \mu\text{m}$ . The graticule must be recalibrated with the stage micrometer for the new objective, because the eyepiece unit represents a different actual length at each magnification.
Resolution of the light microscope is limited to about 200 nm (0.2 µm) by the wavelength of light; points closer together than this cannot be distinguished; so higher magnification only enlarges the blurred image (empty magnification) without revealing new detail.
(a) $26 \times 10 = 260\ \mu\text{m}$ . (b) $M = 130\,000\ \mu\text{m} \div 260\ \mu\text{m} = \times 500$ . (c) Cells vary in size; a mean of several gives a more representative (more reliable) value and reduces the effect of an unusually large or small cell or a measuring error.
The total magnification would be $\times 2000$ , which is higher, but this does not improve resolution. The resolution of the light microscope is limited by the wavelength of light to about 200 nm. A 150 nm structure is below this limit, so it cannot be distinguished from its surroundings however much it is magnified; the student is wrong. It would need an electron microscope, whose shorter wavelength gives a resolution of about 0.5 nm.

Units for measuring cells

Magnification

Magnification of a microscope

Scale bars

Measuring with an eyepiece graticule and stage micrometer

Resolution

Why some organelles are only visible with an electron microscope

Light and electron microscopes compared

Making temporary preparations

Practice questions

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