11 September 2026

Making Glue from Milk — The Chemistry of Casein, Coagulation and Precipitation

Milk does not immediately suggest itself as a building material.

We pour it over cereal, add it to tea and coffee, turn it into yoghurt and cheese, and perhaps occasionally forget about it at the back of the fridge.

But hidden inside milk is a substance that can be separated, treated and turned into something quite unexpected:

glue.

The key ingredient is casein, the main family of proteins found in cow's milk.

By adding acid to milk, we can make those proteins come out of suspension as solid curds. Separate those curds, remove as much liquid as possible, and then treat the casein appropriately, and we can produce a surprisingly effective adhesive.

It is an excellent experiment because what initially looks like a simple kitchen activity opens the door to some serious chemistry.

We encounter:

proteins;
acids;
pH;
electrical charge on molecules;
colloids;
precipitation;
coagulation;
filtration;
neutralisation;
polymers;
intermolecular forces;
and the science of adhesives.

It also provides a wonderful reminder that chemistry is not simply about producing coloured solutions in test tubes.

Sometimes chemistry produces useful materials.

Milk Is Much More Complicated Than It Looks

At first glance, milk appears to be a simple white liquid.

Chemically, however, it is a remarkably complicated mixture containing:

water;
proteins;
fats;
lactose;
calcium compounds;
vitamins;
minerals;
and many other dissolved or suspended substances.

Approximately 80% of the protein in cow's milk is casein.

But casein is not simply floating around as individual protein molecules.

Much of it is organised into tiny structures called casein micelles.

These microscopic particles remain dispersed through the water in milk, contributing to its familiar white appearance.

Under normal conditions, the micelles repel one another sufficiently to remain dispersed.

Change the chemistry of their surroundings, however, and that stability can disappear.

That is exactly what we are going to do.

The Key Idea — Make the Casein Precipitate

One of the easiest ways of separating casein from milk is to make the milk more acidic.

Ordinary white vinegar works very well because it contains dilute ethanoic acid, also known as acetic acid.

Milk normally has a pH somewhere around 6.5 to 6.8.

Casein proteins contain groups that can gain or lose H+ ions depending upon the pH.

As the pH falls towards approximately 4.6, casein reaches what chemists call its isoelectric point.

This is extremely important.

At the isoelectric point, the overall electrical charge on the protein is approximately zero.

The protein particles therefore repel each other much less strongly.

Instead of remaining distributed through the liquid, they begin sticking together.

The casein coagulates and precipitates.

Suddenly our smooth white milk begins separating into:

solid curds and liquid whey.

Anyone who has made cheese will recognise what is happening.

Precipitation, Coagulation and Cheese Chemistry

This gives us an opportunity to introduce several useful scientific words.

Precipitation

A substance that was previously dispersed or dissolved comes out of the liquid as a solid.

Coagulation

Small particles come together to form larger clumps or masses.

In this experiment the casein particles lose much of the electrostatic repulsion that normally keeps them apart.

They aggregate.

We see this as curds forming in the milk.

The remaining liquid is often called whey.

This is very similar to some of the chemistry used in food production.

But our objective is not cheese.

We are going to turn our casein into an adhesive.

What You Will Need

For a straightforward investigation you need:

about 100 mL of skimmed or semi-skimmed milk;
approximately 10-15 mL of white vinegar;
a small saucepan, beaker or heat-resistant container;
a thermometer if available;
a spoon or stirring rod;
filter paper, muslin, cheesecloth or a fine kitchen sieve;
paper towel;
sodium bicarbonate;
a small container for making the glue;
two wooden lolly sticks or pieces of wood for testing it.

Skimmed milk is particularly useful because the lower fat content generally gives a cleaner casein preparation.

Whole milk will still work, but the additional fat can make the separated material feel greasier.

Stage One — Warm the Milk

Measure approximately 100 mL of milk.

Warm it gently to around 40-50 degrees C.

It does not need to boil.

In fact, vigorous boiling is unnecessary and can complicate the experiment.

The warming simply helps the acid interact with the milk and allows the casein to coagulate relatively quickly.

Already there is a useful scientific point here.

Students often assume that whenever heat is used in an experiment, heat must be causing the chemical change.

Here it is mainly helping the process occur efficiently.

The acid is the crucial ingredient.

Stage Two — Add the Vinegar

Add approximately 10 mL of white vinegar while stirring gently.

The transformation can be remarkably rapid.

Within moments the previously smooth milk begins looking lumpy.

White solids appear.

The liquid surrounding them becomes more transparent and slightly yellowish.

Those solids contain the precipitated casein.

Add a little more vinegar if necessary until separation appears reasonably complete.

It is worth stopping at this stage and simply looking.

This is one of those practical experiments where the change is visually obvious enough that very little explanation is initially required.

Something fundamental has happened to the milk.

What Has the Acid Actually Done?

A very simplified explanation would be:

acid makes the casein precipitate.

But the underlying chemistry is more interesting.

Casein molecules contain acidic and basic groups.

The electrical charge carried by the proteins therefore depends upon the surrounding pH.

At normal milk pH, casein micelles carry sufficient charge to help keep them dispersed.

Adding ethanoic acid increases the concentration of H+ ions.

As the pH approaches the isoelectric point of casein, the overall charge decreases.

Repulsion between neighbouring protein particles becomes weaker.

They begin aggregating.

At the same time, acidification affects the calcium phosphate associated with the casein micelles, further destabilising their structure.

The result is the spectacular coagulation that we can actually see.

Is This Just Protein Denaturation?

Students may immediately think of cooking an egg.

Heating egg white causes proteins to unfold and form a solid network.

That is commonly described as protein denaturation.

Casein precipitation is slightly different.

Caseins do not have the same tightly folded structures as many other proteins.

Here, reducing the electrical charge and destabilising the casein micelles is especially important.

So although the words coagulation and denaturation are sometimes used rather loosely in everyday explanations, the chemistry deserves a little more care.

What we are primarily observing is acid-induced casein precipitation and aggregation.

Stage Three — Separate the Casein

Pour the mixture through filter paper, muslin or a fine sieve.

The liquid whey passes through.

The solid casein remains behind.

Press the casein gently with paper towel to remove as much liquid as possible.

You can rinse the curds with a little clean water and filter them again if you want to remove some of the remaining acid and soluble material.

Eventually you should have something resembling a soft white paste or crumbly putty.

At this stage it still does not look particularly promising as glue.

But we have now separated a natural polymer from milk.

Stage Four — Turn the Casein into Glue

Transfer the casein to a small container.

Add a small amount of sodium bicarbonate.

Start with perhaps a quarter of a teaspoon for casein obtained from around 100 mL of milk.

Mix thoroughly.

You may notice some gentle fizzing.

This occurs because sodium bicarbonate reacts with remaining acid.

A simplified ionic equation is:

H+ + HCO3- -> CO2 + H2O

The carbon dioxide produces the bubbles.

The bicarbonate also raises the pH.

This helps transform our acidic casein curds into a smoother and more usable adhesive paste.

Add a few drops of water if necessary.

The objective is not to produce a thin liquid.

You want something resembling a thick glue.

Why Should Protein Work as Glue?

This is perhaps the most interesting question in the entire experiment.

Why should something extracted from milk stick pieces of wood together?

Proteins are enormous molecules.

Casein molecules contain many different chemical groups capable of interacting with other substances.

When casein glue is spread across a surface, it can make close contact with microscopic irregularities in the material.

At the molecular level there can be interactions including:

hydrogen bonding;
electrostatic interactions;
attraction between polar groups;
and mechanical interlocking with pores and rough surfaces.

As water leaves the adhesive during drying, the casein molecules become increasingly concentrated.

Eventually they form a solid protein-rich layer between the two surfaces.

We have effectively created a natural polymer adhesive.

Test the Glue

A scientific investigation should not finish with:

"It looks like glue."

We should test whether it actually works.

Take two wooden lolly sticks.

Overlap them by perhaps 2 cm.

Spread approximately the same amount of casein glue over the overlapping region.

Clamp them together or place a small weight on top while the adhesive dries.

Leave them for several hours, preferably overnight.

Then try pulling them apart.

The result can be surprisingly convincing.

Turn It into a Proper Investigation

This experiment becomes much more interesting when students begin changing variables.

For example:

Does milk type matter?

Compare:

skimmed milk;
semi-skimmed milk;
whole milk.

Keep everything else constant.

Which produces the most casein?

Which produces the strongest glue?

How Much Casein Can You Obtain?

You can also turn the practical into a quantitative experiment.

Weigh a clean dry filter paper before filtration.

Collect the casein and allow it to dry thoroughly.

Weigh everything again.

Calculate:

Mass of casein = final mass - mass of filter paper

You could then calculate percentage yield relative to the mass of milk used:

Percentage yield = mass of dry casein / mass of milk x 100

Students should be careful with their interpretation.

Milk contains plenty of water, so we are not expecting an enormous percentage yield.

Does the Amount of Acid Matter?

Try adding different quantities of vinegar to identical volumes of milk.

For example:

2 mL;
5 mL;
10 mL;
15 mL;
20 mL.

Measure the mass of casein obtained.

At first, increasing the acid concentration should promote more complete precipitation.

Eventually, however, adding more acid should produce little additional benefit.

This is a useful demonstration of an important experimental principle:

more reagent does not necessarily mean more product indefinitely.

Measure the pH

If you have a pH meter or suitable pH probe, the experiment becomes considerably more informative.

Measure the starting pH of the milk.

Then add vinegar gradually while monitoring the pH.

Watch carefully as coagulation becomes extensive near the casein isoelectric region.

This converts what looks like an elementary kitchen experiment into a very good piece of analytical chemistry.

You can plot:

mass of casein precipitated against pH

or perhaps:

turbidity against pH

if suitable sensors are available.

Which Acid Works Best?

Another extension would be to compare different food-safe acids.

You might investigate:

white vinegar;
lemon juice;
citric acid solution.

Use solutions of comparable acidity where possible.

Students could investigate whether the type of acid matters or whether the principal factor is simply the pH achieved.

This is where experimental design becomes important.

If one sample receives much more acid than another, we cannot confidently say that differences arose because the acids themselves were different.

How Strong Is Our Milk Glue?

The most enjoyable extension may be engineering rather than chemistry.

Prepare several identical wooden joints.

Glue each pair using a different adhesive.

For example:

casein glue;
PVA glue;
flour paste;
starch adhesive.

Allow each sample to dry for the same length of time.

Then gradually add mass until the joint fails.

A simple results table might contain:

Adhesive	Overlap area	Drying time	Maximum load before failure
Casein	4 cm2	24 h	...
PVA	4 cm2	24 h	...
Flour paste	4 cm2	24 h	...

Now students are not simply making glue.

They are carrying out materials testing.

Be Careful About What You Call "Strong"

Suppose one glue supports a heavier mass than another.

Is that enough to declare it better?

Perhaps not.

We might also ask:

How long did it take to dry?
Was the joint waterproof?
Did the glue remain flexible?
Did it become brittle?
How easily could it be applied?
How long could it be stored?
Did it stick better to wood than plastic?
What happened in humid conditions?

Real engineering decisions rarely depend upon a single measurement.

The "best" material depends upon what we want the material to do.

A Glue with a Long History

Casein adhesives are not simply a classroom curiosity.

Before modern synthetic glues became widespread, casein-based adhesives were important materials for woodworking and plywood manufacture.

They offered a way of creating useful adhesives from naturally occurring proteins.

Modern synthetic adhesives such as PVA, epoxies and polyurethane products have largely replaced casein glue for many applications because they can offer better consistency, durability and water resistance.

Nevertheless, making casein glue gives students a glimpse of an earlier form of materials technology.

It also challenges an assumption we make increasingly often:

that useful manufactured materials must begin with petroleum or sophisticated industrial chemicals.

Nature already produces extraordinarily complicated polymers.

Sometimes chemistry is about learning how to separate and use them.

Milk, Cheese and Glue Are Connected by Chemistry

One of my favourite features of this experiment is the way it links apparently unrelated objects.

Milk.

Cheese.

Protein.

Glue.

They appear to belong to completely different worlds.

But at molecular level the connections become obvious.

Cheese making relies upon manipulating milk proteins.

Our glue-making experiment does something related, but instead of preparing food we deliberately recover the protein as a functional material.

This is one of the strengths of practical science.

The divisions between "food science", "chemistry" and "materials science" start disappearing.

There is simply matter — and what happens when we alter its conditions.

A Good Experiment for Discussing Colloids

Milk also gives us an opportunity to discuss something that receives surprisingly little attention in school science:

colloids.

Not every mixture is simply a solution or a suspension.

Milk contains extremely small particles dispersed through another substance.

Its proteins and fats interact with water in complicated ways.

Colloids are everywhere.

Examples include:

milk;
mayonnaise;
fog;
smoke;
paint;
shaving foam;
gelatin;
many cosmetics;
and numerous medicines.

Changing the conditions surrounding a colloid can cause it to become unstable.

Our precipitating casein is a beautiful example.

Common Problems

Nothing seems to happen

The milk may not be sufficiently warm, or you may not have added enough acid.

Add vinegar gradually while stirring.

The mixture is very greasy

You may be using milk with a high fat content.

Try skimmed milk.

The casein glue is too runny

Too much water has probably been added.

Add water only a few drops at a time.

The glue is too crumbly

Mix the casein more thoroughly with a small quantity of sodium bicarbonate and a few drops of water.

The joint seems weak

Allow considerably longer for drying.

Casein adhesive needs water to evaporate before maximum strength develops.

Also check that your surfaces are clean and make reasonably close contact.

Safety

Although this is a comparatively low-risk practical, normal laboratory precautions still apply.

Do not eat or drink laboratory materials.
Milk proteins can cause allergic reactions in people with milk allergies.
Take care when heating liquids.
Do not boil the milk unnecessarily.
Wash hands after the experiment.
Clean surfaces and equipment afterwards.
Once milk has been used experimentally, treat it as laboratory material rather than food.
Do not store homemade casein glue for long periods. Make a fresh batch when required.

Young students should carry out heating and chemical handling with appropriate adult supervision.

What Students Are Really Learning

At first sight, this might appear to be a novelty experiment.

"Make glue from milk."

But scientifically it contains far more depth than that description suggests.

Students encounter:

Biology:
Proteins and their properties.

Chemistry:
Acids, pH, neutralisation, precipitation and molecular charge.

Physics:
Intermolecular forces and material behaviour.

Materials science:
Polymers, adhesives and mechanical testing.

Experimental science:
Variables, controls, measurement, repeatability and data interpretation.

That combination makes it particularly valuable.

A good practical does not merely illustrate something students already know.

It gives them something new to think about.

From Breakfast to Materials Science

Perhaps the most memorable moment comes at the very beginning.

You start with an ordinary glass of milk.

Add a little acid.

Suddenly the liquid separates.

Filter it.

Treat the solid.

Spread it between two pieces of wood.

The following day those pieces may be firmly attached.

Nothing magical has occurred.

We have simply changed the conditions surrounding a naturally occurring polymer.

But that is precisely why the experiment is so satisfying.

Science allows us to look at an everyday substance and ask a completely different question.

Not:

"Can I drink this?"

but:

"What is actually inside it, how can I separate those substances, and what else could they do?"

That change of perspective is at the heart of good science.

Milk is not merely milk.

It is water, sugars, minerals, fats and proteins assembled into an extraordinarily complicated material.

And hidden among those proteins is casein — waiting for a little chemistry to turn breakfast into glue.

10 September 2026

There Are Barcodes Hidden in Starlight

Look up at a star on a clear night and, to the naked eye, it does not seem to give us very much information.

It is a point of light.

Perhaps it looks slightly blue, yellow or orange. Perhaps it is brighter than another star nearby. But that seems to be about it.

And yet astronomers can use that tiny quantity of light to work out an extraordinary amount about an object that may be hundreds, thousands or even millions of light-years away.

They can determine what elements it contains.

They can estimate its temperature.

They can measure whether it is moving towards us or away from us.

They can sometimes determine how rapidly it is rotating.

They can investigate the gases in the atmosphere of a distant planet.

And in some circumstances they can even infer the presence and strength of magnetic fields.

All of this begins with one deceptively simple idea:

Split the light apart and look carefully at the colours.

That is spectroscopy.

And it is one of the finest examples in science of how careful measurement can reveal information that appears, at first, to be completely inaccessible.

Light Contains More Information Than Our Eyes Can See

When we look at ordinary white light, our eyes simply interpret it as white.

Pass that light through a prism or diffraction grating, however, and something remarkable happens.

The light separates into its component wavelengths.

We see a spectrum.

The familiar visible spectrum runs approximately from:

violet;
blue;
green;
yellow;
orange;
red.

But the spectrum is not always a smooth rainbow.

Sometimes it contains bright coloured lines.

Sometimes it contains dark gaps.

Sometimes certain wavelengths are much stronger than others.

Those details form a kind of scientific fingerprint.

Or, perhaps more accurately for modern students, a barcode.

The pattern tells us something about the atoms, molecules and physical conditions that produced the light.

That is why spectroscopy is such a powerful idea to introduce beyond the normal school syllabus.

Students are not simply observing colour.

They are learning that light carries encoded information about matter.

Start Somewhere Much Closer Than the Stars

One of the best ways to introduce astronomical spectroscopy is not to begin with astronomy at all.

Begin in the laboratory.

Look at ordinary light sources.

Even quite simple equipment can produce surprisingly interesting results.

A diffraction grating, handheld spectroscope or suitably arranged spectrometer can be used to examine:

an incandescent lamp;
an LED lamp;
a fluorescent tube;
a sodium lamp;
daylight;
different coloured LEDs;
computer and television screens.

Students very quickly discover that "white light" is not always produced in the same way.

And that is where the experiment becomes interesting.

An Incandescent Lamp — A Continuous Spectrum

An old-style incandescent lamp works by heating a filament until it becomes extremely hot.

Look at its light through a spectroscope and you see something reasonably close to a continuous rainbow.

There is light across a wide range of visible wavelengths.

This is very different from what we see from many modern sources.

It also gives us a useful introduction to the idea of thermal radiation.

A hot object emits a range of wavelengths.

As its temperature increases, the distribution of those wavelengths changes.

We can see this in everyday life.

A piece of metal being heated may first glow dull red.

At a higher temperature it becomes orange.

Eventually it may appear yellow-white.

Temperature is changing the spectrum.

Stars behave in a related way.

Their colour therefore tells astronomers something about their surface temperature.

A red star is not simply "painted red".

Its colour is connected with its physical temperature.

LEDs — Not All White Light Is the Same

Modern LED lamps provide a particularly good surprise.

Students may expect a white LED bulb to produce the same smooth rainbow as an incandescent lamp.

Often it does not.

Many white LEDs are made using a blue LED together with phosphor materials that convert some of the blue light into longer wavelengths.

Depending upon the lamp, the resulting spectrum may show a strong blue peak combined with a broader region at other wavelengths.

Different LED lamps can produce noticeably different spectra even though they all look white to the human eye.

This immediately gives students an important lesson.

Objects that appear identical to our senses may be physically very different when measured scientifically.

Our eyes integrate many wavelengths together.

A spectroscope separates them again.

Fluorescent Lamps — A Forest of Lines

Fluorescent lighting gives another very different spectrum.

Instead of a smooth rainbow, students are likely to see several particularly bright lines or bands.

These arise from the gases and phosphors involved in producing the light.

Suddenly spectroscopy begins to look much more like a barcode.

There are particular wavelengths present much more strongly than others.

Those wavelengths can act as clues to the substances involved.

This leads naturally towards atomic emission spectra.

Sodium — A Beautiful Demonstration

If a suitable sodium source is available, it provides one of the classic spectroscopy demonstrations.

Sodium produces extremely characteristic yellow emission close to 589 nm.

With sufficient resolution, the familiar yellow region can be resolved into the famous sodium D lines.

The important point for students is not necessarily the precise wavelength.

It is the principle.

Sodium atoms do not emit every possible colour equally.

They produce very specific wavelengths.

Those wavelengths are connected with changes in the energy states of electrons within the atom.

Each element has its own characteristic pattern.

Hydrogen has one pattern.

Helium has another.

Neon has another.

Sodium has another.

That makes spectroscopy a method of chemical identification.

Why Do Atoms Produce Particular Colours?

This is where the experiment begins to connect with atomic physics.

Electrons in atoms are not allowed to possess just any energy.

They occupy particular energy levels.

If an electron moves from a higher energy state to a lower one, energy can be released as a photon.

The energy of that photon is related to its frequency by:

E = hf

where:

E = photon energy
h = Planck's constant
f = frequency

Because only certain energy differences are permitted within the atom, only particular photon energies are produced.

That means only particular frequencies — and therefore particular wavelengths — appear in the spectrum.

The result is a set of spectral lines.

The positions of those lines are characteristic of the element producing them.

It is rather like giving every element its own optical signature.

Emission Lines and Absorption Lines

There are two particularly important types of spectrum to introduce.

Emission spectra

A hot, low-density gas can produce bright lines at specific wavelengths.

Those bright lines show the wavelengths emitted by atoms or molecules in the gas.

Absorption spectra

If continuous light passes through a cooler gas, particular wavelengths may be absorbed.

The spectrum then contains dark lines.

The remarkable thing is that the positions of those dark absorption lines correspond to wavelengths that the same substance can emit.

This becomes enormously important in astronomy.

We cannot travel to a star, scoop up a sample of its atmosphere and bring it back to the laboratory.

But light from deeper, hotter regions of a star passes through cooler material in the star's atmosphere.

Atoms in that atmosphere absorb particular wavelengths.

The resulting dark absorption lines tell us what substances are present.

We read the lines.

The lines tell us the chemistry.

How Do We Know What Stars Are Made Of?

This is perhaps the most extraordinary part of spectroscopy.

Suppose we observe a dark line at a particular wavelength in the spectrum of a star.

How do we know what caused it?

We compare it with laboratory measurements.

Scientists can excite samples of hydrogen, helium, sodium, calcium, iron and many other substances here on Earth.

They measure the wavelengths at which those substances absorb or emit light.

Then they compare those laboratory patterns with spectra from stars.

If the lines match, we have evidence that the same element is present.

This is one of those moments in science that deserves to be appreciated.

The laws of physics appear to work in the same way in a laboratory on Earth and in stars vast distances away.

The sodium atom in a lamp in a laboratory behaves according to the same physics as a sodium atom in the atmosphere of a distant star.

That is a profound idea.

A Wonderful Historical Twist — Helium Was Found in the Sun First

Spectroscopy also produced one of the loveliest stories in the history of science.

During observations of the Sun in the nineteenth century, astronomers noticed a spectral line that did not correspond to any element then known on Earth.

The line was associated with a previously unknown element.

It was named helium after Helios, the Greek Sun god.

Only later was helium identified on Earth.

In other words, an element was detected in the Sun before it was found terrestrially.

A substance nearly 150 million kilometres away was identified using nothing more than the light arriving from it.

That should give students some sense of just how powerful spectroscopy can be.

Temperature Is Written into the Spectrum Too

Spectroscopy does more than reveal composition.

The overall shape of the spectrum contains information about temperature.

Hot objects produce thermal radiation across a range of wavelengths.

As temperature increases, the wavelength at which the radiation is most intense shifts.

Qualitatively:

cooler stars tend to appear redder;
hotter stars tend to appear bluer.

This sometimes surprises students because everyday experience teaches us to associate red with hot and blue with cold.

In astronomy, the opposite applies to stellar colour.

Blue stars are generally hotter than red stars.

For example, the surface temperature of a cool red star may be only a few thousand kelvin, while a hot blue star may exceed 10,000 K.

That is another reason why colour in astronomy is not merely aesthetic.

It is data.

Stars Can Tell Us Whether They Are Moving

Spectroscopy becomes even more impressive when we consider motion.

Suppose we know where a particular hydrogen absorption line should appear.

If the star is moving towards us, its spectral lines may appear shifted slightly towards shorter wavelengths.

This is a blueshift.

If the star is moving away, the lines shift towards longer wavelengths.

This is a redshift.

For relatively low speeds, the relationship can be approximated by:

v / c = change in wavelength / original wavelength

or:

v / c = Δλ / λ

where:

v = radial velocity of the object
c = speed of light
Δλ = change in wavelength
λ = original wavelength

This means astronomers can measure motion along our line of sight without seeing the star physically move across the sky.

Again, the information is hidden inside the light.

Finding Planets Without Seeing Them

This provides a lovely connection with another astronomical topic: exoplanets.

A planet orbiting a star does not simply travel around a perfectly stationary object.

The star and planet actually orbit their common centre of mass.

As a result, the star moves slightly backwards and forwards.

That movement can cause its spectral lines to alternate between tiny redshifts and blueshifts.

This is the radial velocity method of exoplanet detection.

We may never directly see the planet.

Instead we detect the extremely small gravitational effect it has upon its star.

This is a wonderful example of indirect scientific reasoning.

We observe one thing.

We infer another.

Can Spectroscopy Tell Us How Fast a Star Rotates?

It can.

Imagine one side of a rotating star moving towards us while the opposite side is moving away.

Light from one side is slightly blueshifted.

Light from the other side is slightly redshifted.

The combined effect can broaden the spectral lines.

By studying that broadening, astronomers can estimate how rapidly the star is rotating.

This is a much more advanced application, but it is an excellent example to mention because it demonstrates how much information is contained within the precise shape of a spectral line.

Not merely whether a line exists.

Not merely where it is.

But even how wide it is.

Magnetic Fields Can Leave Their Mark as Well

Strong magnetic fields can alter atomic energy levels.

This can cause spectral lines to split into multiple components.

The effect is known as the Zeeman effect.

Astronomers can use this splitting to investigate magnetic fields in stars and other astronomical objects.

At this point spectroscopy has moved far beyond simply identifying chemicals.

The spectrum has become a diagnostic tool for the physical environment.

Composition.

Temperature.

Velocity.

Rotation.

Magnetism.

All encoded in light.

Reading the Atmosphere of Another World

One of the most exciting modern applications of spectroscopy involves exoplanet atmospheres.

Imagine a planet passing in front of its star.

Most of the starlight travels directly towards us.

But a small fraction passes through the planet's atmosphere before reaching our telescopes.

Atoms and molecules in that atmosphere absorb particular wavelengths.

By comparing the spectrum during the transit with the normal stellar spectrum, astronomers can sometimes identify substances in the planetary atmosphere.

Depending upon the planet and the quality of the observations, spectroscopy can reveal signatures associated with substances such as:

water vapour;
sodium;
carbon dioxide;
methane;
other atmospheric gases.

This does not mean that every molecule automatically indicates life.

That is an important scientific caution.

Atmospheric chemistry is complicated, and biological and non-biological processes can sometimes produce similar substances.

But spectroscopy gives us something that would have seemed astonishing only a few generations ago:

the ability to study the atmosphere of a planet orbiting another star.

A Practical Spectroscopy Investigation

This topic lends itself beautifully to a home laboratory, school laboratory or astronomy club.

You do not need a professional observatory to introduce the underlying science.

Equipment

Depending upon what is available, you might use:

a handheld spectroscope;
a diffraction grating;
a simple educational spectrometer;
a camera with a diffraction grating;
suitable spectrum-analysis software;
several different lamps or light sources.

Suitable sources might include:

incandescent filament bulbs;
LED lamps;
coloured LEDs;
fluorescent lamps;
sodium lamps where safely available;
computer displays;
phone or tablet displays;
daylight.

Investigation 1 — Are All White Lights Actually the Same?

Place several apparently white light sources side by side.

For example:

an incandescent lamp;
a warm-white LED;
a cool-white LED;
a fluorescent source.

Look at each through the spectroscope.

Ask students to describe the differences.

They might consider:

Is the spectrum continuous?
Are particular colours stronger?
Are there obvious bright lines?
Are there gaps?
How do two different white LEDs compare?

This is a wonderfully simple experiment because the student's eyes initially say:

"They are all white."

The spectroscope says:

"No, they are not."

That is science in miniature.

Measurement reveals structure that ordinary observation misses.

Investigation 2 — Compare Coloured LEDs

Use red, green and blue LEDs.

Observe their spectra.

A red LED does not simply contain "white light with the other colours removed".

Its output is concentrated into a relatively narrow region of wavelengths.

Students can compare different LED colours and consider why a nominally single-colour light source still has a finite spectral width.

More advanced students could investigate the relationship between LED colour and photon energy.

Because:

E = hf

and:

c = fλ

we can combine them to obtain:

E = hc / λ

Shorter wavelength photons therefore have more energy than longer wavelength photons.

Blue LED photons have more energy than red LED photons.

That provides a useful bridge between visible colour, wave physics and quantum physics.

Investigation 3 — Look at a Computer Screen

This is particularly effective because it connects spectroscopy with something students use every day.

Display a white image on a computer monitor, tablet or television and examine it through a spectroscope.

Depending upon the display technology, students may be able to see separate red, green and blue contributions.

Then display:

red;
green;
blue;
yellow;
cyan;
magenta;
white.

Ask what changes in the spectrum.

Students begin to see that the screen is creating perceived colour by controlling a small number of primary emitters.

White on a display is constructed.

It is not necessarily the same spectrum as white daylight.

Investigation 4 — Match an Unknown Spectrum

This turns the activity into a genuine scientific puzzle.

Provide spectra from several known sources.

Then present an unknown.

Students must identify it by comparing the pattern.

This mimics the basic reasoning astronomers use when identifying chemical elements.

The task can be made increasingly sophisticated.

At first students may simply match obvious patterns visually.

Later they could measure approximate wavelengths.

They could produce a table such as:

Observed wavelength	Possible element
486 nm	Hydrogen
589 nm	Sodium
656 nm	Hydrogen

The exact activity will depend upon the resolution of the equipment, but the principle is powerful.

Students are no longer merely observing.

They are interpreting evidence.

Investigation 5 — From Laboratory Spectrum to Stellar Spectrum

This is probably the strongest extension.

Give students a published spectrum of a star.

Provide laboratory reference spectra for several elements.

Ask:

Which elements appear to be present?

Students can look for matching patterns.

One matching line is usually weak evidence.

Several matching lines provide a much stronger case.

That becomes a useful lesson in scientific reasoning.

Scientists do not normally identify a substance because one feature happens to look similar.

They search for a consistent pattern of evidence.

A Further Challenge — Can We Build a Simple Spectrometer?

For students who enjoy engineering as well as astronomy, a homemade spectrometer is an excellent project.

A simple design can use:

a narrow entrance slit;
a diffraction grating;
a dark enclosure;
a camera.

The slit restricts the incoming light.

The diffraction grating separates it by wavelength.

The camera records the spectrum.

With suitable calibration, pixel position across the photograph can be related to wavelength.

Calibration might use a known spectral line from a particular source.

Students then move from merely looking at spectra to actually measuring them.

That is a significant conceptual step.

What Does a Diffraction Grating Actually Do?

A diffraction grating contains a very large number of closely spaced lines.

Light passing through or reflecting from the grating interferes.

Different wavelengths emerge strongly at different angles.

A simplified diffraction-grating relationship is:

nλ = d sin θ

where:

n = diffraction order
λ = wavelength
d = spacing between grating lines
θ = diffraction angle

Students who have studied waves may recognise this as another application of interference.

Spectroscopy therefore connects astronomy with wave physics.

The grating does not somehow "colour" the light.

It separates wavelengths that were already present.

What About Looking at the Sun?

The Sun is obviously an exceptionally interesting source for spectroscopy.

Its spectrum contains thousands of absorption lines.

Historically these dark lines are strongly associated with the work of Joseph von Fraunhofer and are often called Fraunhofer lines.

But this also introduces an essential safety issue.

Never look directly at the Sun through optical equipment

Students should never aim:

a telescope;
binoculars;
magnifying lenses;
cameras with optical viewfinders;
homemade optical systems

directly at the Sun unless the equipment is specifically designed and correctly filtered for solar observation.

Concentrated sunlight can cause permanent eye damage extremely rapidly.

For simple educational spectroscopy, use safely projected sunlight or diffuse daylight rather than direct solar viewing.

This is a topic where the science is fascinating, but correct optical safety must come first.

Why I Like This Experiment So Much

There are some experiments that demonstrate a fact.

And then there are experiments that change how a student thinks about what it means to observe something.

Spectroscopy belongs firmly in the second category.

A student looks at an LED and sees white light.

Then they look through a spectroscope and discover structure.

They look at a fluorescent lamp and discover lines.

They look at a sodium source and discover a characteristic signature.

Then you show them a stellar spectrum.

And suddenly the leap becomes possible.

The same physics applies.

The laboratory is no longer disconnected from astronomy.

The student has effectively learned one of the tools used to investigate the Universe.

That is what I particularly like about practical science.

You can begin with an ordinary lamp sitting on a laboratory bench and finish by discussing what distant stars and planets are made of.

The Bigger Lesson — Science Often Means Learning How to Ask Nature Better Questions

The human eye is an extraordinary instrument, but it has limits.

Looking harder at a star does not tell us very much more.

Building a better question does.

Instead of asking:

"What colour is the star?"

we ask:

"Exactly which wavelengths of light are present?"

Instead of asking:

"Does this star appear to move?"

we ask:

"Have its spectral lines shifted?"

Instead of asking:

"What is its atmosphere made of?"

we ask:

"Which wavelengths have been absorbed?"

This is one of the deeper lessons of science.

Progress often comes not from observing the same thing more intensely, but from inventing a new way to measure it.

A spectroscope gives us a different way of looking.

And once we look in that way, the apparently featureless point of light becomes an extraordinary source of information.

Conclusion — Every Star Is Sending Us a Message

Stars are impossibly distant by everyday standards.

We cannot touch them.

We cannot collect samples from most of them.

We cannot place thermometers in their atmospheres.

We cannot follow them with speed cameras.

Yet they continually send something across space towards us.

Light.

And hidden within that light is information.

Chemical composition.

Temperature.

Motion.

Rotation.

Magnetic fields.

Atmospheric chemistry.

Perhaps even clues about planets orbiting stars that our ancestors did not know existed.

All we have to do is learn how to read it.

A spectrum is therefore much more than a rainbow.

It is a message.

And spread across that message are the barcodes of the Universe.

Questions to Explore

For students who want to take the idea further:

Why does a hot solid produce a different spectrum from a hot low-density gas?
Why do absorption and emission lines for the same element occur at the same wavelengths?
Why are blue stars hotter than red stars?
How can spectral lines reveal the speed of a star?
How can line broadening reveal stellar rotation?
Why might several spectral lines be needed before confidently identifying an element?
How can an exoplanet atmosphere affect the spectrum of its parent star during a transit?
Why would finding oxygen in an exoplanet atmosphere not automatically prove that life exists?
How could you calibrate a homemade spectrometer?
What other parts of the electromagnetic spectrum can astronomers use besides visible light?

09 September 2026

What Happens if Euclid Was Wrong? — Geometry on a Curved World

Everyone knows that the angles in a triangle total 180 degrees — until they don't.

For most students, geometry begins with rules that seem almost unbreakable.

Angles on a straight line add to 180 degrees.

Parallel lines never meet.

The angles inside a triangle add to 180 degrees.

Pythagoras tells us that:

a^2 + b^2 = c^2

These ideas become so familiar that it is easy to forget something rather important:

They depend on the kind of space in which we are doing the geometry.

At GCSE, and for much of A-level Mathematics, we are working with Euclidean geometry — the geometry of a flat plane.

But the surface of the Earth is not flat.

The universe may not be perfectly flat either.

And once we allow our geometry to take place on curved surfaces, some of the apparently unquestionable rules of school mathematics begin to change.

This does not mean Euclid was wrong.

It means Euclid was describing one particular kind of geometry.

And there are others.

The Triangle That Adds Up to 270 Degrees

Let us begin with something that sounds impossible.

Imagine standing at the North Pole.

You travel directly south until you reach the equator.

You then turn through 90 degrees and travel one quarter of the way around the equator.

At that point you turn through another 90 degrees and travel directly north.

Eventually you arrive back at the North Pole.

You have travelled along three sides and returned to your starting point.

In other words, you have made a triangle.

Now examine its angles.

At the first point on the equator, the angle is 90 degrees.

At the second point on the equator, the angle is also 90 degrees.

And when the two routes from the equator meet at the North Pole, they can also meet at 90 degrees.

So:

90 + 90 + 90 = 270 degrees

We have constructed a triangle whose angles add to 270 degrees.

No cheating.

No distorted ruler.

No mathematical mistake.

The only thing that has changed is the surface on which we are drawing the triangle.

We have moved from a flat plane to the curved surface of a sphere.

Try It Without Travelling to the North Pole

Fortunately, you do not need an expedition to the Arctic to investigate this.

Find a reasonably large ball.

A football will do. A globe is even better.

Use removable tape, string or a whiteboard marker if the surface allows it.

Choose a point at the top to represent the North Pole.

Now draw or mark:

a line from the North Pole to the equator;
a quarter-turn around the equator;
another line from the equator back to the North Pole.

Try estimating the three angles.

The triangle looks very strange compared with the triangles students normally draw on paper.

That is precisely the point.

Our intuition about geometry has largely developed from working on flat surfaces.

So Was Euclid Wrong?

No.

And this is perhaps the most interesting lesson in the whole subject.

Euclid's geometry is based upon a set of assumptions, or postulates.

If we accept those assumptions, Euclidean geometry follows logically from them.

One particularly important assumption concerns parallel lines.

In simplified form, Euclidean geometry tells us that through a point outside a given line, there is exactly one line parallel to the original line.

That sounds obvious.

But mathematicians spent centuries wondering whether this statement really had to be true.

What happens if we change it?

Something extraordinary happens.

We get completely different — but still logically consistent — geometries.

What Is a Straight Line on a Sphere?

This question is more difficult than it first appears.

If I draw a straight line on a piece of paper, we all know roughly what I mean.

But what counts as the equivalent of a straight line on a sphere?

On a sphere, the important paths are called great circles.

A great circle is a circle drawn around the sphere whose centre is also the centre of the sphere.

The equator is a great circle.

Lines of longitude also form great circles when continued around the entire Earth.

Most lines of latitude, however, are not great circles.

The 50 degree north line of latitude, for example, forms a smaller circle around the Earth.

Why are great circles important?

Because travelling along a great-circle route gives the shortest path between two points on a spherical surface.

That brings curved geometry directly into the real world.

Why Airline Routes Look Curved on Maps

Look at the route of a long-distance flight on a conventional flat map.

A flight from London to somewhere on the west coast of North America may appear to curve surprisingly far north.

At first sight, that can look inefficient.

Surely a straight line across the map would be shorter?

The problem is not the aircraft.

It is the map.

We are trying to represent the curved surface of the Earth on a flat sheet of paper or computer screen.

That inevitably introduces distortion.

The shortest path across the spherical Earth is approximately a section of a great circle.

When that great-circle route is transferred onto many types of flat map, it appears curved.

So the aircraft can appear to be flying along a curved route on the map while actually following something close to the shortest available route across the Earth.

This is a lovely example of mathematics changing the way we interpret something familiar.

What Happens to Parallel Lines?

Now things become even stranger.

Take two lines of longitude.

Near the equator, they are separated.

Travel north along them and they become closer together.

Eventually they meet at the North Pole.

Travel south instead and they meet at the South Pole.

So our familiar idea that parallel lines remain the same distance apart and never meet no longer works in the same way.

Indeed, on spherical geometry, great circles always eventually intersect.

There are effectively no parallel great circles.

Compare that with ordinary Euclidean geometry, where parallel lines never meet.

Already we have two very different geometrical worlds.

There Is Another Possibility: Hyperbolic Geometry

A sphere curves one way.

But mathematicians can also study spaces with a different sort of curvature.

This leads to hyperbolic geometry.

One way of imagining this is to think of a saddle-shaped surface, although the full mathematical idea is more general than simply drawing on a saddle.

In hyperbolic geometry something remarkable happens.

Through a point outside a line, more than one line can be drawn that never meets the original line.

And triangles behave differently again.

On a flat Euclidean plane:

Triangle angle total = 180 degrees

On a sphere:

Triangle angle total > 180 degrees

In hyperbolic geometry:

Triangle angle total < 180 degrees

So there is nothing universally sacred about 180 degrees.

It belongs to one particular geometry.

A Surprisingly Deep Connection Between Area and Angles

For A-level students wanting to take the idea slightly further, spherical triangles contain another beautiful result.

Suppose the angles of a spherical triangle are A, B and C.

Calculate how much their total exceeds 180 degrees.

This difference is called the spherical excess.

For example, our North Pole triangle has:

A + B + C = 270 degrees

so its excess is:

270 - 180 = 90 degrees

On a sphere, this excess is related directly to the area of the triangle.

In a more advanced treatment, if the excess E is measured in radians:

Area = R^2 x E

where R is the radius of the sphere.

That means the angles of a spherical triangle tell us something about its physical size.

That is quite different from ordinary plane geometry.

On a flat sheet of paper, I can draw a tiny triangle and an enormous similar triangle with exactly the same three angles.

On a sphere, curvature changes the relationship.

An Experiment With Three Different-Sized Triangles

This makes a useful investigation.

Take a globe or large ball and construct several spherical triangles.

Make one fairly small.

Make another much larger.

Try to measure their angles as accurately as possible.

You should find that very small triangles behave rather like ordinary Euclidean triangles.

Their angles may add to something very close to 180 degrees.

But make the triangle large enough and the curvature becomes important.

The departure from 180 degrees becomes increasingly noticeable.

This gives us another fascinating idea.

Euclidean Geometry Can Be a Very Good Approximation

The surface of the Earth is curved.

Yet if I draw a triangle on my desk, I do not need spherical geometry to calculate its angles.

Why?

Because my triangle is tiny compared with the Earth.

Across a sufficiently small region, the curved surface looks almost flat.

It is rather like standing in a large field.

The ground beneath you appears flat even though you know that the Earth as a whole is approximately spherical.

This idea — that something curved can look flat when examined over a sufficiently small region — appears in many areas of mathematics and physics.

From School Geometry to Einstein

There is an even bigger reason why non-Euclidean geometry matters.

It eventually became essential to modern physics.

Einstein's general theory of relativity describes gravity not simply as a mysterious force pulling objects towards one another, but in terms of the geometry of spacetime.

Mass and energy affect the geometry of spacetime.

Objects then move through that geometry.

The mathematics required to describe this is far beyond GCSE and A-level Mathematics, but the underlying idea is accessible:

Geometry does not merely have to describe shapes drawn on paper. It can describe the structure of the universe itself.

A subject that can begin with rulers, compasses and triangles can eventually lead towards black holes, gravitational lensing and the expansion of the universe.

Why This Matters to Mathematics Students

There is a broader lesson here that I particularly like students to encounter.

At school it is very easy to get the impression that mathematics consists of a collection of rules.

Learn the rule.

Apply the rule.

Get the answer.

But mathematics is much more interesting than that.

We also ask:

Why is the rule true?

What assumptions does it depend upon?

What happens if we change those assumptions?

Does the new system remain logically consistent?

Those questions move us from simply using mathematics towards actually thinking mathematically.

The statement:

"The angles of a triangle add to 180 degrees"

is therefore incomplete.

A better statement would be:

"The angles of a triangle drawn in a Euclidean plane add to 180 degrees."

That extra qualification changes everything.

A Challenge for GCSE Students

Suppose someone tells you:

"Parallel lines never meet."

Ask:

Where?

On an ordinary flat plane, yes.

On the surface of a sphere, our equivalent "straight lines" — great circles — do meet.

Now consider the Earth.

Which of the following are great circles?

the equator;
the Greenwich meridian;
the Tropic of Cancer;
the Arctic Circle.

The equator is a great circle.

A complete meridian, together with the opposite meridian, forms a great circle.

The Tropic of Cancer and Arctic Circle do not.

That distinction matters when calculating shortest routes over the Earth.

A Challenge for A-Level Students

Try researching the three major geometrical possibilities:

Euclidean geometry

Flat curvature.

Triangle angles total 180 degrees.

Spherical geometry

Positive curvature.

Triangle angles total more than 180 degrees.

Hyperbolic geometry

Negative curvature.

Triangle angles total less than 180 degrees.

Then ask a much more difficult question:

How could you determine the geometry of the space you were living in without being able to look at it from outside?

One possibility would be to construct extremely large triangles and measure their angles very accurately.

If they consistently total 180 degrees, space may be approximately flat.

If they total more, that suggests positive curvature.

If they total less, that suggests negative curvature.

Suddenly measuring the angles of a triangle has become an experiment about the nature of space itself.

The Most Important Lesson Is Not About Triangles

For me, the most valuable part of this topic is not remembering the words "spherical geometry" or "hyperbolic geometry".

It is discovering something about mathematics itself.

Students spend years being taught mathematical statements that appear absolute.

Then they encounter a subject like non-Euclidean geometry and discover that mathematics often starts with assumptions.

Change those assumptions carefully, and a completely different mathematical world may emerge.

A triangle does not always have to contain 180 degrees.

Parallel lines do not always have to behave as expected.

A "straight line" depends partly upon the space through which we are travelling.

And the geometry learned at school turns out to be one member of a much larger family of possible geometries.

Euclid was not wrong.

He was describing a flat world.

The remarkable discovery was that mathematics did not have to stop there.

Everyone knows that the angles in a triangle total 180 degrees — until they ask what sort of world the triangle is drawn on.