Colour, Dispersion and What the Spectrum Is Used For

The waves module already established the things this lesson would otherwise have to prove: that light is an electromagnetic wave, that all such waves travel at c in a vacuum, that wave speed equals frequency times wavelength, and that the spectrum runs in a fixed order from long-wavelength radio to short-wavelength gamma. This lesson does not repeat any of that. It answers the two questions that treatment leaves open — what makes white light separate into colours when it passes through glass, and what each band of the spectrum is actually used for — and then defines two words, polarisation and diffraction, that turn up in answer options far more often than they turn up in the syllabus.

White light is a mixture, and a prism does not add anything to it

Sunlight, and the light from an ordinary filament lamp, looks colourless. Pass it through a triangular glass prism, though, and what emerges is a fan of colours in a fixed order: red, orange, yellow, green, blue, violet. Pass that fan through a second prism turned the other way and you get white light back. Block one colour with a card and the recombined light is no longer white but tinted. The conclusion is forced: the colours were present in the white light all along, and the prism only sorted them out. It is a filing operation, not a manufacturing one, and the process is called dispersion.

Why the colours separate

The mechanism is one line long, and it is a small honest correction to Lesson 3. There, the refractive index of a material was treated as a single number. In fact the refractive index of glass is very slightly different for different wavelengths of light: it is a little higher for the short wavelengths at the violet end and a little lower for the long wavelengths at the red end. For a typical glass the index might be 1.51 for violet and 1.50 for red — a difference of well under one per cent, which is why ignoring it everywhere else was legitimate.

That tiny difference is enough. A higher refractive index means slower light and stronger bending, so violet is refracted more sharply than red at both faces of the prism, and the two deviations add. By the time the beam leaves, the colours that entered together are travelling in measurably different directions, and the fan spreads further the further it goes. Because red has the longest wavelength and the lowest index it is deviated least; violet has the shortest wavelength and the highest index and is deviated most. Everything else falls in between in wavelength order, which is exactly why the spectrum comes out in that order rather than jumbled.

A rainbow is the same effect performed by raindrops. Light enters a drop and is refracted, reflects off the inside of the back surface, and is refracted again on the way out; each refraction sorts the colours a little, and the geometry of a sphere sends the sorted light back towards the Sun's direction in a cone of fixed angle. That is why a rainbow is always a circular arc, why it always appears opposite the Sun, and why red is on the outside — red is deviated least, so it emerges at the wider angle.

Colour, wavelength and frequency

Within the visible band, what your eye reports as colour is a reading of wavelength. Red light has the longest wavelength of the visible colours, around 700 nanometres — a nanometre being a billionth of a metre — and violet the shortest, around 400. Everything else lies between: orange, yellow, green, blue in that order as the wavelength shortens. Since the speed is fixed and speed equals frequency times wavelength, frequency has to run the opposite way, so red is the lowest-frequency visible light and violet the highest. The two orderings are always reverses of each other, and confusing them is one of the easiest marks to give away.

That relationship is the one from the waves module with the speed of light substituted in, and it is worth restating because both of the worked examples below use it.

Rearranged for wavelength it reads $\lambda = \frac{c}{f}$, by dividing both sides by f; rearranged for frequency it reads $f = \frac{c}{\lambda}$, by dividing both sides by λ. Because c is fixed, the two quantities are locked in opposition: double the frequency and the wavelength halves.

One further point about colour, since the word has now been used a great deal. An object is not coloured in itself; it looks a colour because of which wavelengths it sends to your eye. A red book absorbs most of the wavelengths falling on it and diffusely reflects the long ones, so red is what reaches you. A white surface reflects all of them roughly equally and a black one absorbs nearly all of them, which is why a black surface in sunshine warms faster — it is keeping the energy instead of returning it. Illuminate the red book with pure blue light and it has no red to reflect and nothing else it can send back, so it looks almost black.

The bands, and what each is used for

Visible light occupies a startlingly narrow slice of the spectrum — roughly 400 to 700 nanometres out of a range spanning from kilometres to fractions of an atom's width. Everything to the long-wavelength side of red is infrared, then microwave, then radio; everything to the short side of violet is ultraviolet, then X-ray, then gamma. The bands have no hard borders, because there is nothing physically different about them: they are all the same kind of wave, they all travel at c in a vacuum, and the names are labels for regions of a continuous range picked out by how the waves happen to be produced and used.

At the long end, radio waves are used for broadcasting and for any communication over a distance, because their great wavelength lets them diffract around obstacles and, for the longest of them, follow the curve of the Earth. Microwaves are shorter radio waves, used for satellite links and mobile phones because they pass through the atmosphere cleanly, and for cooking because their frequency happens to be well absorbed by water molecules, so the water in the food is heated directly, well below the surface, rather than only by conduction inwards from the outside. Infrared is the band immediately beyond red, emitted by everything warm — this is the thermal radiation of the heat module, seen from the optical side — so it is used for thermal imaging, for remote controls, and for any heating that works by radiating rather than by contact.

At the short end the wavelengths are small enough to interact with individual atoms, which makes the radiation both more useful and more dangerous. Ultraviolet, just beyond violet, causes suntan and sunburn, makes some materials fluoresce — the basis of security marking and of the coating inside a fluorescent tube — and sterilises by damaging the cells of micro-organisms. X-rays pass through soft tissue but are absorbed by denser material such as bone and metal, which is what makes radiography and security scanning possible. Gamma rays, shorter still, come from atomic nuclei and are used to sterilise surgical instruments and to treat tumours. The general rule is that the shorter the wavelength, the more energy each part of the wave carries and the more damage it can do to living tissue, which is why exposure to the short end is controlled and exposure to the long end is not.

Scattering, and why the sky is blue

Scattering is what happens when light meets particles much smaller than its own wavelength — the individual molecules of the air, for instance. Instead of being reflected in a definite direction or refracted through a definite angle, a little of the light is absorbed and immediately re-radiated in all directions, and the effect is much stronger for short wavelengths than for long ones. Blue and violet are therefore scattered far more than red and orange by the atmosphere.

The daytime sky is bright away from the Sun because of that scattered light, and it is blue because blue is what gets scattered most — you are seeing sunlight that came in on some other path and was redirected towards you by the air. Violet is scattered even more than blue, but there is less violet in sunlight and the eye is less sensitive to it, so the sky reads blue rather than purple. The same mechanism, run the other way, gives red sunsets: with the Sun low, its light travels a long slanting path through the atmosphere, most of the blue is scattered out of the beam before it reaches you, and what arrives directly is the remaining long-wavelength red and orange.

Polarisation

Light is a transverse wave, which means that whatever is oscillating in it does so at right angles to the direction the wave is travelling — side to side rather than back and forth along the ray. That leaves a choice the wave equation says nothing about: side to side in which of the many directions perpendicular to the ray? In ordinary light from a lamp or the Sun, every one of those directions is represented in equal measure, jumbled and changing constantly; the light is unpolarised. Polarised light is light in which the oscillation has been confined to a single plane. A polarising filter transmits only the component lying in one plane and blocks the rest, which is why it cuts brightness roughly in half; put a second filter behind the first and rotate it, and at ninety degrees it blocks nearly everything, because the light reaching it has no oscillation left in the direction the second filter would pass. Light reflected at a shallow angle off water or a road surface comes away partly polarised horizontally, which is what polarised sunglasses are built to reject.

Diffraction

Diffraction is the spreading of a wave as it passes the edge of an obstacle or goes through a gap, and it is the one respect in which the straight-line rule from Lesson 1 is only an approximation. A wave squeezing through an opening does not continue as a beam of exactly the opening's width; it fans out beyond it, and the narrower the gap the wider the fan. How much matters depends entirely on the comparison between the gap and the wavelength: the effect is pronounced when the two are of similar size and negligible when the gap is much the larger. That is why the metre-scale wavelengths of radio diffract usefully around hills and buildings while visible light, with wavelengths under a thousandth of a millimetre, casts shadows sharp enough that Lesson 1 could treat light as travelling in perfectly straight lines. Diffraction of light is real but needs an aperture measured in fractions of a millimetre before it becomes obvious.

Why it matters in aviation

Colour carries information in aviation because it can be taken in at a glance, with nothing to read or measure. Navigation lights are the clearest case: red on the left wingtip, green on the right and white at the tail, so another pilot who sees two of them at night can infer which way that aircraft is travelling from the colours alone, before any shape is visible. Approach slope indicators use the same economy, signalling high or low by colour rather than by a figure to be interpreted. Inside the cockpit, weather radar returns are coded by intensity in colour, so a glance at the display conveys how strong a return is without the crew working along a scale.

All of that is why colour vision is a medical requirement rather than a preference: a pilot who cannot separate red from green loses information the whole system assumes has been received. And dispersion is why those colours exist to be sorted in the first place — a prism, or a raindrop, separates white light into its components because glass and water bend the short wavelengths slightly more than the long ones.

What the test asks

The signature distractor here is that the prism adds colour to white light, or that it converts white light into coloured light — sometimes dressed up as the glass filtering or staining the beam. It does neither: the colours were in the beam already and the prism sorts them, which is why a second prism can put them back together. Expect the wavelength ordering offered backwards, with violet as the longest wavelength, and expect the frequency ordering offered as if it matched the wavelength ordering rather than reversing it. A third family of items uses the bands: infrared paired with sterilising, or ultraviolet with thermal imaging, so it is the uses rather than the order that has to be right. And because polarisation and diffraction show up almost exclusively as tempting wrong answers, check what the item is actually describing before picking one — if colours are separating, that is dispersion by refraction, not diffraction and not polarisation.