Some effects are frequency dependent

Devices for lighting a room switch power to a particular pathway: the heating by radiation pathway. If the source emits at least the frequencies that our built-in detectors respond to, you'll see the environment in colour. However bright or dim the beam, the colour doesn't change. This suggests that there is something intrinsic to whatever it is that forms the physical basis of the beam that is not connected to the amplitude.

The SPT: Light topic established the connection between seeing a particular spectral colour and the frequency of vibration of the beam. This is correct, but a useful and necessary refinement has been added since the turn of the last century.

Increasing the brightness of the beam increases the power in the lighting pathway. For some processes, this description is not good enough: these depend on something about the beam other than there simply being enough power in the pathway. Some effects of the beam are frequency dependent. This should not really be a surprise – even seeing colour is clearly a frequency-dependent effect.

Some effects cannot be produced just by making the light brighter

No matter how bright a beam of red light shone onto a white wall, the wall will never appear violet. There are a whole range of phenomena like this, for which a rather simple modification to the SPT: Light topic model of lighting provides the most plausible, intelligible and fruitful explanation. That is not to say that the deeper consequences of the theory are easy to understand, but it is easy to get started.

Lighting is granular – a patter of very small drops, each shifting a very small amount (a quantum) of energy. Determining the power in a pathway is then a matter of finding the rate of arrival of the drops and the energy shifted by each drop.

The photon model of lighting: granular shifting of energy

This granular delivery of energy during lighting is the photon model of light. This was invented by Planck and Einstein in about 1905, but physicists and philosophers are still arguing about how to interpret it. You'll meet some of these issues in episode 04.

If our eyes had evolved to be about ten times more sensitive, then we'd have got started a lot earlier, because we'd see the individual flashes of light arriving at low beam intensities.

What we can say with confidence, based on reliable empirical evidence, is that power in a lighting pathway depends on energy being shifted from sources in small chunks and also being absorbed in these chunks. These chunks are of a particular size, so are called quanta of energy. The quantum of lighting, and indeed all electromagnetic radiating, is the photon. The evidence is not direct, because we cannot detect single photons, but there are phenomena that can only be explained by this model. Now we can build instruments that do detect single photons. You may have heard the clicks that indicate gamma radiation arriving using a Geiger–Muller tube (more in episode 04).

So a beam of light, on the nanoscale, can be pictured as a stream of photons. But, and it turns out to be a big but, anything apart from the emitting and detecting is inferential. There is very good evidence that emission and absorption happen in chunks. However, we simply don't have any evidence for granularity in transit. How could we have? As soon as you detect a photon – it's destroyed, so you cannot spot it in transit.

Lighting is done by variable sized quanta: red patters; blue batters

Lighting in a red beam (spectral red) is done in small chunks: each granule, or quantum, is typically 3 × 10^-19 joule.

Lighting in a green beam (spectral green) is done in larger chunks: each quantum (plural quanta) is typically 3.8 × 10^-19 joule.

Lighting in a violet beam (again spectral, not perceptual) is typically 4.8 × 10^-19 joule.

These are quite small numbers – between 3.0 and 5.0 attojoule (1 attojoule is 1 × 10^-19 joule. That's right down at the scale of energies in atomic systems (30–50 attojoule), which is again a clue as to the quantum origins of light.

To get a brighter beam in each case, simply deliver more quanta in each second. A green beam that seems to be green to us (so a perceptual colour, not a spectral colour) may consist of a range of frequencies (see SPT: Light topic), and so a range of photons.

So monochromatic beams of light vary in the effects they can produce as the energy shifted by each photon varies with the colour. The same applies to other radiations, which are called monochromatic by extension, even though there is no colour. Perhaps you can see how this might begin to explain why ultraviolet light causes sunburn, yet bright red light does not, and maybe even why you cannot pick up (i.e. see) radio stations, or indeed most of the electromagnetic spectrum. (Although there are stories in the press of people picking up Radio 4 through fillings in their teeth, these intriguing anecdotes are best left to post-16 studies, where you can explore the mechanisms with your class.)

Droplet by droplet, where droplet size depends on frequency

In lighting, energy arrives tiny shot by tiny shot. Typically the pathway fills a thermal store. Energy can be modelled by an orange liquid, so the thermal store becomes a pot of orange liquid, more or less full.

As the store is filled, think of the inbound liquid not as a steady stream but as rather small droplets.

You might think of the pot representing the store being filled by small but variable measures of orange liquid, rather than as a steady stream.

A set of measuring spoons might be used to add the liquid to the pot, each labelled, from smallest to largest, as red photon, yellow photon, blue photon.

More exactly, you might say, photon causing yellow lighting, but you would not want to make a habit of a mouthful like that so the contraction is probably a good idea; just be aware that it is a contraction.

Suitable ratios follow the frequencies of the photons, as the energy shifted is proportional to the frequency, so you might choose:

Teacher Tip: The ratio of frequencies of red light:green light:violet light is 1:1.5:2 and you can model that by doling out orange liquid with different spons, in fact the ratio is teaspoon:dessertspoon:tablespoon.

Research might even reveal a set of coloured spoons of the correct hues in your local kitchen shop.

Photons are only detected when they are destroyed

There is a perplexing thing about photons that follows directly from these same photons being something used to model lighting. You may remember the experiment strongly recommended in the SPT: Light topic where chalk dust is used to scatter the light from the beam to reveal where the beam was going. Notice the past tense. Even in that simple experiment, and with the simple 11–14 model to hand, careful thought reveals that there is a significant philosophical tussle to be had if you insist on asking the question What is light? or even Where is the light?

This arises because you cannot see light: in an explanation we now have access to, you have to destroy the photons before you can know where they are (whoops – were). It was the same with the light beam, only more difficult to explain and picture exactly what was happening: as each segment of the chalk dust is traversed, some of the intensity of the beam is transmitted, some is reflected, and some is absorbed.

After 11–14 we could say that some of the amplitude of the vibrations travelled on and some of the amplitude was reflected by the dust. This is unsatisfactory as a model to think about unless we have a rather sophisticated mathematical model of the amplitude splitting. It is certainly quite hard to picture what is happening. We think that the photon account is easier to deal with here: some photons go on; some are absorbed; and some are reflected. Thinking in terms of a stream of individuals turns out to be easier than imagining what is happening with a continuous wave.

The power in a beam depends on the frequency of the photons and the activity

The frequency of the light associated with each photon sets the energy shifted by each photon.

Take two equally bright beams of monochromatic light (all photons in a beam have the same frequency and so appear to be the same colour to us) – one that shows up blue and one that shows up green. The energy shifted by the blue beam will arrive in fewer and larger chunks. The power in the pathway associated with the green beam is identical to that of the blue beam: they are the same brightness. However, the energy is shifted by more and lower-energy photons.

The power in the beam is the product of two factors of the stream of photons:

• The energy shifted by each photon.
• The number of photons emitted each second (the activity).

Compensation

The energy shifted by each photon increases as the frequency increases (in fact, the energy per photon is proportional to the frequency). So you can compensate for low-energy photons by supplying many of them: there is a trade-off to obtain the same brightness. The character of the pathway alters, just as in the SPT: Electricity and energy topic, where the trade-off was between potential difference and current.

However, there are some effects that depend on the nature of the photons, such as seeing some effects as coloured: only photons of certain frequency are reflected or transmitted.

Differential absorption of photons explains filter action

Beams of white light consist of photons of a range of frequencies. There could be several combinations that all appear white to us. The photon model can be used to explain how filters work. Photons with certain frequencies are absorbed, while others are transmitted. The balance between the numbers of photons of different frequencies in the stream is altered, so the colour of the beam changes.

Different materials can be engineered to make filters that absorb particular frequencies. Such frequency-specific filters are expensive. However, simple filters that absorb a range of different frequencies to change the colour of beams are quite inexpensive. How might this happen?

Photons could be selected by energy as this varies with frequency. So some processes within the material are enabled if the correct quantity of energy is offered by the photon, and the photon is absorbed. The photon is rejected (for filters, by transmission) if there is no match in energies between what the photon shifts and what the process requires. This is a simple model and it fits in well with the idea that the energy available simply tells you what can and cannot happen (more in the SPT: Energy topic). However, notice something new here: there has to be a match in energy, not just more than enough. This is a difference from the previous model that will be explored.

Frequency and energy shifted by each photon are linked

The frequency of a visible photon is measured in terahertz (400–700 terahertz). The energy of such photons is measured in attojoules (30–50 attojoule).

The energy increases with the frequency, but you're not getting many joules for each hertz. The increase is proportional.

The constant of proportionality is rather famous: Planck's constant. It is a very small number, h is 6.67 × 10^-34 joule inverse hertz.

Then the connection between the energy and frequency of a photon is remarkably simple: E = h × f.

Energy related to frequency

The proportionality between the energy shifted by each photon and the frequency of that photon was established in the early years of the 20th century, and was the start of the revolution in our understanding of the universe that is quantum physics. Nothing was ever quite the same again. This was especially traumatic for Planck, a rather conservative thinker, who did such fundamental work in the area that his name is used for the constant that relates energy to frequency. It's now a quantum signature: whenever you meet h, Planck's constant, you are in the realm of the quantum. This is where the physics of the very small rules. And the rules are often counter-intuitive. Think about this for a while and you won't be so surprised: our intuitions are developed over timescales of seconds, and distances of metres – far removed from the time and space where individual photons interact.

Photons used to explain the interaction of light with matter

Photons are all-or-nothing entities: you cannot emit or absorb half a photon. (Remember that to detect a photon you have to destroy that photon.) On destruction, a photon shifts all of the energy to a store, filling that store by a tiny and characteristic amount.

The power switched from the lighting pathway depends on the number of photons destroyed each second and the energy shifted by each. You cannot half-destroy a photon – it is all or nothing. Thus there are discrete micro-steps in the accumulation of energy in the store. This graininess led to the quantum name. The steps for blue photons are larger than the steps for red photons.

Inside materials, considering individual atoms and molecules, there are similar energetic steps: the stores can only be filled by discrete increments. Where there is a close enough match between the energy shifted by the photon and the energy the store can accept, the photon is destroyed and a process within the material is enabled. This explains processes like filtering by frequency: this is just filtering by energy, as the energy depends on the frequency.

In other cases, what is happening is different, and there is a threshold effect. So long as the photon provides enough energy, the process is enabled, and the excess is dissipated in some way.

Two kinds of absorption of photons

A well-rehearsed example of the threshold effect, which is important historically, is the photo-electric effect, where photons eject electrons from metals. Once there is enough energy to eject the electron, any extra energy turns up in the kinetic store of the ejected electron.

If there is no such dissipative mechanism, providing a store where the excess energy shifted by the photon can be dissipated, then only photons with a narrow band of energies will be absorbed. This is often called a resonant effect, and is much studied in further physics. Perhaps the simplest example, and so well worn, is that of a child on a swing. If you match the frequency of pushes to the natural frequency of the swing, you can easily augment the energy in the vibrational store. Pushing with the wrong frequency can be painful and does not facilitate the energy being shifted.

Resonant matching also underpins much of the information we have about the universe. By seeing which photons are absorbed on their way to us, you can work out what lies between Earth and the source.

Later you'll also see how emission also depends on this matching process, so allowing you to infer rather complete descriptions of the atoms and molecules literally light-years away.

Closer to home, plants are green because of the combination of photons that they reject by reflection.

Power in the beam is determind by the energy of each photon and the number of photons emitted per second

The power switched to the heating by radiation pathway is set by the energy of each photon and the number of photons emitted per second. If the beam is not monochromatic, then you'll have to sum across all the frequencies of photons present in the beam, working out the product of activity and energy shifted for each frequency present. This is complex and time consuming but clear and simple in principle.

This power will ultimately fill a store, but the mechanisms will vary over the huge range of frequencies. Remember that lighting is just a part of what the radiations that make up the electromagnetic spectrum do. Heating (microwaves, infrared) is another significant process that is important to humans, as are the carrying of radio and television signals, as in episode 01. The photon description applies right across the range of radiations that make up the electromagnetic spectrum.

Beams can be pictured as directed streams of photons, but remember that this is only a picture – it's only on departure or arrival where we can be certain of the granularity. The intensity of a beam is just the power for each square metre of cross-section of the beam. So intensity is measured in watt metre^-2. The greater the intensity, the brighter the beam, as more energy per second is detected by the absorbers placed in the beam (power = intensity × collision area of detector).

Streams of photons plot the evolution of the beam

Beams have a history in travelling from source to detector. They may spread; be refracted; be reflected; or be partially absorbed. Each of these may have an effect on the intensity.

These effects can be accounted for in terms of the stream of photons picture. It's easy and perhaps helpful to speak as if the photons actually make the journey. If the beam goes through a fog, for example, you can describe the resultant reduction in intensity as a fraction of the photons being absorbed by each metre of fog traversed. This gives rise to an important pattern in radiation protection, which is met again later. A certain thickness of absorber is needed to reduce the chance that a photon makes it through: high up on mountains the ultraviolet photons have traversed less atmosphere to reach you, so there is a greater chance of each one making it through. Multiplied across a whole stream, this increased chance leads to more ultraviolet photons striking your skin. More chance of sunburn.

Spreading is a matter of geometry. For the beam, the same power is spread across increasing areas (measured at right angles to the beam); for the stream, the same number of photons intersects an increasing number of square metres.

Reflection at surfaces can be partial or complete: you can model both by altering the chance that each photon is reflected. Multiply across the whole stream to predict the behaviour of the beam. You can predict the angle of reflection by considering what each photon might do, and we come back to that in episode 03.

Refraction is again a matter of considering the chance that each photon takes a particular path. Again, there is more on that in episode 03.

Power in a pathway is measured in watts: visible power in lumens

The power in the heating by radiation pathway is measured in watts. That's simple and is often called the radiant power. More complex is to think about the flow or flux through a particular area – the number of watts per square metre. This is called the radiant flux.

However, neither of these takes into account the sensitivity of the eye to different frequencies, so they cannot really be measures of brightness. Both the radiant power and the radiant flux could be very high, and yet you could see nothing, because all of the frequencies fall outside the visible range. The energy shifted by the photons in the beam do not match the energy required to trigger the processes in your eye that allow you to see.

There are a range of measures (used in photometry) that are tuned to the standard eye that you may come across. This is a complex area, and a salient selection are dealt with here.

The power of the light detected by the human eye is a good place to start, and is the analogue of the radiant power, adjusted for the human eye. It is measured in lumens. On purchasing a light bulb, you'd be well advised to go for the highest number of lumens per watt you can find, and so maximise the ratio of visible photons: invisible photons. Or, as covered in the SPT: Energy and electricity topic, most of the power will be in the lighting pathway and only a little in the heating pathway.

The lux is a unit that measures detectable brightness

The lumen does not tell you about the brightness, because brightness is about the detectable photon stream per unit area, and there is a photometric equivalent of the radiant flux (wattmetre²) or 1 W m^-2) to perform this function. This is the lux. One lux is 1 lumen metre^-2. You are perhaps most likely to come across it in specifications for the sensitivity of electronic imaging devices (such as video cameras).

Highly sensitive sensors need only a few lux to operate, gathering in only a few photons. A less sensitive sensor can compensate by increasing its area, as the pupil of your eye does when the light grows dim.

Lumens are the modern equivalent of candlepower

There is one more step of interest here. Just as power is of most interest to humans in practical situations (remember the unit horsepower, to show how many horses a new-fangled steam engine could replace), so lighting is of most interest when we put it to work. The candlepower performed the same function as the horsepower for many years as the unit of light intensity. Take one standard candle – of fixed size and constituents – and compare its output with the source that needs calibrating. The luminous intensity of a source depends on the power emitted in a particular direction, as we're usually interested in lighting something, not just lighting.

The modern unit is the candela. If a source is of 1 candela, uniformly in all directions, then it emits a luminous power of 4PI lumens. The candela is now one of six SI base units, to which all others are related, so you have burrowed down to the operationally defined bedrock on which the whole system of units is constructed. That seems a good place to stop – before things get too complicated.

These are the base units:

quantity	unit	symbol
length	metre	m
mass	kilogram	kg
time	second	s
electric current	ampere	A
thermodynamic temperature	kelvin	K
amount of substance	mole	mol
luminous intensity	candela	cd

The candela is used to define the lumen, and the lumen to define the lux.

Candles have not quite been banished – astronomers still refer to standard candles. These are objects of known brightness. From this and the intensity detected on Earth they can work out how far away these objects are, following the candela–lumens–lux route.

Emission and detection in discrete chunks

Lighting and other electromagnetic radiating are emitted and absorbed in discrete chunks. Describing lighting as myriad individual photons streaming from an emitter and streaming to a detector makes many properties of light beam rather easy to explain.

The power in the heating by radiation pathway is a good starting point. The power is set by the number of individuals per second multiplied by the energy shifted by each individual, which is easy to picture and to model.

As photons get absorbed, so the intensity of the beam drops, and the power in the pathway decreases.

If the beam spreads out, then there are fewer photons in each cross-sectional area of the beam and the intensity of the beam again decreases.

Colours are simply due to the frequency of the photons absorbed.

Probabilistic accounts underpin macroscopic phenomena

Beams can alter direction, by reflection and refraction. Reflection caused Newton, who developed and defended a particle theory of light, all kinds of difficulty. He could not really provide a convincing account of partial reflection, where some of the beam goes on, and some is reflected. As with monochromatic photons, all of his particles were identical, yet some had to pass on and some had to be reflected. There was no reason why some of the identical particles would be reflected and some transmitted. We have been a little circumspect up until now as we've always stated what will happen to each individual photon as a probability. It turns out that this is just right, and that the universe, much to Einstein's disgust, does function probabilistically at these very small scales. The average behaviour over the many, many photons in the stream correctly predicts what the beam will do, so long as we can correctly calculate the probabilities.

These calculations can even explain why the angle of incidence is equal to the angle of reflection and what the angle of refraction will be when the beam changes medium. In episode 03 we'll show you the first steps in doing these calculations. Further steps are more appropriate to post-16 studies and even to post-physics degree studies, so we'll tread carefully. The important thing to realise is that here we have an honest starting point.

Colour is a matter of the selection of photons offered to the eye

Coloured lighting can be a beam of monochromatic photons: identical individuals of the same energy and frequency. This is an example of a spectral colour. Change the individuals making up the beam and the colour changes.

Coloured lighting can appear identical to the first case but also be a mixture of photons, each of a single frequency, but with many frequencies present in the beam. This is then an account of perceptual colour.

The matching between the photons and some processes in materials explains selective absorption, on which much of our knowledge about the world seems to depend, since we infer so much from the frequency and number of photons arriving. Again, much more depth is possible in these explanations, but we are off on the right lines and one model is shown to have wide applicability.