# 03Multiple contributions

• ## 01 Things you'll need to decide on as you planRa03TLnugget01 Decisions

### Bringing together two sets of constraints

Focusing on the learners:

Distinguishing–eliciting–connecting. How to:

• make connections to prior studies of reflection, propagation and refraction
• exploit the simple idea of being in-step
• keep refraction and diffraction separate
• build on the idea of do like me – but later

Teacher Tip: These are all related to findings about children's ideas from research. The teaching activities will provide some suggestions. So will colleagues, near and far.

Focusing on the physics:

Representing–noticing–recording. How to:

• bring the phenomena into focus through well-managed demonstrations
• attach specific and precise meaning to new technical terms
• exploit the ideas of paths and trip times and contributions

Teacher Tip: Connecting what is experienced with what is written and drawn is essential to making sense of the connections between the theoretical world of physics and the lived-in world of the children. Don't forget to exemplify this action.

• ## 02 A common pattern across many different phenomenaRa03TLnugget02 Introduction

### Waves interacting

This episode starts by thinking about what happens when two trains of waves meet one another.

The waves in question might be water waves in the ocean, or sound waves at a music concert or light waves from the Sun.

The same underlying principles apply to all such examples when considering how the trains add together.

Later there are not such obvious trains, but the same patterns of reasoning turn out to be reliable in predicting what happens.

• ## 03 Sources in stepRa03TLnugget03 Challenge

### Two waves interacting: it is essential to know about the starting conditions

Wrong Track: To find out whether two sets of waves are in step at a certain common point, all we need to know is the trip time. If the trip time is the same for both waves they must arrive in step.

Right Lines: If you have two sets of waves from different sources they will arrive at a common point in step if they are in step with each other at their respective starting points; they are of the same frequency; and they have the same trip time. The technical term for two sources being in step is that they are coherent. To be coherent, the two sources need not be exactly in step: they might be exactly out of step or somewhere in between. The critical point is that there is a constant, unchanging phase relationship between the two sources.

• ## 04 Technical termsRa03TLnugget04 Teaching tip

### Defining new terms: superposition and interference

From a teaching and learning point of view it is well worth the time and effort to introduce new terms carefully.

When two sets of waves interact and combine, the phenomenon is termed superposition and the waves are said to interfere.

If the two sets of waves are directly in phase (or in step) at a certain point, the wave amplitudes add together and full constructive interference occurs.

If the two sets of waves are directly out of phase (or out of step) at a certain point, the wave amplitudes cancel each other out and full destructive interference occurs.

Teacher Tip: If two contributions superpose then there is interference.

Teacher Tip: Contributions out of step are out of phase:

Superposition  → destructive interference.

Teacher Tip: Contributions in step are in phase:

Superposition  → constructive interference.

### Water waves and ripple tanks

There is a long tradition of starting with water waves when teaching about waves and radiation in physics. This makes a lot of sense because, unlike with light and sound, it is possible actually to see the water waves being reflected, refracted, diffracted and interfering.

In addition, the first hand nature of water waves is a good starting point for explaining interference effects with:
• Constructive interference leading to the creation of double-sized water waves
• Destructive interference leading to flat water

It would be worth checking to see whether your school has a ripple tank that can be used to demonstrate all of these effects.

Teacher Tip: You'll need to practice, and to pay particular attention to the setting up instructions – getting the depth of the water correct is often crucial.

• ## 06 Bending and spreadingRa03TLnugget06 Teaching tip

In our experience, students often confuse the terms, refraction and diffraction. With this in mind it's useful to practice the following mantra:

Teacher: So! Let's just remind ourselves, what's the difference between refraction and diffraction of light?

Teacher: Exactly! Refraction involves the bending of light at some interface between two media, such as air and glass. Diffraction involves the spreading of light around a barrier or through a gap.

Teacher Tip: Bend a beam  → refraction.

Teacher Tip: Spread a beam  → diffraction.

• ## 07 Conservation of energy and two-slit interferenceRa03TLnugget07 Challenge

### What happened to the energy?

Wrong Track: OK, so in some places there are dark fringes in the interference pattern. This means that there is no light arriving and so no energy is being shifted. Destructive interference has destroyed some energy.

Right Lines: You're absolutely right! No energy is arriving at those points on the screen where there are dark fringes. But, the dark fringes are compensated for by the bright fringes. No energy is being shifted to the dark fringes but extra energy is being shifted to the bright fringes to compensate.

• ## 08 Interference patterns from a single slitRa03TLnugget08 Challenge

### How can a single slit produce an interference pattern?

Wrong Track: It can't be possible to get an interference pattern from a single slit. You need two slits to get the two sets of waves to interfere.

Right Lines: A narrow single slits does produce an interference pattern. You need to think about rays of light coming from different points along the single slit and interfering constructively and destructively.

### Think about rays from different points along the slit

Many students find it counter-intuitive that a single narrow slit can produce an interference pattern, especially if interference ideas have been introduced by considering a two-slit case.

A good starting point for teaching about single-slit diffraction is to show your students the physical effect:

Teacher: So you can see what is produced on the screen when the light is passed through a single slit. What does it look like?

Naomi: It looks a bit like an interference pattern: fringes sort of thing.

Teacher: And where did we see that?

Emmy: With the twin slits…

Teacher: OK! You're right! But this is odd! How on earth is it possible to get an interference pattern with a single slit? What's doing the interfering? Any thoughts?

In this way the problem of how the interference pattern might be produced is raised and tossed back to the students to think about. In our experience some students do edge towards the correct solution of thinking about interference between contributions from different points along the single slit. These contributions interfere constructively and destructively due to the differences in trip times as they travel out to a screen from different points along the slit.

• ## 09 Trip times and path differencesRa03TLnugget09 Exposition

### What's the difference between trip times and path differences?

The concept of trip time is introduced in the Physics Narrative for this episode and this might be a new idea for you. Furthermore, it is quite likely that you have previously come across the idea of path differences in thinking about and explaining phenomena such as Young's fringes. So, what's the difference between the two?

In relation to explaining Young's fringes there is no real difference in thinking in terms of either trip times or path distances. If light rays pass through the two slits and take the same time to travel to a point on the screen (often by travelling the same distance to a point on the screen), then they will arrive at that point in step and constructive interference, creating a bright fringe on the screen. Because the speed of light is constant, the analyses in terms of time or distance lead to the same outcome.

So things might seem balanced, but we believe that the advantage, even here, rests with the time-based description. If you get back to basics – that is back to do like me, but later – then you should notice that it's all about the time. For two contributions to add (superpose constructively), it's the relationship between their laters that's important.

The value of an approach using trip time becomes even clearer when analysing a situation where the speed of light changes due to the light travelling through different media. Thus in the case of refraction the actual path taken by a ray of light as it passes through, say, a prism, can be identified as the one that takes least time.

The big advantage in thinking about trip times is that this single idea can be used to account for a whole list of phenomena, including reflection, refraction and interference.

• ## 10 Waves of what?Ra03TLnugget10 Exposition

### What do wave ideas tell us about light?

In thinking about the production of dark and light fringes on a screen as light passes through two slits to create interference effects, the basic questions of interest are:

Where on the screen will photons of energy arrive? Where are the light places, where are the dark places?

These questions are answered by using wave ideas, and thinking about trip times and possibly path differences. At places where wave theory tells us that the amplitudes of the interfering waves add constructively, we can expect to find lots of photons arriving. Where wave theory tells us that the amplitudes of the waves add to nothing through destructive interference, we can expect not to find photons arriving.

In this way we use wave ideas to predict the probability of photons arriving at certain places. In fact, the probability of photons arriving is proportional to the square of the amplitude of the resultant wave at that point. With these procedures in mind, we might say that light waves are probability waves telling us where photons of energy are most likely to arrive.

• ## 11 A bit of philosophy?Ra03TLnugget11 Exposition

### Thoughts from Richard Feynman

One distinction that is made by philosophers about the nature of science is in terms of it being a positivist or realist activity.

Positivists see the role of science as developing theories that successfully account for empirical measurements. Questions such as But what is really there? are of no interest to positivists. On the other hand, realists see the role of science as being one of discovering what the physical world is actually like.

In the realms of quantum theory, light is considered to have both wave-like and chunks of energy properties, which goes against expectations developed from direct experience of the natural world. In the natural world we expect that things are either one (waves) or the other (chunks of energy).

Richard Feynman, in the introduction to his book, QED: The strange theory of light and matter, has something to say on matters of this kind: There is this possibility: after I tell you something, you just can't believe it. You can't accept it. You don't like it. It's a problem that physicists have learned to deal with: they've learned to realise that whether they like a theory is not the essential question. Rather it is whether or not the theory gives predictions that agree with experiment. The theory of QED describes nature as absurd from the point of view of common sense. And it agrees fully with experiment. So I hope you can accept Nature as she is… absurd.

Thus Feynman argues that the quantum view of the world doesn't seem to make sense in relation to common experience. However, this is not what counts. He takes a straight positivist point of view in stating that what matters is whether or not the theory gives predictions that agree with experiment.

In typical Feynman fashion he goes further:

It is my task to convince you not to turn away because you don't understand it [the theory of QED]. You see my physics students don't understand it either. That is because I don't understand it. Nobody does.

These are not just points of abstract philosophy, but are of importance in thinking about teaching and learning in this area. If you and your students think that the wave/photon ideas are somewhat strange, then you are in the very good company of Feynman. You are exactly right in your thinking and this is a message that is worth sharing with students.

Feynman would probably agree that thinking about light as waves allows us to predict where the light is likely to arrive, while the photon story tells us about how the energy is being shifted.

• ## 12 Thinking about actions to takeRa03TLnugget12 Suggestions

### There's a good chance you could improve your teaching if you were to:

Try these

• explicitly linking what happens in one place with what happens in another – after a delay
• treating superposition as fundamental
• linking all phenomena back to superposition
• emphasising the role of geometry, trip time and contributions

Teacher Tip: Work through the Physics Narrative to find these lines of thinking worked out and then look in the Teaching Approaches for some examples of activities.

Avoid these

• accounting for different phenomena by ad-hoc rules, or homely analogies
• settling for descriptions of the phenomena, rather than predictive accounts

Teacher Tip: These difficulties are distilled from: the research findings; the practice of well-connected teachers with expertise; issues intrinsic to representing the physics well.

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