Three possibilities

What happens when light travels through the air and meets the surface of an object, such as a table, mirror, window, or curtain? Various outcomes are possible.

Notice that all of the energy of the incident beam can only be shared out amongst the three possibilities: energy is conserved.

If the object is:

• Opaque: no light is transmitted (the light is reflected and absorbed to varying degrees).
• Translucent: some light is transmitted (the rest of the light is reflected and absorbed to varying degrees).
• Transparent: ideally all light is transmitted (although in practice some light will be reflected and absorbed).

Notice that all the energy must be accounted for – energy is conserved.

Reflection from surfaces

Light beams are reflected from surfaces according to the law of reflection, which states that the angle of incidence is equal to the angle of reflection.

Here an explanation of the law builds up, step by step. (Remember that rays are figments of your imagination.)

The angles of incidence (i) and reflection (r) are measured between the incident (incoming) and reflected (outgoing) rays and the normal line. The normal line is a construction line drawn perpendicular to the reflecting surface at the point where the incident ray strikes.

Choosing the normal line

You might wonder why the angles of incidence and reflection are measured between the rays and the normal line, and if you don't there is a good chance that one of your pupils will ask about this. For a flat or plane mirror we could take either the angle between the ray and the normal line, or the angle between the ray and the mirror. In each case the designated angles of incidence and reflection will be equal.

However, if we are using mirror which is a curved surface things are not so straightforward. To measure any angle we need two straight lines, for a curved mirror we might be tempted to pick the tangent as our second line. However, for a curved surface there are many different tangential lines (in fact making a tangential plane) but just one, unique normal line. This makes the normal line the easiest option for more complicated mirror shapes, so the convention is to measure all angles of incidence and reflection in relation to the normal line.

Reflection from any surface

The law of reflection is usually illustrated in science textbooks with flat or plane mirrors. You should be aware, however, that it applies to the reflection of light at any surface, not just the shiny ones that you might usually associate with reflection.

For example, each point on a stone wall reflects light such that the angle of incidence equals the angle of reflection. Here you need to picture a tiny piece of the wall's surface, which acts as a plane reflector. Having to hand a piece of rock containing mica flakes, which are shiny, might help to make the link to the reflection of light from a duller rock.

Once again, you can see why the angles of incidence and reflection are measured in relation to the normal line. In this case of reflection from an uneven stone wall, the reflecting surface does not provide a straight line to measure angles against. Reflection from such a rough surface is sometimes referred to as diffuse reflection. It's what enables us to see many of the objects in our environment.

Paint and reflections

Surfaces are made to be reflective in different ways to create different moods.

DIY shops sell different kinds of paint which are designed to provide contrasting effects not only in terms of colour but also in the ways in which light is reflected from the surface. The two extremes of finish are gloss and matt, with satin in between.

For gloss paint the particles at the surface of the paint are very small and when the paint dries they end up forming what is in effect a very flat, plane surface which acts just like a mirror. Any light shining onto this surface is reflected regularly and it may be possible to see the image of an object (your face!) as light is reflected.

At a microscopic level the surface of matt paint, when it dries, is very uneven. When magnified it resembles a pebbled beach. Here the light from a luminous source will hit each pebble and whilst each small part of each pebble will reflect light according to the laws of reflection, the overall effect is that the light is scattered in all directions. Our eyes gather light from parts of many different pebbles as diffuse reflection occurs, making the matt finish appear dull in comparison with the gloss surface.

A smooth reflection

Imagine the scene. You are standing at the edge of a large lake, gazing out across the water at a range of mountains which rears up into the sky. You can see the mountain peaks directly and you are also aware that there is a perfect reflection of the mountain from the water. So you imagine two rays from a pair of selected points – one point near the top of the mountain, and one near the bottom.

To model the direct view of the mountain you imagine rays drawn straight from those points to your eye. To model the reflection of the mountain, you imagine rays drawn down to the lake surface from the mountain and being reflected from the flat surface to your eye.

How do these pairs show that the top and bottom will be reversed in the reflection?

The same rays, regrouped by the view to which they contribute

Here we've redrawn the scene, and hope that helps. Now the rays are grouped differently, with the rays coloured to show their origin.

To get further you'll have to model the eye as a pinhole camera (more on that in episode 02), to remember that the eye inverts all images that appear on the retina. You might like to draw out a ray diagram to see if you can figure out what is going on, before moving on.

Tracing rays inside the eye

Here we've simplified the eye (right down to a pinhole eye), taking the rays from the previous diagram. By the time it gets to be as simple as the pinhole camera, so just a box, you can very clearly see the predictions of the ray model of the original view of the mountains.

The green rays, predicting what the light beams from the top of the mountain will do, swap positions with the blue rays (that predict what the light beams from the bottom of the mountain will do) as you move from the reflected to the direct view, and back again.

As they swap position, top for bottom, and bottom for top, so the eye will see the mountain up the right way and upside down. Now all you need to do is find a mountain and a lake on a clear still day and see if the predictions are correct.

A rippled surface

Just then, a sudden squall of wind blows up across the lake, disturbing the water's surface. The reflected image of the mountain disappears as the rays of light are now reflected in all directions. You can use the models you've just developed to make sense of this.

For each ray the angle of incidence is equal to the angle of reflection, but the incident rays strike different regions of water, which are inclined at different angles to each other. The outgoing rays are reflected at many different angles and so the image is jumbled up.

Paint and reflections

Surfaces are made to be reflective in different ways to create different moods.

DIY shops sell different kinds of paint which are designed to provide contrasting effects not only in terms of colour but also in the ways in which light is reflected from the surface. The two extremes of finish are gloss and matt, with satin in between. What different effects do these paints produce and how are they achieved?

With gloss paint the particles at the surface of the paint are very small and when the paint dries they end up forming what is in effect a very flat, plane surface which acts just like a mirror. Any light shining onto this surface is reflected regularly and it may be possible to see the image of an object (your face!) as light is reflected.

At a microscopic level the surface of matt paint, when it dries, is very uneven. An analogy is that when magnified it resembles a pebbled beach. Here the light from a luminous source will hit each pebble and whilst each small part of each pebble will reflect light according to the laws of reflection, the overall effect is that the light is scattered in all directions. Our eyes gather light from parts of many different pebbles as diffuse reflection occurs, making the matt finish appear dull in comparison with the gloss surface.

Mirror images

What is going on when you look at your own face in the mirror? Put simply, light beams from every point on your face travel to the mirror, where they are reflected. Some of those reflected beams will travel towards your eyes where they will be detected. The image that you see has two interesting features:

• The image of your face appears to be behind the mirror. Indeed the farther you step back away from the mirror, the farther behind the mirror the image is.
• The image of your face that you see in the mirror seems to be the wrong way round. For example, if you hold your right ear and look in the mirror, you see your own image with your hand holding onto your left ear. Check it!

How can we explain these two features? With a ray diagram!

From the diagram you can see that the image (from which the rays appear to come) is as far behind the mirror as the object (face) is in front. You can also see that right and left seem to be reversed on the image. The apparent reversal of right and left is referred to as lateral inversion.

Reading in reverse

You may have noticed that ambulances and police cars sometimes have writing or electronic signs with the letters reversed on the front of them. The reason for this is so that drivers in front of these vehicles can, when they look in their rear view mirror, see the writing the correct way round.

More thinking about lateral inversion

We advise you to read the following passage whilst in front of a mirror!

The ray diagram shows quite clearly that the image is laterally inverted, with right appearing as left. But in class, every now and again, you will get this question:

Why does the mirror swap right and left but not up and down – how does it know which way up things are?

The problem is in saying that the image in the mirror swaps right and left: It doesn't. If a person raises their right arm, the image in the mirror raises an arm that is on the right of the image. That is all very simple and there is no lateral inversion. Then we get thinking about things and it seems to us that the person in the mirror has swapped right for left. They seem to be raising their left arm. The only way we could look like that is if we turn round. Right and left are not actually reversed in the image; it is just our interpretation of the image.

In fact what the mirror does is swap front for back. The back of our heads are furthest from the mirror and end up furthest behind it in the image. Our faces start closest and end up closest. The mirror just turns us back to front.

Here is something that sometimes convinces a class. First, find a large mirror which is safe to stand on without breaking and be sure you are wearing clothes which allow you to stand on the mirror (trousers!).

When the class see the image it is clear this time top and bottom have been swapped, not left and right. As before, in fact, the mirror has turned us back to front.

And here is the final test to show that it is not really about left and right. Get a pupil to lie in front of a biggish mirror. The pupil will tell you that left and right have been swapped. The other pupils will tell you that up and down have been swapped (their up and down). Both are just describing the event from their own point of view – the mirror has simply turned the pupil back to front.

Reflection from a newspaper

At first sight, it may seem a little odd that although you can't see your face in the newspaper, as you can see the surface of the newspaper perfectly clearly and are able to pick out and read all of the print.

This is explained by the idea of diffuse reflection. Plenty of light is reflected from the newspaper, but it is jumbled – the surface is not smooth and shiny, so light coming in from one direction heads off in all directions (just like the lake).

If you wanted to model this process: rays strike each and every point on the surface at every possible angle and all of these rays are reflected such that the angle of incidence equals the angle of reflection. Plenty of light leaves the surface, but not in an orderly fashion. So you can see by the light leaving the newsprint – lots from a white spot on the page, not much from a black spot (colour papers in the next episode!)

Of course, we see everything around us in this way. Ray diagrams are intended to make things look simple by selecting key rays to model what beams will do. What is actually happening here is that countless beams are striking the surface of the newspaper every-which-way, being reflected every-which-way (that's why you can see the newspaper from many angles) and the eye picks up just some of those reflected rays. Which rays depends on the angle that you look at the paper from.

Light changing media

Supposing a beam of light travels through air and meets a glass block.

If the beam meets the glass block straight-on, at right angles, it continues on its path through the glass. If you think that this is hardly a surprising event, you'd be right. You're probably very familiar with the fact that light can travel through glass.

However, rather stranger things start happening if the light beam meets the block at some other angle. In this case the beam of light does not travel straight on, but changes direction as it passes into and out of the glass.

This change in direction is referred to as the refraction of light.

The consequences of light travelling quickly in some things and slowly in others

When the beam of light changes from a fast medium (say air) to a slow medium (say glass), it changes direction so that it bends towards the normal.

The incident beam does not travel straight on, but is refracted towards the normal line. In drawing rays to predict beam behaviour, we need to draw the ray in the same way.

When the beam of light changes from a slow medium (say water) to a fast medium (say air), it changes direction such that it bends away from the normal.

The incident beam does not travel straight on, but is refracted away from the normal line. Again we need to draw the rays to show this.

Parallel rays

The overall effect is that the light beam leaving the glass block (the emergent beam) is parallel to the beam entering but shifted slightly to one side.

Why does light bend?

Why is light refracted as it passes between different media? To offer a satisfactory answer to this question we need to think about the wave properties of light. The explanation for refraction is not needed for the 11–14 age range. It turns out that the properties of light lead to the path taken by the beam being the shortest travel time possible. (There is more on this in the SPT: Radiations and radiating topic.)

Like all good answers, that immediately leads to another question. How does the beam know which the shortest path is? That is a good question! Quantum physics can answer that one, but not right here.

Using refraction

The fact that a beam of light shifts its path as it passes through a glass block may not seem to be of particular importance. You might be tempted to think: Well so what! In fact the idea of refraction can be used to explain a whole range of apparently disparate phenomena.

For example:

• How do lenses work?
• Why does the water in a swimming pool always appear to be shallower than it really is?
• How can a glass prism split light up into different colours?

The answers to the first two questions are addressed in the Teaching Approaches section, while ideas about colour will be considered in episode 04.

Propagation: transmission; absorption; reflection; refraction modelled by rays

Light propagates from a source. As it travels, there are several characteristic patterns which are named phenomena.

• reflection – at a surface
• absorption – in the body of a material
• refraction – on entry or exit from a material

These paths can be predicted by drawing rays (although the diagram for absorption is not very instructive). The simple patterns formed by the rays can be used to think about the design of more complex optical devices, such as prisms and lenses.