5.3.1 Wavelength and how substances affect waves

Four ways a substance affects a wave

1. When an electromagnetic wave reaches the surface of a substance, it can be reflected, transmitted, refracted or absorbed.
2. Reflection sends the wave back from the interface into the material it came from, as happens when light meets a mirror.
3. Transmission lets the wave carry on through the substance and out of the other side, as light does through a clean window.
4. Refraction is a change in the direction of a transmitted wave as it crosses an interface at an angle.
5. Absorption transfers the energy carried by the wave to the substance, which usually increases its thermal energy store so that it warms up.
6. These four effects are not alternatives where only one can happen, because a single beam is normally shared between several of them at the same interface.
7. Light striking a window pane is mostly transmitted, but a small fraction is reflected from each surface of the glass and a little is absorbed inside it.
8. The reflected fraction is the reason you can see a faint reflection of yourself in a shop window while most of the light still passes straight through.
9. Energy is conserved at the interface, so the energy reflected, transmitted and absorbed always adds up to the energy carried by the incident wave.

Why wavelength matters

1. Different parts of the electromagnetic spectrum have very different wavelengths, from radio waves that can be kilometres long to gamma rays smaller than an atom.
2. The way a substance responds to a wave depends on the wavelength of the wave as well as on the substance itself.
3. One substance can therefore transmit one wavelength, absorb a second wavelength and reflect a third.
4. Words such as transparent and opaque only make sense when you also say which wavelength you are describing.
5. Ordinary window glass is transparent to visible light, but it absorbs most ultraviolet and much of the infrared at longer wavelengths.
6. This is why you are unlikely to get sunburnt sitting behind a closed window, even on a bright summer day.
7. It also explains why a greenhouse or a parked car warms up in the sun, because visible light passes in through the glass and is absorbed by the plants or the seats.
8. The warmed surfaces then give out longer-wavelength infrared, which the glass absorbs rather than transmits, so the energy stays inside.
9. A brick wall is opaque to visible light, but it transmits most radio waves, which is why a radio still picks up a station inside a house.
10. Metal surfaces reflect radio waves and microwaves strongly, so the metal mesh in the door of a microwave oven keeps the microwaves inside.
11. The holes in that mesh are much smaller than the wavelength of the microwaves but much larger than the wavelength of visible light, so you can still see your food cooking.
12. Water molecules absorb microwaves of the wavelength used in a microwave oven, so the water in food gains energy and the food heats up.
13. Soft tissue in the body transmits most X-rays, while bone absorbs them much more strongly, which is the idea behind an X-ray photograph.
14. The Earth's atmosphere transmits visible light and most radio waves, but the ozone layer absorbs much of the Sun's ultraviolet and gases such as carbon dioxide absorb some infrared.

Refraction varies with wavelength too

1. Refraction also depends on wavelength, so different wavelengths change direction by slightly different amounts when they cross the same interface.
2. When a narrow beam of white light passes through a glass prism, violet light is refracted through a larger angle than red light.
3. The colours that make up white light therefore separate and fan out into a spectrum on a screen placed beyond the prism.
4. Water droplets in the air separate sunlight in the same way, which is how the colours of a rainbow appear.

5.3.2 Wave velocity in different substances

Wave speed depends on the substance

1. All electromagnetic waves travel through a vacuum at the same speed, about $3.0\times 10^{8}m/s$.
2. When an electromagnetic wave enters a transparent substance, it travels more slowly than it does in a vacuum.
3. The amount by which the wave slows down depends on the substance, so light has a different speed in air, water and glass.
4. Light in air travels at almost exactly its speed in a vacuum, so the two speeds are treated as equal in most calculations.
5. Light in water travels at about $2.25\times 10^{8}m/s$, which is roughly three quarters of its speed in air.
6. Light in glass travels at about $2.0\times 10^{8}m/s$, which is roughly two thirds of its speed in air.
7. A material in which light travels more slowly is often called optically denser, which is not the same as having a greater mass per cubic metre.
8. Other electromagnetic waves, such as microwaves, infrared and ultraviolet, also change speed when they pass from one substance into another.
9. A change of speed at an interface between two substances is the cause of several effects you can see every day, and the most important of these is refraction.

How a change of speed causes refraction

1. A beam of light can be pictured as a series of wavefronts, which are lines joining the crests of the wave drawn at right angles to its direction of travel.
2. Picture a set of straight wavefronts travelling through air and meeting the flat surface of a glass block at an angle.
3. One end of each wavefront reaches the glass first and slows down, while the other end is still moving at the faster speed in air.
4. For a short time the end inside the glass covers less distance than the end in the air, so each wavefront swings round.
5. When the whole wavefront is inside the glass, it is travelling in a new direction, and this change of direction is refraction.
6. The wavefronts inside the glass are also closer together than those in the air, because each one moves forward a smaller distance in the same time.
7. A wave that slows down as it crosses an interface bends towards the normal, so its angle of refraction is smaller than its angle of incidence.
8. A wave that speeds up as it crosses an interface bends away from the normal, so its angle of refraction is larger than its angle of incidence.
9. A wave that meets an interface along the normal changes speed but not direction, because every part of each wavefront reaches the new substance at the same moment.
10. Refraction depends entirely on the change of speed, so if two substances carried light at exactly the same speed a ray would cross the interface without bending.

Frequency stays the same but wavelength changes

1. The frequency of a wave is set by the source that produces it, so it does not change when the wave passes into a new substance.
2. Every wavefront that arrives at an interface must leave it on the other side, so the number of waves passing each second is the same in both substances.
3. Wave speed, frequency and wavelength are linked by the wave equation $v=f\lambda$.
4. If the frequency stays constant while the speed falls, the wavelength must fall by the same proportion.
5. Light passing from air into glass keeps the same frequency, but both its speed and its wavelength fall to about two thirds of their values in air.
6. Light passing from glass back into air speeds up again, so its wavelength returns to its original value.

Why white light splits into colours

1. In a vacuum every colour of light travels at the same speed, but in glass or water the speed depends slightly on the wavelength.
2. Violet light, which has the shortest wavelength in the visible spectrum, travels a little more slowly in glass than red light, which has the longest.
3. Violet light therefore has the largest change of speed at each surface of a prism and is refracted through the largest angle.
4. Red light has the smallest change of speed and is refracted the least, so the colours spread out into a spectrum.
5. This spreading of white light into its colours is called dispersion, and the same process inside raindrops produces a rainbow.

Everyday effects of changing wave speed

1. A straw standing in a glass of water looks bent or broken where it enters the water.
2. Light from the underwater part of the straw speeds up as it passes from water into air, so it bends away from the normal at the water surface.
3. Your brain assumes that light reaching your eye has travelled in a straight line, so it traces the ray straight back and places the underwater part of the straw higher than it really is.
4. A swimming pool looks shallower than it is for the same reason, because light from the bottom bends away from the normal as it leaves the water.
5. Seen from directly above, the bottom of a pool appears to be only about three quarters of its real depth.
6. A fish in a pond is deeper than it appears, so a kingfisher diving for it must aim below the position where it sees the fish.
7. In each case nothing has moved or bent, because only the path of the light has changed as its speed changed at the water surface.

5.3.3 Convex and concave lenses

How a lens changes the path of light

1. A lens is a shaped piece of transparent glass or plastic with curved surfaces that changes the direction of light by refraction.
2. Light refracts once as it enters the lens and again as it leaves, so each ray changes direction at both surfaces.
3. The surfaces are curved, so rays striking different parts of the lens meet the surface at different angles and are bent by different amounts.
4. Rays striking near the edge of a lens are bent the most, while a ray passing through the very centre carries straight on without changing direction.
5. The principal axis is the line through the centre of the lens at right angles to it, and ray diagrams for lenses are built around this line.
6. In a ray diagram, a lens is drawn as a vertical line with a symbol at each end, and each ray is shown changing direction once at that line to keep the diagram clear.
7. Every ray is drawn as a straight ruled line with an arrowhead showing the direction in which the light travels.

Convex lenses make rays converge

1. A convex lens bulges outwards, so it is thicker at its centre than at its edges.
2. It is also called a converging lens, because it refracts rays that are parallel to the principal axis inwards so that they converge.
3. After passing through the lens, these parallel rays all meet at one point on the principal axis called the principal focus, labelled $F$.
4. The distance from the centre of the lens to the principal focus is the focal length.
5. A lens has a principal focus on each side, at the same distance from its centre, because light can pass through it in either direction.
6. A fatter, more strongly curved convex lens bends light more, so it has a shorter focal length.
7. In a ray diagram, a convex lens is drawn as a vertical line with outward-pointing arrowheads at both ends.
8. Light really does pass through the principal focus of a convex lens, so a convex lens can focus light onto a screen.

Concave lenses make rays diverge

1. A concave lens curves inwards, so it is thinner at its centre than at its edges.
2. It is also called a diverging lens, because it refracts rays that are parallel to the principal axis outwards so that they spread apart.
3. If the spreading rays are traced backwards with dashed lines, they all appear to come from one point on the same side of the lens as the incoming light.
4. This point is the principal focus of the concave lens, and it is a virtual focus because no light actually passes through it.
5. In a ray diagram, a concave lens is drawn as a vertical line with inward-pointing arrowheads at both ends.
6. The rays leaving a concave lens never meet, so a concave lens cannot focus light from a distant object onto a screen.

Images formed by lenses

1. An image forms where rays of light from one point on an object meet again, or where they appear to have come from.
2. A real image forms where rays actually meet, so it can be caught on a screen.
3. A virtual image forms where rays only appear to come from, so you can see it by looking through the lens but you cannot catch it on a screen.
4. Three standard rays are used to find the image formed by a convex lens.
   1. A ray parallel to the principal axis is refracted through the principal focus on the far side of the lens.
   2. A ray through the centre of the lens carries straight on without changing direction.
   3. A ray through the principal focus on the near side of the lens leaves the lens parallel to the principal axis.
5. The point where these rays cross on the far side of the lens marks the top of the image, and any two of them are enough to locate it.
6. An object more than two focal lengths from a convex lens forms a real image that is inverted and diminished, which is how a camera forms an image on its sensor.
7. An object between one and two focal lengths from a convex lens forms a real image that is inverted and magnified, which is how a projector throws a large picture onto a screen.
8. An object closer to a convex lens than its principal focus forms a virtual image that is upright and magnified, which is how a magnifying glass works.
9. As an object moves from far away towards the principal focus, its real image moves further from the lens and becomes larger.
10. A concave lens always forms a virtual image that is upright and diminished, wherever the object is placed.

Comparing convex and concave lenses

1. Similarities between the two types of lens are listed below.
   1. Both lenses change the direction of light by refraction at their two surfaces.
   2. Both lenses have a principal axis and a principal focus on each side at the same distance from the centre.
   3. Both lenses let a ray through their centre pass straight on without bending.
2. Differences between the two types of lens are listed below.
   1. A convex lens is thickest at its centre, while a concave lens is thinnest at its centre.
   2. A convex lens makes parallel rays converge, while a concave lens makes them diverge.
   3. A convex lens has a real principal focus, while a concave lens has a virtual principal focus.
   4. A convex lens can form real or virtual images, while a concave lens forms only virtual images.

Correcting vision with lenses

1. The eye contains its own convex lens, which focuses light from an object onto the retina at the back of the eye to form a sharp image.
2. In a short-sighted eye, light from distant objects comes to a focus in front of the retina, because the eyeball is too long or the eye lens is too strongly curved.
3. A concave lens placed in front of a short-sighted eye makes the light diverge slightly before it enters, so the eye lens then brings it to a focus on the retina.
4. In a long-sighted eye, light from near objects would come to a focus behind the retina, because the eyeball is too short or the eye lens is too weak.
5. A convex lens placed in front of a long-sighted eye makes the light converge slightly before it enters, so it comes to a focus on the retina.
6. You can tell the two kinds of glasses apart by feeling them, because lenses for short sight are thicker at the edges and lenses for long sight are thicker in the middle.

5.3.4 Ray diagrams for reflection and refraction

Rays, normals and angles

1. A ray is a straight line with an arrowhead that shows the path and direction of travel of a narrow beam of light.
2. A ray diagram is drawn in two dimensions on flat paper, with a ruler and a sharp pencil, because it is an accurate drawing of where the light goes.
3. The ray travelling towards a surface is the incident ray, and the point where it meets the surface is the point of incidence.
4. The normal is drawn through the point of incidence at exactly $90^{\circ }$ to the surface, usually as a dashed line so that it cannot be mistaken for a ray.
5. Every angle in a ray diagram is measured between a ray and the normal, never between a ray and the surface.
6. The angle of incidence, $i$, is the angle between the incident ray and the normal.
7. To measure an angle, place the centre of a protractor on the point of incidence and line up its zero mark with the normal.
8. A ray that travels along the normal has an angle of incidence of $0^{\circ }$.
9. If a question gives the angle between a ray and the surface, subtract it from $90^{\circ }$ to find the angle between the ray and the normal.

Reflection from a plane mirror

1. A plane mirror is a flat, highly polished surface that reflects almost all of the light that falls on it.
2. The ray leaving the mirror is the reflected ray, and the angle of reflection, $r$, is the angle between the reflected ray and the normal.
3. The law of reflection states that the angle of reflection is equal to the angle of incidence, so $i=r$.
4. The incident ray, the reflected ray and the normal all lie in the same flat plane, which is why reflection can be drawn on a sheet of paper.
5. A ray that strikes a mirror along the normal is reflected straight back along its own path.
6. To construct a reflection ray diagram, carry out these steps in order.
   1. Draw the mirror as a straight line and shade a few short lines behind it to show its non-reflecting back.
   2. Draw the incident ray with a ruler up to the mirror and add an arrowhead pointing towards the mirror.
   3. Draw a dashed normal at $90^{\circ }$ to the mirror through the point of incidence.
   4. Measure the angle of incidence from the normal with a protractor.
   5. Draw the reflected ray on the other side of the normal at the same angle, and add an arrowhead pointing away from the mirror.
7. The image in a plane mirror is virtual, upright, the same size as the object and the same distance behind the mirror as the object is in front of it.
8. To locate the image, draw two rays from the same point on the object, reflect each one using the law of reflection, and extend both reflected rays backwards behind the mirror as dashed lines.
9. The point where the dashed lines cross is the image of that point, and your brain sees the light as if it came from there.
10. The image is also laterally inverted, so its left and right sides appear swapped, which is why the word AMBULANCE is printed in mirror writing on the front of an ambulance.

Refraction through a rectangular glass block

1. The ray that travels on into the second material after crossing an interface is the refracted ray.
2. The angle of refraction is the angle between the refracted ray and the normal.
3. A ray entering glass from air slows down and bends towards the normal, so its angle of refraction is smaller than its angle of incidence.
4. A ray leaving glass for air speeds up and bends away from the normal, so its angle of refraction is larger than its angle of incidence.
5. A ray that meets an interface along the normal passes straight through without changing direction.
6. When a ray passes through a rectangular block with parallel sides, the bend at the second face reverses the bend at the first face.
7. The ray that comes out of the block is therefore parallel to the ray that went in, but it is shifted sideways.
8. To construct a refraction ray diagram for a glass block, carry out these steps in order.
   1. Draw the outline of the block and mark the point where the incident ray meets the first face.
   2. Draw a dashed normal through this point, extending it a short way into the glass.
   3. Draw the refracted ray inside the block at a smaller angle to the normal than the incident ray, and continue it to the second face.
   4. Draw a second dashed normal where the ray reaches the second face.
   5. Draw the emerging ray bending away from this normal so that it leaves parallel to the original incident ray.
   6. Add an arrowhead to each section of the ray to show the direction of travel.
9. Some light is also reflected at each face of the block, so a faint reflected ray can usually be seen as well as the refracted one.

Refraction through a triangular prism

1. A triangular prism has faces that are not parallel, so the bend at the second face does not cancel the bend at the first face.
2. Light entering the first face bends towards the normal, and light leaving the second face bends away from the normal.
3. The two faces slope towards each other, so both changes of direction turn the ray the same way, towards the thicker base of the prism.
4. The emerging ray therefore leaves the prism travelling in a very different direction from the incident ray.
5. To draw the path through a prism, construct a separate normal at each face and apply the towards or away rule at each interface in turn.

5.3.5 Colour, absorption and reflection

White light and colour

1. White light, such as sunlight or the light from a white LED bulb, is a mixture of all the colours of visible light.
2. The colours of the visible spectrum, in order of decreasing wavelength, are red, orange, yellow, green, blue, indigo and violet.
3. Red light has the longest wavelength, at about $700nm$, and violet light has the shortest, at about $400nm$.
4. Each colour is a range of wavelengths, and your eye and brain interpret each range as a particular colour.
5. The colour of an object depends on which wavelengths from the light falling on it end up reaching your eye.
6. Light reaches your eye from an object only if the object reflects it or transmits it, because absorbed light never leaves the object.

The colour of opaque objects

1. An opaque object transmits no visible light, so every wavelength falling on it is either reflected or absorbed.
2. Most objects show differential absorption, which means they absorb some wavelengths strongly and reflect others.
3. The colour you see is the colour of the wavelengths that are reflected into your eye.
4. A red post box looks red in daylight because its paint reflects red wavelengths and absorbs the other colours in white light.
5. A green leaf looks green because it reflects green wavelengths and absorbs most of the red and blue light.
6. A white object, such as a sheet of paper, reflects all visible wavelengths roughly equally, so the full mixture reaches your eye and it looks white.
7. A black object, such as a car tyre, absorbs all visible wavelengths, so very little light is reflected and it looks black.
8. The absorbed light transfers energy to the object, which is why a black car seat becomes much hotter in summer sunshine than a white one.
9. An object can only reflect colours that are present in the light shining on it.
10. A red post box seen under pure blue light looks black, because it absorbs the blue light and there is no red light for it to reflect.
11. A white object takes on the colour of the light shining on it, so a white shirt looks green under green light.

Transparent objects and colour filters

1. A transparent coloured object, such as a bottle of green glass, transmits some wavelengths and absorbs the rest.
2. Its colour is the colour of the light it transmits, because that is the light that passes through to your eye.
3. A colour filter is a thin sheet of coloured plastic or glass that transmits one band of colours and absorbs all the others.
4. A red filter placed in front of a white lamp transmits red light and absorbs every other colour, so the light that emerges is red.
5. The filter does not add colour to the light or change one colour into another, because it can only remove the wavelengths it absorbs.
6. Red light shone at a red filter passes through almost unchanged, because red is the colour that the filter transmits.
7. Blue light shone at a red filter is absorbed, so almost no light emerges and the screen behind it looks dark.
8. White light sent through a red filter and then a green filter is almost completely blocked, because the red filter removes everything except red and the green filter then absorbs the red.
9. Every filter absorbs a little of the colour it transmits as well, so the light that emerges is always slightly dimmer than the light that went in.
10. Stage lighting and traffic lights both use this idea, with a white lamp behind a coloured filter giving the coloured beam.

Specular reflection and scattering

1. Every ray that reflects from a surface obeys the law of reflection at the exact point where it strikes, with the angle of reflection equal to the angle of incidence.
2. Specular reflection happens at a very smooth surface, such as a mirror, a still pond or polished metal.
3. On a smooth surface the normals at neighbouring points all point the same way, so a set of parallel incident rays leaves as a set of parallel reflected rays.
4. The reflected rays keep their arrangement, so specular reflection produces a clear image, as you see in a bathroom mirror.
5. Scattering, also called diffuse reflection, happens at a rough surface, such as paper, cloth or a painted wall.
6. On a rough surface the normals at neighbouring points point in many different directions, so parallel incident rays are reflected in many different directions.
7. Scattered light does not form an image, but it reaches your eye from every viewing angle, which is why you can read a poster from anywhere in a classroom.
8. Most objects around you are seen by scattered light, and their colour comes from the wavelengths that they scatter rather than absorb.
9. A gloss-painted door shows a bright shiny patch where light is reflected specularly, while a matt-painted wall of the same colour looks evenly lit from every angle.
10. A wet road at night looks like a mirror because a film of water makes its surface smooth, while the same road when dry scatters the light from headlights.
11. A translucent material, such as frosted glass or tracing paper, transmits light but scatters it as it passes through, so objects seen through it look blurred.