Physics - Assets - Cambridge University...

PhysicsDavid Sang

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© Cambridge University Press 2001

First published 2001

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Contents

Chapter 1 Describing motion 11.1 Measuring speed 2

1.2 Distance–time graphs 8

1.3 Changing speed 12

1.4 Velocity–time graphs 16

1.5 The equations of motion 20

Chapter 2 Forces and motion 262.1 Forces produce acceleration 27

2.2 Balanced and unbalanced forces 31

2.3 Friction and drag 36

2.4 The force of gravity 39

Chapter 3 Forces and momentum 493.1 Collisions and explosions 50

3.2 Momentum and force 56

Chapter 4 Turning effects of forces 634.1 The moment of a force 64

4.2 Stability and centre of mass 68

Chapter 5 Forces and matter 715.1 Density 72

5.2 Forces acting on solids 74

Further questions Section A 79

Secti

on A

Chapter 6 Energy resources 846.1 The energy we use 86

6.2 Storing energy 90

6.3 Renewable energy technologies 93

Chapter 7 Energy transformations, energytransfers 98

7.1 Forms of energy 98

7.2 Conservation of energy 104

7.3 Energy efficiency 108

Chapter 8 Work and power 1128.1 Gravitational potential energy 113

8.2 Kinetic energy 115

8.3 KE–GPE transformations 117

8.4 Doing work 120

8.5 Power 124

Chapter 9 The kinetic model of matter 1279.1 Changes of state 128

9.2 Particles, forces and the

kinetic model 131

9.3 Thinking about the kinetic model 136

9.4 Internal energy 138

9.5 Temperature and temperature scales 140

Chapter 10 Thermal energy transfers 14710.1 Conduction 148

10.2 Convection 152

10.3 Radiation 154

10.4 Effective insulation 158

10.5 Specific heat capacity 160

Secti

on BSection A Forces and movement

Section B EnergySection C WavesSection D Electricity and magnetismSection E Atomic physicsSection F The Earth and space

Chapter 11 The gas laws 16411.1 Properties of a gas 164

11.2 Boyle’s law 167

11.3 Charles’ law 170

11.4 The pressure law 173

11.5 Combining the three gas laws 175

Further questions Section B 178

Chapter 12 Sound 18312.1 Making sounds 184

12.2 At the speed of sound 185

12.3 Seeing sounds 189

12.4 How sounds travel 194

12.5 Using ultrasound and infrasound 197

Chapter 13 How light travels 20013.1 Travelling in straight lines 201

13.2 The speed of light 202

13.3 Reflecting light 205

Chapter 14 Refraction of light 21014.1 Refraction effects 211

14.2 Total internal reflection 215

14.3 Lenses 218

14.4 Light and colour 224

Chapter 15 The electromagnetic spectrum 227

15.1 Extending the visible spectrum 228

15.2 Infrared and ultraviolet radiation 232

15.3 Radio waves and microwaves 235

15.4 X-rays and gamma rays 238

Chapter 16 Waves 24116.1 Describing waves 242

16.2 Speed, frequency and wavelength 247

16.3 Reflection and refraction of waves 249

16.4 Diffraction 253

Further questions Section C 259

Secti

on B

Secti

on C

Chapter 17 Static electricity 26317.1 Charging and discharging 265

17.2 What is electric charge? 270

17.3 The hazards and uses of

static electricity 274

Chapter 18 Electric circuits 27818.1 Current in electric circuits 280

18.2 Electrical resistance 285

18.3 Resistive components 291

18.4 Combinations of resistors 295

Chapter 19 Electricity and energy 30019.1 Using electrical appliances 301

19.2 Voltage and energy 304

19.3 Domestic electricity supply 308

Chapter 20 Electromagnetic forces and electric motors 315

20.1 Electromagnets 316

20.2 Uses of electromagnets 319

20.3 How electric motors are constructed 323

20.4 The motor effect 326

20.5 Electric motors revisited 331

Chapter 21 Electromagnetic induction 33321.1 Generating electricity 334

21.2 The principles of electromagnetic

induction 336

21.3 Power lines and transformers 339

Chapter 22 Electronic control circuits 34722.1 Electronic processors 348

22.2 Input devices 353

22.3 Output devices 356

Further questions Section D 360

Secti

on D

Chapter 23 Atoms, nuclei and electrons 36623.1 The size of atoms 367

23.2 Electrons 368

23.3 Inside atoms 372

23.4 Protons, neutrons and electrons 375

Chapter 24 Radioactivity 38024.1 Radioactivity all round 381

24.2 The microscopic picture 384

24.3 Using radioactive substances 388

24.4 Radioactive decay 391

Chapter 25 Nuclear fission 39925.1 Nuclear fission 401

Further questions Section E 408

Secti

on E Chapter 26 The active Earth 411

26.1 Inside the Earth 412

26.2 Plate tectonics 415

Chapter 27 Around the Earth 42027.1 Gravity 421

27.2 Into orbit 424

27.3 Spacecraft at work 427

Chapter 28 The Solar System 43028.1 The moving Earth 431

28.2 Moon and Sun 433

28.3 The nine planets 434

Chapter 29 The Universe 44329.1 Stars and galaxies 444

29.2 The life of a star 447

29.3 The life of the Universe 449

Further questions Section F

Secti

on F

A glossary of terms and answers to questions can be found

on the Cambridge University Press website. Go to

http://uk.cambridge.org/education/secondary/SANG

Topics

in th

is chapter

Section C Chapter 13

200 How light travels

How light travels◆ straight-line travelling

◆ speed of light

◆ law of reflection of light

◆ image in a plane mirror

When Apollo astronauts visited the Moon, they left behind reflectors on

its surface. These are used to measure the distance from the Earth to the

Moon. A laser beam is directed from an observatory on Earth (Figure

13.1) so that it reflects back from the lunar surface. The time taken by the

light to travel there and back is measured and, knowing the speed of light,

the distance can be calculated. This is the same idea as echo-sounding,

discussed in Chapter 12, page 197 but using light rather than ultrasound.

e

Figure 13.1 A laser beam travels in a straight lineto the Moon. It is reflected by mirrors on theMoon’s surface, so that it returns to Earth,where it can be detected. From the time takenfor the round trip, together with the speed oflight, the Earth–Moon distance can be foundwith great accuracy.


How light travels 201

The Moon travels along a slightly elliptical orbit around the Earth,

so that its distance varies between 356 500 km and 406 800 km. The

laser measurements of its distance are phenomenally accurate – to

within 30 cm. This means that they are accurate to within one part in a

billion. The Moon is gradually slowing down and drifting away from

the Earth, and it is possible with the help of such precise measurements

to work out just how quickly it is drifting.

These measurements make use of three ideas that we will look at in

this chapter: the way that light travels in straight lines, how fast it trav-

els, and how it is reflected by mirrors.

13.1 Travelling in straight linesLight usually travels in straight lines. It only changes direction if it is

reflected, or if it travels from one material into another. You can see

that light travels in a straight line using a ray box, as shown in Figure

13.2. A light bulb produces light, which spreads out in all directions. By

placing a narrow slit in the path of the light, you can see a single

narrow beam or ray of light. If the ray shines across a piece of paper,

you can record its position by making dots along its length. Laying a

ruler along the dots shows that they lie in a straight line.

Figure 13.2 a A ray box produces a broad beamof light. b This can be narrowed down using a metal plate with a slit in it. Marking the lineof the ray with dots allows you to record itsposition.

You may see demonstrations using a different source of light, a

laser. A laser (Figure 13.3) has the great advantage that all of the light

it produces comes out in a narrow beam. This is because the light

bounces back and forth inside the laser, reflected by a mirror at either

end. It gathers energy as it passes back and forth, and emerges as a sin-

gle beam. All of the energy is concentrated in this beam, rather than

spreading out in all directions (as with a light bulb). The total amount

of energy coming from the laser is probably much less than the total

amount from the bulb, but it is much more concentrated. That is why

it is dangerous if a laser beam gets into your eye.

a b



When the Channel Tunnel was built, it was vital that the engineers

tunnelling from the English end should arrive at exactly the same

point as those working from the French end. This was achieved using

laser beams (Figure 13.4) to guide the tunnelling equipment.

partially silvered mirror(allows beam to emerge)

connections to power supplymirror(100% reflection)

glass tube withsloping ‘windows’

+ –

mixture of gases(helium and neon)

Figure 13.3 A laser gives a narrow,concentrated beam of light, which ismore intense than the ray from a raybox. The light reflects back and forthbetween the two mirrors, and picksup energy as it passes through thegas mixture. One mirror letsthrough a small amount of light toform the beam, which emerges fromthe end.

Figure 13.4 The red laser beam on the right wasused to guide tunnelling equipment duringthe construction of the Channel Tunnel. Thisensured that the two teams working fromopposite ends met in the middle with pinpointaccuracy.

Question

13.1 The beam of a cinema projector is often shown up as it

reflects off particles of dust (and sometimes smoke!) in the

air. You can see clearly that light travels in straight lines.

Give two more examples of everyday phenomena that you

have seen that show this.

?

13.2 The speed of lightLight travels very fast – as far as we know, nothing can travel any faster

than light. Its speed as it travels though empty space is a fundamental

quantity, which is given its own symbol, c, the same symbol as appears

in Einstein’s famous equation E = mc2.

The speed of light c is exactly 299 792 458 m/s.

300 000 000 m/s or 3 ¥ 108 m/s

For most purposes we can round off the value to

It is not obvious to our eyes that light takes any time to travel. When

we see something happen nearby, perhaps in the same room as us, we

assume that it happens at the instant that we see it. This is a safe

assumption because the light takes only a tiny fraction of a micro-

second to reach us, far too short a time interval for us to notice.

Astronomers do have to worry more about the speed of light, because

the distances to stars and galaxies are much greater than we are used to

on Earth, and the time for light to travel such huge distances is much

more significant. (There is more about this in Section F.)



When we discussed the gap between seeing lightning and hearing

thunder (page 186), we explained that it came about because sound

travels much more slowly than light – at about one-millionth of the

speed of light. We see the lightning only an instant after it is produced,

but the sound takes longer to reach us.

The first reasonably accurate measurement of the speed of light was

made by Ole Romer, a Danish astronomer working in Paris in the

1670s. He made accurate records of the movement of Jupiter’s moons;

he wanted to be able to predict when they would be eclipsed as they

passed behind the planet. He found that his records showed a strange

variation. Sometimes, a moon was eclipsed a few minutes later than

expected. He realised that this happened when the Earth was on the

opposite side of the Sun from Jupiter, (Figure 13.5). Light from Jupiter

had further to travel to reach the Earth than when the two planets were

on the same side, so events appeared to happen later than he predicted.

Io moving into eclipse behind JupiterJupiter

shorterdistance

Earth

Earth

Sunlongerdistance

Figure 13.5 The Danish astronomer Ole Romerrealised that, when Jupiter and the Earth wereon opposite sides of the Sun, light had furtherto travel from Jupiter to reach Earth. Thusevents such as the eclipsing of Jupiter’s moonIo was seen later than expected, by up to 10minutes. From this and the distances of theplanets, he could deduce a value for the speedof light, about 225 000 km/s. This is reasonablyclose to today’s agreed value.

The surveyor shown in Figure 13.6 is measuring a distance by

timing a beam of light (or, more usually, a beam of infrared radiation

– see Chapters 10 and 15). The beam is sent out by one instrument,

placed on top of a tripod. It is reflected back by a prism on the second

instrument. Knowing the speed of light, the distance between the two

instruments can be found. These instruments can be used to track

moving objects, so they have to calculate quickly using a built-in

microprocessor (a computer microchip). Data from the survey can

later be transferred to a larger computer, which generates a chart of the

area surveyed.

Different materials, different speedsAlthough we refer to c as ‘the speed of light’, we should remember that

this is its speed in empty space (a vacuum). In any material, it travels



more slowly, because the material slows it down. Table 13.1 shows the

speed of light in some different materials.

Figure 13.6 This surveyor is using an instrumentthat measure distances by timing a beam oflight or infrared radiation. The beam is timedas it travels from one instrument to the otherand back again. An on-board computer calcu-lates the distance and stores the answer fordownloading later into a more powerful com-puter, which draws an accurate plan of thearea.

Table 13.1 The speed of light in some transpar-ent materials. (The value for a vacuum isshown, for comparison.) Note that the valuesare only approximate. The third column showsthe factor by which the light is slowed down.(This is the material’s refractive index – seeChapter 14.)

Material Speed of light (m/s) Speed in vacuum

Speed in material

vacuum 2.998 ¥ 108 1 exactly

air 2.997 ¥ 108 1.0003

water 2.3 ¥ 108 1.33

Perspex 2.0 ¥ 108 1.5

glass (1.8–2.0) ¥ 108 1.5–1.7

diamond 1.25 ¥ 108 2.4

Questions

13.2 Someone tells you that ‘the speed of light is 3 ¥ 108m/s’.

How could you make this statement more accurate?

13.3 Look at the values for the speed of light shown in Table 13.1.

a In which of the materials shown does light travel most

slowly?

b Why do you think that a range of values is shown

for glass?

13.4 The speed of light in empty space, c, is exactly299792458m/s. In calculations, we often use an

approximate value for c. Which of the following are good

approximations?

300000000m/s, 30000km/s, 300000km/s,

3 ¥ 108m/s, 3 ¥ 109m/s

13.5 Explain why the surveyor shown in Figure 13.6 would have

problems if light did not travel in straight lines.

?



13.3 Reflecting lightMost of us look in a mirror at least once a day, to check on our appear-

ance (Figure 13.7). It is important to us to know that we are presenting

ourselves to the rest of the world in the way we want. Archaeologists

have found bronze mirrors over 2000 years old, so the desire to see

ourselves clearly has been around for a long time.

Modern mirrors give a very clear image. They are made by coating

the back of a flat sheet of glass with mercury. When you look in a mir-

ror, rays of light from your face reflect off the shiny surface and back to

your eyes. You seem to see a clear image of yourself behind the mirror.

(The ‘extension material’ on the next page will help you to understand

why this is.)

For now, we will consider just a single ray of light, and see what we

can learn about reflection. When a ray of light reflects off a mirror or

other reflecting surface, it follows a path as shown in Figure 13.8. The

ray bounces off, rather like a ball bouncing off a wall. The two rays are

known as the incident ray and the reflected ray. By doing many exper-

iments, the angle of incidence i and the angle of reflection r are found

to be equal to each other. This is the first law of reflection of light:

Figure 13.7 Psychologists use mirrors to test theintelligence of animals. Does an animal recog-nise that it is looking at itself? Apes clearlyunderstand that the image in the mirror is animage of themselves – they make silly faces atthemselves. Other animals, such as cats anddogs, do not – they may even try to attack theirown reflection.

When a ray of light is reflected by a surface, the angle of incidence isequal to the angle of reflection.

i = r

In symbols:

Note that, to find the angles i and r, we have to draw the normal to

the reflecting surface. This is a line drawn perpendicular (at 90°) to the

surface, at the point where the ray strikes it. Of course, the other two

angles (between the rays and the flat surface) are also equal. However,

we would have trouble measuring these angles if the surface was

curved, so we measure the angles relative to the normal. The first law

of reflection thus also works for curved surfaces, such as concave and

convex mirrors.

normal

mirror

incident ray reflected ray

angle ofincidence i

angle ofreflection r

Figure 13.8 The first law of reflection of light. Thenormal is drawn perpendicular to the surface of the mirror. Then the angles are measured relative to the normal. The angle of incidenceand the angle of reflection are then equal: i = r.

If this were not the case, we would not be able to draw this diagramon a flat sheet of paper. The reflected ray would come out of the paper,or go back into the paper.

The image in a plane mirrorWhy do we see such a clear image when

we look in a plane (flat) mirror? And why

does it appear to be behind the mirror?

Figure 13.9a shows how an observer

can see an image of a candle in a plane

mirror. Light rays from the flame are

reflected by the mirror; some of them

enter the observer’s eye. In the diagram,

the observer has to look forward and

slightly to the left to see the image of the

candle. The brain assumes that the image

of the candle is in that direction, as

shown by the dashed lines behind the

mirror in Figure 13.9b. (Our brains

assume that light travels in straight lines,

even though we know that light is reflect-

ed by mirrors.) The dashed lines appear

Extension material

to be coming from a point behind the mirror, at the same distance

behind the mirror as the candle is in front of it. You can see this from

the symmetry of the diagram.

The image looks as though it is the same size as the candle. Also, it is

(of course) a mirror image; that is, it appears left–right reversed. You

will know this from seeing writing reflected in a mirror.

The image of the candle is not a real image. A real image is an image

that can be projected onto a screen. If you place a piece of paper at the

position of the image in a mirror, you will not see a picture of the can-

dle on it, because no rays of light from the candle reach that spot. That

is why we drew dashed lines, to show where the rays appear to be

coming from. We say that it the image in a mirror is a virtual image.

To summarise, when an object is reflected in a plane mirror:

● The image is the same size as the object.

● The image is the same distance behind the mirror as the object is in

front of it.

● The image appears left – right reversed.

● The image is virtual.

Figure 13.9 a Looking in the mirror, the observer sees an image of the candle. The image appears to be behind the mirror.b The ray diagram shows how the image is formed. Rays from the candle flame are reflected according to the law ofreflection. The dashed lines show that, to the observer, the rays appear to be coming from a point behind the mirror.

a

mirror

observer

reflectedrays

candle

imageb



The second law of reflection states that:when a ray of light is reflected by a surface, the incident ray, thereflected ray and the normal all lie in the same plane.


Ray diagramsFigure 13.9b is an example of a ray

diagram. Such diagrams are used to

predict the positions of images in mirrors

(or when lenses or other optical devices

are being used – see Chapter 14) from the

positions of the object and the mirror (or

lens). The idea is as follows. First we draw

in the positions of the things that are

known (e.g. the candle and the mirror).

Then we need to draw in some rays of

light. But not just any rays! They must be

carefully chosen if they are to show up

what we want to see. The rough position of

the observer (usually depicted by an eye) is

marked. Two rays are drawn from the

object to the mirror and then the reflected

rays are drawn to the observer. Then these

two reflected rays are extrapolated back,

to show where they appear to be coming

from. These are the dashed lines shown in

Figure 13.9b. This is known as a construc-

tion, and it allows us to mark the position

image

object

curvedmirror

Figure 13.10 This ray diagram is drawn to scale. The curved mirror produces animage that is virtual and smaller than the object.

A small lamp is placed 5 cm from aplane mirror. Draw an accuratescale diagram and use it to showthat the image of the lamp is 5 cmbehind the mirror.The ray diagram is shown in Figure13.11.● Step 1 Draw a line to represent themirror, and indicate its reflecting surface. Mark the position of theobject O. (It helps to work onsquared paper.)

Worked example 1

continued on next page

● Step 2 Mark the rough position of the observer. From O to the mirror,draw two rays that will be reflected towards the observer. Where therays strike the mirror, draw in the normal lines.

● Step 3 Using a protractor, measure the angle of incidence for eachray; mark the equal angle of reflection.

● Step 4 Draw in the reflected rays, and extend them back behind themirror. The point where they cross is where the image is formed;label it I.

From the diagram, it is clear that the image is 5 cm from the mirror,directly opposite the object. The line joining O to I is perpendicular tothe mirror.

of the image. Worked example 1 shows the steps in constructing such a

ray diagram.

Ray diagrams are often drawn to scale. An example, for a curved

mirror, is shown in Figure 13.10. This shows that the image formed is

behind the mirror, but closer to it, so that the image looks smaller.

Such a mirror is often used as the rear-view mirror or wing mirror of a

car, to give the driver a view over a wide area behind the car.

Today, designers of optical equipment such as cameras or micro-

scopes use sophisticated computer software to draw ray diagrams so

that they can be sure that their complicated systems of mirrors

and lenses will give as clear an image as possible.


Worked example 1 continued

Questions

13.6 Write the word AMBULANCE as it would appear when

reflected in a plane mirror. Why is it sometimes written in

this way on the front of an ambulance?

13.7 Draw a diagram to illustrate the law of reflection. Which

two angles are equal, according to the law?

13.8 A ray of light strikes a flat, reflective surface such that its

angle of incidence is 30°. What angle does the reflected

ray make with the surface?

13.9 Some children think that we see an object because light

from our eyes is reflected back by the object. Draw a

diagram to represent this incorrect idea. Draw another

diagram to show how diffuse reflection (scattering)

explains correctly how we see things.

13.10 What does it mean to say that a plane mirror produces a

virtual image?

?



mirror

O

Figure 13.11 The steps in drawing a ray diagram for a plane mirror.

Step 1

mirror

O

Step 3

mirror

O

Step 2

mirror

I

O

Step 4



◆ Light travels in straight lines.

◆ Light travels at a speed of almost 300000000m/s in a vacuum. It travels more slowly in transparent materials.

◆ The first law of reflection states that, when a ray of light isreflected by a surface, the angle of incidence is equal to theangle of reflection (i = r). Angles are measured relative to the normal to the surface.

◆ The second law of reflection states that, when a ray of light isreflected by a surface, the incident ray, the reflected ray andthe normal all lie in the same plane.

◆ The image formed by a plane mirror is the same size as theobject, is as far behind the mirror as the object is in front ofit, appears left–right reversed, and is virtual.

Sum

mar

ye

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