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PhysicsDavid Sang
PUBLISHED BY THE PRESS SYNDICATE OF THE UNIVERSITY OF CAMBRIDGE
The Pitt Building, Trumpington Street, Cambridge, United Kingdom
CAMBRIDGE UNIVERSITY PRESS
The Edinburgh Building, Cambridge CB2 2RU, UK
40 West 20th Street, New York, NY 10011–4211, USA
10 Stamford Road, Oakleigh, VIC 3166, Australia
Ruiz de Alarcón 13, 28014 Madrid, Spain
Dock House, The Waterfront, Cape Town 8001, South Africa
http://www.cambridge.org
© Cambridge University Press 2001
First published 2001
Printed in Italy by G. Canale & C. S.p.A., Borgaro T.se, (Turin)
Typeface Minion System QuarkXPress®
A catalogue record for this book is available from the British Library
ISBN 0 521 77802 6 paperback
Produced by Gecko Ltd, Bicester, Oxon
NOTICE TO TEACHERS
It is illegal to reproduce any part of this work in material form (including
photocopying and electronic storage) except under the following circumstances:
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(iii) where you are allowed to reproduce without permission under the
provisions of Chapter 3 of the Copyright, Designs and Patents Act 1988.
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.
Section C Chapter 13
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
Section C Chapter 13
202 How light travels
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.)
Section C Chapter 13
How light travels 203
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
Section C Chapter 13
204 How light 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.
?
Section C Chapter 13
How light travels 205
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
Section C Chapter 13
206 How light travels
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.
Section C Chapter 13
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.
How light travels 207
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?
?
Section C Chapter 13
208 How light travels
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
Section C Chapter 13
How light travels 209
◆ 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