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Physics
David Sang
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© Cambridge University Press 2001
First published 2001
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Section A
Section A
Section B
Section C
Section D
Section E
Section F
Forces and movement
Energy
Waves
Electricity and magnetism
Atomic physics
The Earth and space
Chapter 1 Describing motion
1.1
1.2
1.3
1.4
1.5
Section B
Contents
Measuring speed
Distance–time graphs
Changing speed
Velocity–time graphs
The equations of motion
6.1 The energy we use
6.2 Storing energy
6.3 Renewable energy technologies
84
86
90
93
Chapter 7 Energy transformations, energy
transfers
98
1
2
8
12
16
20
Chapter 2 Forces and motion
26
2.1
2.2
2.3
2.4
27
31
36
39
Forces produce acceleration
Balanced and unbalanced forces
Friction and drag
The force of gravity
Chapter 6 Energy resources
7.1 Forms of energy
7.2 Conservation of energy
7.3 Energy efficiency
Chapter 8 Work and power
8.1
8.2
8.3
8.4
8.5
Gravitational potential energy
Kinetic energy
KE–GPE transformations
Doing work
Power
98
104
108
112
113
115
117
120
124
Chapter 9 The kinetic model of matter 127
9.1 Changes of state
9.2 Particles, forces and the
kinetic model
9.3 Thinking about the kinetic model
9.4 Internal energy
9.5 Temperature and temperature scales
128
131
136
138
140
Chapter 3 Forces and momentum
49
3.1 Collisions and explosions
3.2 Momentum and force
50
56
Chapter 4 Turning effects of forces
63
4.1 The moment of a force
4.2 Stability and centre of mass
Chapter 10 Thermal energy transfers
147
64
68
Chapter 5 Forces and matter
71
5.1 Density
5.2 Forces acting on solids
72
74
10.1
10.2
10.3
10.4
10.5
148
152
154
158
160
Further questions Section A
79
Conduction
Convection
Radiation
Effective insulation
Specific heat capacity
164
11.1
11.2
11.3
11.4
11.5
164
167
170
173
175
Properties of a gas
Boyle’s law
Charles’ law
The pressure law
Combining the three gas laws
Further questions Section B
178
Chapter 12 Sound
183
12.1
12.2
12.3
12.4
12.5
184
185
189
194
197
Making sounds
At the speed of sound
Seeing sounds
How sounds travel
Using ultrasound and infrasound
Chapter 13 How light travels
200
13.1 Travelling in straight lines
13.2 The speed of light
13.3 Reflecting light
201
202
205
Chapter 14 Refraction of light
210
14.1
14.2
14.3
14.4
211
215
218
224
Refraction effects
Total internal reflection
Lenses
Light and colour
Chapter 15 The electromagnetic
spectrum
227
15.1
15.2
15.3
15.4
228
232
235
238
Extending the visible spectrum
Infrared and ultraviolet radiation
Radio waves and microwaves
X-rays and gamma rays
Chapter 16 Waves
241
16.1
16.2
16.3
16.4
242
247
249
253
Describing waves
Speed, frequency and wavelength
Reflection and refraction of waves
Diffraction
Further questions Section C
259
Section D
Section B
Section C
Chapter 11 The gas laws
Chapter 17 Static electricity
263
17.1 Charging and discharging
17.2 What is electric charge?
17.3 The hazards and uses of
static electricity
265
270
274
Chapter 18 Electric circuits
278
18.1
18.2
18.3
18.4
280
285
291
295
Current in electric circuits
Electrical resistance
Resistive components
Combinations of resistors
Chapter 19 Electricity and energy
300
19.1 Using electrical appliances
19.2 Voltage and energy
19.3 Domestic electricity supply
301
304
308
Chapter 20 Electromagnetic forces
and electric motors
315
20.1
20.2
20.3
20.4
20.5
316
319
323
326
331
Electromagnets
Uses of electromagnets
How electric motors are constructed
The motor effect
Electric motors revisited
Chapter 21 Electromagnetic induction
333
21.1 Generating electricity
21.2 The principles of electromagnetic
induction
21.3 Power lines and transformers
334
Chapter 22 Electronic control circuits
347
22.1 Electronic processors
22.2 Input devices
22.3 Output devices
348
353
356
Further questions Section D
360
336
339
23.1
23.2
23.3
23.4
The size of atoms
Electrons
Inside atoms
Protons, neutrons and electrons
367
368
372
375
Chapter 24 Radioactivity
380
24.1
24.2
24.3
24.4
381
384
388
391
Radioactivity all round
The microscopic picture
Using radioactive substances
Radioactive decay
Chapter 25 Nuclear fission
399
25.1 Nuclear fission
401
Further questions Section E
408
Section F
Section E
Chapter 23 Atoms, nuclei and electrons 366
Chapter 26 The active Earth
411
26.1 Inside the Earth
26.2 Plate tectonics
412
415
Chapter 27 Around the Earth
420
27.1 Gravity
27.2 Into orbit
27.3 Spacecraft at work
421
424
427
Chapter 28 The Solar System
430
28.1 The moving Earth
28.2 Moon and Sun
28.3 The nine planets
431
433
434
Chapter 29 The Universe
443
29.1 Stars and galaxies
29.2 The life of a star
29.3 The life of the Universe
444
447
449
Further questions Section 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
Section C Chapter 13
Topics in this chapter
How light travels
◆
◆
◆
e
◆
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.
Figure 13.1 A laser beam travels in a straight line
to the Moon. It is reflected by mirrors on the
Moon’s surface, so that it returns to Earth,
where it can be detected. From the time taken
for the round trip, together with the speed of
light, the Earth–Moon distance can be found
with great accuracy.
200
How light travels
Section C Chapter 13
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 travels, and how it is reflected by mirrors.
13.1 Travelling in straight lines
Light 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.
a
Figure 13.2 a A ray box produces a broad beam
of light. b This can be narrowed down using
a metal plate with a slit in it. Marking the line
of the ray with dots allows you to record its
position.
b
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 single 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.
How light travels
201
Section C Chapter 13
Figure 13.3 A laser gives a narrow,
concentrated beam of light, which is
more intense than the ray from a ray
box. The light reflects back and forth
between the two mirrors, and picks
up energy as it passes through the
gas mixture. One mirror lets
through a small amount of light to
form the beam, which emerges from
the end.
glass tube with
sloping ‘windows’
mixture of gases
(helium and neon)
+
–
mirror
(100% reflection)
connections to power supply
partially silvered mirror
(allows beam to emerge)
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.
?
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 light
Figure 13.4 The red laser beam on the right was
used to guide tunnelling equipment during
the construction of the Channel Tunnel. This
ensured that the two teams working from
opposite ends met in the middle with pinpoint
accuracy.
Light 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.
For most purposes we can round off the value to
300 000 000 m/s
or 3 ¥ 108 m/s
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 microsecond 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.)
202
How light travels
Section C Chapter 13
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 Jupiter
Jupiter
shorter
distance
Figure 13.5 The Danish astronomer Ole Romer
realised that, when Jupiter and the Earth were
on opposite sides of the Sun, light had further
to travel from Jupiter to reach Earth. Thus
events such as the eclipsing of Jupiter’s moon
Io was seen later than expected, by up to 10
minutes. From this and the distances of the
planets, he could deduce a value for the speed
of light, about 225 000 km/s. This is reasonably
close to today’s agreed value.
Earth
longer
distance
Sun
Earth
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 speeds
Although 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
How light travels
203
Section C Chapter 13
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 instrument
that measure distances by timing a beam of
light or infrared radiation. The beam is timed
as it travels from one instrument to the other
and back again. An on-board computer calculates the distance and stores the answer for
downloading later into a more powerful computer, which draws an accurate plan of the
area.
Table 13.1 The speed of light in some transparent materials. (The value for a vacuum is
shown, for comparison.) Note that the values
are only approximate. The third column shows
the factor by which the light is slowed down.
(This is the material’s refractive index – see
Chapter 14.)
?
Material
Speed of light (m/s)
Speed in vacuum
Speed in material
vacuum
air
water
Perspex
glass
diamond
2.998 ¥ 108
2.997 ¥ 108
2.3 ¥ 108
2.0 ¥ 108
(1.8–2.0) ¥ 108
1.25 ¥ 108
1 exactly
1.0003
1.33
1.5
1.5–1.7
2.4
Questions
13.2 Someone tells you that ‘the speed of light is 3 ¥ 108 m/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.
13.4
13.5
204
How light travels
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?
The speed of light in empty space, c, is exactly
299 792 458 m/s. In calculations, we often use an
approximate value for c. Which of the following are good
approximations?
300 000 000 m/s, 30 000 km/s, 300 000 km/s,
3 ¥ 108 m/s, 3 ¥ 109 m/s
Explain why the surveyor shown in Figure 13.6 would have
problems if light did not travel in straight lines.
Section C Chapter 13
13.3 Reflecting light
Figure 13.7 Psychologists use mirrors to test the
intelligence of animals. Does an animal recognise that it is looking at itself? Apes clearly
understand that the image in the mirror is an
image of themselves – they make silly faces at
themselves. Other animals, such as cats and
dogs, do not – they may even try to attack their
own reflection.
Most of us look in a mirror at least once a day, to check on our appearance (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 mirror, 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 experiments, 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:
When a ray of light is reflected by a surface, the angle of incidence is
equal to the angle of reflection.
In symbols:
i=r
normal
mirror
angle of
incidence i
Figure 13.8 The first law of reflection of light. The
normal is drawn perpendicular to the surface
of the mirror. Then the angles are measured
relative to the normal. The angle of incidence
and the angle of reflection are then equal: i = r.
incident ray
angle of
reflection r
reflected ray
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.
How light travels
205
Section C Chapter 13
The second law of reflection states that:
when a ray of light is reflected by a surface, the incident ray, the
reflected ray and the normal all lie in the same plane.
If this were not the case, we would not be able to draw this diagram
on a flat sheet of paper. The reflected ray would come out of the paper,
or go back into the paper.
Extension material
The image in a plane mirror
Why 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 reflected by mirrors.) The dashed lines appear
a
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 candle 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.
b
image
mirror
reflected
rays
candle
observer
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 of
reflection. The dashed lines show that, to the observer, the rays appear to be coming from a point behind the mirror.
206
How light travels
Section C Chapter 13
Ray diagrams
Figure 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 construction, and it allows us to mark the position
Worked example 1
A small lamp is placed 5 cm from a
plane mirror. Draw an accurate
scale diagram and use it to show
that the image of the lamp is 5 cm
behind the mirror.
The ray diagram is shown in Figure
13.11.
● Step 1 Draw a line to represent the
mirror, and indicate its reflecting
surface. Mark the position of the
object O. (It helps to work on
squared paper.)
image
curved
mirror
object
Figure 13.10 This ray diagram is drawn to scale. The curved mirror produces an
image that is virtual and smaller than the object.
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 microscopes 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.
● 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 the
rays strike the mirror, draw in the normal lines.
● Step 3 Using a protractor, measure the angle of incidence for each
ray; mark the equal angle of reflection.
● Step 4 Draw in the reflected rays, and extend them back behind the
mirror. 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 to
the mirror.
continued on next page
How light travels
207
Section C Chapter 13
Worked example 1 continued
Step 1
Step 2
mirror
mirror
O
O
I
Step 3
Step 4
mirror
mirror
O
O
Figure 13.11 The steps in drawing a ray diagram for a plane mirror.
?
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?
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?
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.
What does it mean to say that a plane mirror produces a
virtual image?
13.8
13.9
13.10
208
How light travels
Summary
Section C Chapter 13
◆ Light travels in straight lines.
◆ Light travels at a speed of almost 300 000 000 m/s in a
vacuum. It travels more slowly in transparent materials.
◆ The first law of reflection states that, when a ray of light is
reflected by a surface, the angle of incidence is equal to the
angle 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 is
reflected by a surface, the incident ray, the reflected ray and
the normal all lie in the same plane.
e The image formed by a plane mirror is the same size as the
◆
object, is as far behind the mirror as the object is in front of
it, appears left–right reversed, and is virtual.
How light travels
209