Waves Versus Particles; Huygen’s Principle and diffraction

That light carries energy is obvious to anyone who has focused the Sun’s rays with a magnifying glass on a piece of paper and burnt a hole in it. But how does light travel, and in what form is this energy carried?

Historically, this question turned out to be a difficult one. For one thing, light does not reveal itself in any obvious was as being made up of tiny particles no do we see tiny light waves passing by as we do water waves. The evidence seemed to favor first one side and then the other until about 1830, when most physicists had accepted the wave theory. By the end of the nineteenth century, light was considered to be an electromagnetic wave. In the early twentieth century, light was shown to have a particle nature as well. Nonetheless, the wave theory of light retains valid and has proved very successful.

The Dutch scientist Christian Huygens (1629–1695), a contemporary of Newton, proposed a wave theory of light that had much merit. Still useful today is a technique he developed for predicting the future position of a wave front when an earlier position is known. This is known as Huygen’s principle and can be stated as follows: every point on a wave front can be considered as a source of tiny wavelets that spread out in the forward direction at the speed of the wave itself. The new wavelet is the envelope of all the wavelets – that is, the tangent to all of them.

Huygen’s principle is particularly useful when waves impinge on an obstacle and the wave fronts are partially interrupted. Huygen’s principle predicts that waves bend in behind an obstacle. This is just what water waves do. The bending of waves behind obstacles into the “shadow region” is known as diffraction. Since diffraction occurs for waves, but not for particles, it can serve as one means for distinguishing the nature of light.

Test 2

Special Theory of Relativity

A. Reading

Read the text and choose from the list A–F the sentence which best fits each gap in the text. There is one extra sentence which you do not need to use.

The Michelson-Morley Experiment

A. The Michelson-Morley Experiment was designed to measure the speed of the ether – the medium in which light was assumed to travel – with respect to the Earth.

B. The “null” result was one of the great puzzles of physics at the end of the nineteenth century.

C. It is assumed that the “ether wind” is moving with speed v to the right. Alternatively, the Earth is assumed to move to the left with respect to the ether at speed v.

D. The medium for light waves could not be air, since light travels from the Sun to the Earth through nearly empty space.

E. In a reference frame which was not at rest, extra terms would have to be added to take into account the relative velocity.

F. Briefly, what they did was measure the difference in the speed of light in different directions.

With the introduction of the theory of electromagnetism in the last half of the nineteenth century it was assumed that light would have a different speed in different frames of reference. Maxwell’s equations predicted the speed of light to be c = 3 . 108 m/s. This seemed to imply there must be some special reference frame where c would have this value (1;…).

Waves travel on water and along ropes or strings, and sound waves travel in air and other materials. It was natural for nineteenth-century physicists to think that light must travel in some medium (2;…). Therefore, another medium was postulated, the ether. The ether was not only transparent, but because of difficulty in detecting it, was assumed to have zero density.

Scientists soon set out to determine the speed of the Earth relative to this absolute frame, whatever it might be. A number of clever experiments were designed. The most direct were performed by A.A. Michelson and E.W. Morley in the 1880s (3;…). The experiments thus hoped to find an absolute reference frame, one that could be considered to be at rest.

One of the possibilities nineteenth-century scientists considered was that the ether is fixed relative to the Sun, for even Newton had taken the Sun as the centre of the universe. If this were the case (there was no guarantee, of course), the Earth’s speed of about 3 . 104 m/s in its orbit around the Sun would produce a change of 1 part in 104 in the speed of light (3 . 108 m/s). Direct measurement of the speed of light to this accuracy was not possible. But A.A. Michelson, later with the help of E.W. Morley, was able to use his interferometer to measure the difference in the speed of light to this accuracy (4;…). They expected to find a difference depending on the orientation of their apparatus with respect to the ether. For just as a boat has different speeds relative to the land when it moves upstream, downstream, or across the stream, so too light would be expected to have different speeds depending on the velocity of the ether past the Earth.

They detected no difference at all (5;…). One possibility to explain the null result was to apply an idea put forth independently by G.F. Fitzgerald and H.A. Lorentz (in the 1890s) in which they proposed that any length (including the arm of interferometer) contracts by a factor in the direction of motion through the ether. According to Lorentz, this could be due to the ether affecting the forces between the molecules of a substance, which were assumed to be electrical in nature. This theory was eventually replaced by the far more comprehensive theory proposed by Albert Einstein in 1905 – the special theory of relativity.

B. Choose the correct item to fill in the space

1. Within experimental … no contradictions have been found in the theory (mistake, omission, error)

2. Relativity does not … classical mechanics (contradict, satisfy, mind).

3. Matter can be … into energy (modified, remodeled, converted).

4. The time interval between two … even if they are simultaneous, depends on the observer’s reference frame (incidents, events, episodes).

5. The laws of physics … the relativity principle (observe, follow, obey).

6. To accelerate an object up to the speed of light would require … energy (absolute, endless, infinite).

7. A general result of relativity is known as time … (dilation, extension, increase).

8. Mass, another basic mechanical … is measured to increase as its speed increases (magnitude, amount, quantity).

9. The length of an object is measured to be shorter when it is moving relative to the … than when it is at rest (viewer, observer, spectator).

10. Certain … assumptions make sense from everyday experience (unprovable, unverifiable, unchecked).

C. Fill in the correct word derived from the words in brackets

1. Two events are said to occur … (simultaneous) if they occur at … (exact) the same time.

2. Einstein concluded that the … (consistent) he found in electromagnetic theory were due to the … (assume) that an absolute space exists.

3. This … (propose) was embodied in two postulates.

4. … (long) contraction, like time … (dilate), is not noticeable in everyday life.

5. Somehow we feel, just as physicists did before the advent of … (relative), that space and time are … (complete) separate entities.

6. Before Galileo, the vertical … (direct), that in which objects fall, was considered to be … (distinct) different from the two horizontal dimensions.

7. We have recognized the … (valid) of this principle in everyday life.

8. In classical mechanics the … (measure) of space and time doesn’t change from one reference frame to another.

9. We can conclude that … (simultaneous) is not an absolute concept.

10. The effect is … (notice) only when the relative speed of the two reference frames is very large.

D. Choose the right word from the list to fill in the spaces:

Mind, light, set of coordinates, at rest, relative, unaccelerated, relativity, observer, spatial, absolute, definition, in motion, fixed, view.

The 20th century saw remarkable developments in the theory of a) … These developments have been responsible for profound changes in the way that physicists, astronomers and mathematicians b) … the world.

The special theory of relativity is best known as a description of how objects behave when they travel with speeds near that of c) … It leads to an

understanding of time and space as d) … quantities that depend on how a particular observer is moving, rather than absolute quantities measured with respect to a e) … system of coordinates.

The problem of space and time is not a new one. The German philosopher Nicolas of Cusa (1401–1464) argued that space and time are merely products of the f) …, and therefore are inferior to the mind that created them. Giordano Bruno (1548–1600), an Italian philosopher whose ideas anticipated modern science, pointed out that such words as “above”, “below”, “at rest” and g) … are meaningless in the universe of revolving suns and planets, for which there is no fixed centre. In the 17th century, the celebrated English physicist and mathematician, Isaac Newton, contrasted the h) … time of the scientist with the less precise everyday notions of space and time. He regarded the material world as a collection of particles, each one of which could be i) … or moving, not merely in relation to the others, but in relation to absolute space.

Relativity states that it is impossible to give a clear j) … of an “absolute” space and time. Objects in the Universe cannot be measured with respect to some single, fixed system of coordinates. Only relative space and time exist, in which each k) … refers events to their own frame of reference and to each other.

For example, you could choose to measure events in your house relative to their position from your front door and their time according to your kitchen clock.

Any l) … frame of reference is as good as any other for describing events and for carrying out experiments to determine the laws of nature. The system of coordinates needed to describe any frame of reference are the three m) … dimensions, plus time. In other words, relativity is concerned with a four dimensional n) … called space-time, and with how events appear differently when viewed in different frames of reference.

E. Put the verbs in brackets into the correct tense

1. He will be late for the train if he … (not start) at once.

2. If you … (speak) more slowly, he might have understood you.

3. If Paul comes this evening, we … (talk) it over with him.

4. If you were going to travel to Tibet, when … (be) the best time to go?

5. I wouldn’t drink that wine if I … (be) you.

6. If you … (not like) opera, why are you here?

7. If the salary … (be) good, I would have accepted the job.

8. If heat energy continuously … (not remove) from the core of the fission reactor, the fuel rods may fuse.

9. If you hadn’t been in such a hurry, you not … (put) salt into the coffee instead of sugar.

10. It … (be) easier if Leeds were on a direct link to Oxford.

11. If I … (listen) more carefully to his directions, I wouldn’t have got lost.

12. What would you do, if you … (become) President.

13. If I were you, I … (not go) in this weather.

14. If enough strontium-90 … (ingest), it can destroy the bone marrow or perhaps cause cancer.

15. If we get a lift, we … (be) in time.

F. Choose the correct answer:

1. The element hydrogen … in nature as three isotopes: protium, hydrogen, deuterium.

a) is found; b) is being found; c) has found

2. There are lots of books about black holes. William Kaufman’s “Black holes Warped Spacetime” is also worth …

a) to read; b) being read; c) reading.

3. R. Wald’s “Space, Time and Gravity” is an exposition of general relativity for non-scientists. I … it myself, but I’ve heard good things about it.

a) didn’t read; b) haven’t read; c) am not reading.

4. Human beings have long desired to control the weather. However, little progress ... toward achieving this desire.

a) has been made; b) was made; c) is making.

5. If Madame Curie’s work on radium …successful, she wouldn’t have been awarded the Nobel prize in chemistry in 1911.

a) wasn’t; b) couldn’t have been; c) hadn’t been.

6. Madame Curie died in 1934 from leukemia (cancer of the blood) which may … by overexposure to radioactivity.

a) be caused; b) have been caused; c) have caused.

7. She died one year before the Curies’ daughter Irene Joliot Curie, and her husband Fredefic Joliot … the Nobel prize in chemistry.

a) had been awarded; b) were being awarded; c) were awarded.

8. If he helps us, the job … us half an hour.

a) will take; b) would take; c) would have taken.

9. We expect all the alkali metals … similar properties.

a) to be having; b) have; c) to have.

10. The Sun’s temperature … to be about 15 million K at its centre.

a) is believed; b) was believed; c) believed.

11. The temperature at the visible surface of the Sun … at about 6000 K.

a) is being measured; b) had been measured; c) has been measured.

12. When chemists discovered gallium, scandium and germanium, they found that they had the properties that Mendeleev …

a) predicted; b) has predicted; c) had predicted.

13. So far, we … compounds as being either ionic or covalent.

a) classified; b) have classified; c) had classified.

14. The National Weather Service … to getting the weather information to the public by the fastest means available.

a) is dedicated; b) has dedicated; c) dedicated.

15. If the dew point … below 0ºC, the water vapour freezes on condensing

a) will be; b) were; c) is.

G. Translate the following text

The second postulate of the special theory of relativity states that light propagates through empty space with a definite speed c independent of the speed of the source or observer. It may seem hard to accept, for it violates commonsense notions. First of all, we have to think of light traveling through empty space. Giving up the ether is not too hard, however, for after all, it had never been detected. But the second postulate also tells us that the speed of light in vacuum is always the same, 3 . 108 m/s, no matter what the speed of the observer or the source. Thus, a person traveling toward or away from a source of light will measure the same speed for that light as someone at rest with respect to the source. These conflicts with our everyday notions, for we would expect to have to add in the velocity of the observer. Part of the problem is that in our everyday experience, we do not measure velocities anywhere near as large as the speed of light. Thus we can’t expect our everyday experience to be helpful when dealing with such a high velocity. On the other hand, the Michelson-Morley experiment is fully consistent with the second postulate.

Test 3

A. Reading

Choose the most suitable heading from the list A–G for each part (1–7) of the text.

The 21st Century Engineer

A. Integration of disparate components into the whole that exceeds the sum of its respective capabilities.

B. Creating microscopic devices.

C. Advances in modern science and technology that will shape the future of engineering.

D. Skills and abilities that 21st century engineers need.

E. Revolution in the acquisition of knowledge.

F. The capability that facilitates computing.

G. “Chaotic engineering”.

(1;…) What does the 21st century engineer need to know? To attempt an answer, let’s briefly examine some of the new capabilities that are shaping the future of engineering – terascale, nanoscale, complexity, cognition, and holism.

Because science and technology are transforming forces, it will be these emerging fields, the unpredicted territories, that will change and expand our capabilities as engineers and innovators.

(2;…) Terascale. This new capability takes us three orders of magnitude beyond present general-purpose and generally accessible computing capabilities.

In the past, our system architectures could handle hundreds of processors. Now we are working with systems of 10 000 processors. In a very short time, we’ll be connecting millions of systems and billions of “information appliances” to the Internet. Crossing that boundary of one trillion operations per second will launch us toward new frontiers.

(3;…) Nanoscale. This advance will take us three orders of magnitude below the size of most of today’s human-made devices. Nanostructuresare at the confluence of the smallest of human-made devices and the large molecules of living systems, letting us imagine connecting machines to living cells.

Nanotechnology lets us manipulate matter one atom or molecule at a time. It could lead to amazing breakthroughs – for example, to molecular computers that could store the equivalent of the U.S. Library of Congress in a device we could wear.

(4;…) Complexity. Mitch Waldrop writes in his book “Complexity” about a point “where the components of a system never quite lock into place, and yet never quite dissolve into turbulence, either …”. It’s often called the edge of chaos. If we look at science and engineering, we discern this zone of transformation at many scales and in many disciplines. For example, researchers are trying to wed polymers to silicon – a marriage of opposites, because plastics are chaotic chains while silicon consists of orderly crystals. The resulting electronic devices would have marvelous flexibility, be less expensive to make, and, therefore, empower more people. Again, it comes to managing order and disorder, all at once.

(5;…) Cognition. The dictionary defines cognition as “the mental process or facility by which knowledge is acquired”. Because of new knowledge, methods, and tools, I believe we are on the verge of a cognitive revolution. We are poised for many exciting new discoveries in this area. These breakthroughs will lay the foundation for progress in many areas of national importance, from teaching children how to read to understanding learning processes, from building humanlike computers and robots to designing networks and systems capable of cognition.

(6;…) Holism. According to the dictionary, again, holism is “the concept that any entity is greater than merely the sum of its parts”. It refers to new capabilities to put things together – how to integrate seemingly disparate things into a greater whole. This includes social as well as physical and virtual engineering systems.

(7;…) All told, progress in these areas will lay out the capacity for anintegrated design field far beyond what is imaginable with today’s technology.

Taken together, this means that 21st century engineers will need to be astute makers, trusted innovators, agents of change, master integrators, enterprise enablers, technology stewards and knowledge handlers. They will need to embrace complex systems and reach the right decisions about how huge amounts of time, money, people, knowledge and technology are tasked to a common end.

B. Fill in the gaps with an appropriate word from the list:

Spinning motion, conductors, commonsense, non-accelerating, spontaneously, incidence, reverse, interference, charge, ferromagnetic.

1. When in thermal contact, heat flows … from a hotter object to a colder one until they are at the same temperature.

2. Processes that are left to themselves tend to become more and more disordered, never the …

3. Normally when objects are charged by rubbing. They hold their … only for a limited time and eventually return to the neutral state.

4. Metals are generally good … whereas most other materials are insulators.

5. Individual electrons in an atom have a magnetic field due to what is best understood as a …

6. Materials that are highly magnetic are called …

7. The angle of reflection is equal to the angle of …

8. … effects are defined as change in wave motion produced by phase and amplitude relations of two or more waves.

9. The special theory of relativity deals with inertial (…) reference frames.

10. The concept of dilation may be hard to accept, for it violates our … understanding.

C. Fill in the correct word derived from the words in brackets:

1. A beautiful … (atmosphere) phenomenon commonly seen after rain is called the rainbow. The … (colour) arc of a rainbow is the result of several … (optic) effects: refraction, internal … (reflect) and dispersion.

2. The universe can be extreme. There are realms that are tiny and yet … (incredible) massive, therefore requiring that both quantum mechanics and general relativity … (simultaneous) be brought to bear.

3. We use heat energy, either directly or … (direct), to do most of the work that is done in everyday life. The ……. (operate) of heat engines is based on the laws of thermodynamics.

4. The volt is the unit of … (volt) and is equal to one joule per coulomb. … (volt) is caused by a … (separate) of charge.

5. Like poles repel and unlike poles attract. The … (strong) of the attraction or … (repulse) depends on the … (strong) of the magnetic poles.

D. Correct the mistakes:

1. If you will not stop eating chocolates, you’ll put on weight.

2. You look exhausted. What did you do?

3. I don’t mind to lend you the money.

4. My salary is being deposited in my bank account every month.

5. He is late. He might miss the bus.

6. The flat hasn’t tidied yet.

7. Martin is saying to be a good sportsman.

8. He known to have several bank accounts.

9. I hope that the new sports centre is opening soon.

10. I heard him to call for help.

11. I am going to work by bus because my car is repaired at the moment.

12. I usually have my house cleaning by my cleaner.

13. There is no point to worry until you get the results.

14. If I were not busy yesterday, I wouldn’t have helped you.

15. The bank has closed by the time they got there.

E. Translate one of the following texts into Russian or Kazakh:

Text A

What is a black hole?

A black hole is a region of space that has so much mass concentrated in it that there is no way for a nearby object to escape its gravitational pull. Let’s start by thinking about gravity under fairly simple circumstances.

Suppose that you are standing on the surface of a planet. You throw a rock straight up into the air. Assuming you don’t throw it too hard, it will rise for a while, but eventually the acceleration due to the planet’s gravity will make it start to fall down again. If you threw the rock hard enough, though, you would make it escape the planet’s gravity entirely. It would keep on rising forever. The speed with which you need to throw the rock in order that it just barely escapes the planet’s gravity is called escape velocity.

Now imagine an object with such an enormous concentration of mass in such a small radius that its escape velocity was greater than the velocity of light.

Then, since nothing can go faster than light, nothing can escape the object’s gravitational field. Even a beam of light would be pulled back by gravity and would be unable to escape.

Massive objects distort space and time, so that the usual rules of geometry don’t apply any more. Near a black hole, this distortion of space is extremely severe and causes black holes to have some very strange properties. In particular, a black hole has something called an event horizon. This is a spherical surface that marks the boundary of the black hole, the horizon has a very large velocity. In fact, it is moving outward at the speed of light! That explains why it is easy to cross the horizon in the inward direction, but impossible to get back out.

Text B

The Forces

The world around us is replete with means of exerting influence: balls can be hit with bats, bungee enthusiasts can through themselves earthward from high platforms, magnets can keep superfast trains suspend just above metallic tracks, Geiger counters can tick in response to radioactive material, nuclear bombs can explode. We can influence objects by vigorously pushing, pulling, or shaking them; or by freezing, heating, or burning them. During the past hundred years physicists have accumulated mounting evidence that all of these interactions between various objects and materials can be reduced to combinations of four fundamental forces. One of these is the gravitational force. The other three are the electromagnetic force, the weak force, and the strong force.

Gravity is the most familiar of the forces, being responsible for keeping us in orbit around the Sun as well as keeping our feet firmly planted on earth. The mass of an object measures how much gravitational force it can exert as well as feel. The electromagnetic force is the next most familiar of the four. It is the force driving all of the conveniences of modern life – lights, computers, TVs, telephones. It underlies the awesome might of lightning storms and the gentle touch of a human hand.

The strong and weak forces are less familiar because their strength rapidly diminishes over all but subatomic distance scales; they are the nuclear forces.

This is why these two forces were discovered much more recently. The strong force is responsible for keeping quarks “glued” together inside of protons and neutrons and keeping protons and neutrons tightly crammed together inside atomic nuclei. The weak force is best known as the force responsible for the radioactive decay of substances such as uranium and cobalt.

Text C

Quantum Mechanics – A New Theory

The new theory, called quantum mechanics, unifies the wave – particle duality into a single consistent theory. As a theory, quantum mechanics has been extremely successful. It has successfully dealt with the spectra emitted by complex atoms, even the fine details. It explains the relative brightness of spectral lines and how atoms form molecules. It is also a much more general theory that covers all quantum phenomena from blackbody radiation to atoms and molecules. It has explained a wide range of natural phenomena and from its predictions many new practical devices have become possible. Indeed, it has been so successful that it is accepted today by nearly all physicists as the fundamental theory underlying physical processes.

Quantum mechanics deals mainly with microscopic world of atoms and light.

But in our macroscopic world, we do perceive light and we accept that ordinary objects are made up of atoms. This new theory must therefore also account for the verified results of classical physics. That is, when it is applied to macroscopic phenomena, quantum mechanics must be able to produce the old classical laws.

This, the corresponding principle is met fully by quantum mechanics. This doesn’t mean we throw away classical theories such as Newton’s laws. In the everyday world, the latter are far easier to apply and they give an accurate description. But when we deal with high speeds, close to the speed of light, we must use the theory of relativity; and when we deal with the tiny world of the atom, we use quantum mechanics.

Ключи к тестам (1-3)

Test 1

A. 1 – D; 2 – F; 3 – A; 4 – B; 5 – E.

B. 1) constructive; 5) paths;

2) transmitted; 6) illusions;

3) total; 7) audible.

4) denser;

C. 1) propagation; 5) preferential;

2) randomly; 6) partial;

3) directions; 7) partially;

4) unpolarized; 8) linearly.

D. 1) parallel; 6) white;

2) diffuse reflection; 7) violet; red;

3) incident; 8) dispersion; internal reflection;

4) away from; 9) sound waves; light waves;

5) toward; 10) interference.

E. 1) to know; 6) wear;

2) deflect; 7) sink;

3) give; 8) to rise;

4) to pass; 9) to illustrate;

5) use; 10) burst.

F. 1) wondering; to run; 6) walking;

2) traveling; 7) getting up;

3) wasting; to do; 8) doing;

4) seeing; 9) understand;

5) to get up; 10) complaining.

G. 1 – b; 2 – a; 3 – c; 4 – c; 5 – b; 6 – a; 7 – a; 8 – c; 9 – c; 10 – b.

Test 2

A. 1 – E; 2 – D; 3 – A; 4 – F; 5 – B.

B. 1) error; 6) infinite;

2) contradict; 7) dilation;

3) converted; 8) quantity;

4) events; 9) observer;

5) obey; 10) unprovable.

C. 1) simultaneously; exactly; 6) direction; distinctly;

2) inconsistencies; assumption; 7) validity;

3) proposal; 8) measurement;

4) length; dilation; 9) simultaneity;

5) relativity; completely; 10) noticeable.

D. a) relativity; h) absolute;

b) view; i) at rest;

c) light; j) definition;

d) relative; k) observer;

e) fixed; l) unaccelerated;

f) mind; m) spatial;

g) in motion; n) set of coordinates.

E. 1) doesn’t start; 9) wouldn’t have put;

2) had spoken; 10) would be;

3) ‘ll talk; 11) had listened;

4) would be; 12) became;

5) were; 13) wouldn’t go;

6) don’t like; 14) is ingested;

7) had been; 15) ‘ll be.

8) is not continuously removed;

F. 1) a; 6) b; 11) c;

2) c; 7) c; 12) c;

3) b; 8) a; 13) b;

4) a; 9) d; 14) a;

5) c; 10) a; 15) c.

Test 3

A. 1 – C; 2 – F; 3 – B; 4 – G; 5 – E; 6 – A; 7 – D.

B. 1) spontaneously; 6) ferromagnetic;

2) reverse; 7) incidence;

3) charge; 8) interference;

4) conductors; 9) non-accelerating;

5) spinning motion; 10) commonsense.

C. 1) atmosphere; colourful; optical; reflection;

2) incredibly; simultaneously;

3) indirectly; operation;

4) voltage (2); separation;

5) strength; repulsion; strength.

D. 1. If you don’t stop eating chocolates, you’ll put on weight.

2. You look exhausted. What have you been doing?

3. I don’t mind lending you the money.

4. My salary is deposited in my bank account every month.

5. He is late. He might have missed the bus.

6. The flat hasn’t been tidied yet.

7. Martin is said to be a good sportsman.

8. He is known to have several bank accounts.

9. I hope that the new sports centre will open soon.

10. I heard him call/calling for help.

11. I am going to work by bus because my car is being repaired at the moment.

12. I usually have my house cleaned by my cleaner.

13. There is no point in worrying until you get the results.

14. If I hadn’t been busy yesterday, I wouldn’t have helped you.

15. The bank had closed by the time they got there.