Английский язык. Ч.3 (Units 9,10): Практикум

ɎȿȾȿɊȺɅɖɇɈȿ ȺȽȿɇɌɋɌȼɈ ɉɈ ɈȻɊȺɁɈȼȺɇɂɘ ȽɈɋɍȾȺɊɋɌȼȿɇɇɈȿ ɈȻɊȺɁɈȼȺɌȿɅɖɇɈȿ ɍɑɊȿɀȾȿɇɂȿ ȼɕɋɒȿȽɈ ɉɊɈɎȿɋɋɂɈɇȺɅɖɇɈȽɈ ɈȻɊȺɁɈȼȺɇɂə «ȼɈɊɈɇȿɀɋɄɂɃ ȽɈɋɍȾȺɊɋɌȼȿɇɇɕɃ ɍɇɂȼȿɊɋɂɌȿɌ»

ɇ.Ⱥ. ɂɥɶɢɱɟɜɚ, ɂ.ȼ. Ⱦɪɨɡɞɨɜɚ, ȿ.ɇ. ɉɨɞɬɟɥɟɠɧɢɤɨɜɚ

ȺɇȽɅɂɃɋɄɂɃ əɁɕɄ ɑɚɫɬɶ 3 (Units 9, 10) ɉɪɚɤɬɢɤɭɦ ɞɥɹ ɜɭɡɨɜ

ɂɡɞɚɬɟɥɶɫɤɨ-ɩɨɥɢɝɪɚɮɢɱɟɫɤɢɣ ɰɟɧɬɪ ȼɨɪɨɧɟɠɫɤɨɝɨ ɝɨɫɭɞɚɪɫɬɜɟɧɧɨɝɨ ɭɧɢɜɟɪɫɢɬɟɬɚ 2007

ɍɬɜɟɪɠɞɟɧɨ ɧɚɭɱɧɨ-ɦɟɬɨɞɢɱɟɫɤɢɦ ɫɨɜɟɬɨɦ ɮɚɤɭɥɶɬɟɬɚ ɪɨɦɚɧɨ-ɝɟɪɦɚɧɫɤɨɣ ɮɢɥɨɥɨɝɢɢ 3 ɚɩɪɟɥɹ 2007 ɝ., ɩɪɨɬɨɤɨɥ ʋ 4

Ɋɟɰɟɧɡɟɧɬ ɞɨɰɟɧɬ ɤɚɮɟɞɪɵ ɚɧɝɥɢɣɫɤɨɝɨ ɹɡɵɤɚ ɮɚɤɭɥɶɬɟɬɚ ɢɧɨɫɬɪɚɧɧɵɯ ɹɡɵɤɨɜ ȼȽɉɍ, ɤɚɧɞ. ɮɢɥɨɥ. ɧɚɭɤ ȼ.ȼ. Ȼɟɡɪɭɤɨɜɚ

ɉɪɚɤɬɢɤɭɦ ɩɨɞɝɨɬɨɜɥɟɧ ɧɚ ɤɚɮɟɞɪɟ ɚɧɝɥɢɣɫɤɨɝɨ ɹɡɵɤɚ ɮɚɤɭɥɶɬɟɬɚ ɪɨɦɚɧɨɝɟɪɦɚɧɫɤɨɣ ɮɢɥɨɥɨɝɢɢ ȼɨɪɨɧɟɠɫɤɨɝɨ ɝɨɫɭɞɚɪɫɬɜɟɧɧɨɝɨ ɭɧɢɜɟɪɫɢɬɟɬɚ. Ɋɟɤɨɦɟɧɞɭɟɬɫɹ ɞɥɹ ɫɬɭɞɟɧɬɨɜ ɜɬɨɪɨɝɨ ɤɭɪɫɚ ɞ/ɨ ɮɢɡɢɱɟɫɤɨɝɨ ɮɚɤɭɥɶɬɟɬɚ.

Ⱦɥɹ ɫɩɟɰɢɚɥɶɧɨɫɬɟɣ: 010701 (010400) – Ɏɢɡɢɤɚ; 010801 (013800) – Ɋɚɞɢɨɮɢɡɢɤɚ ɢ ɷɥɟɤɬɪɨɧɢɤɚ; 010803 (014100) – Ɇɢɤɪɨɷɥɟɤɬɪɨɧɢɤɚ ɢ ɩɨɥɭɩɪɨɜɨɞɧɢɤɨɜɵɟ ɩɪɢɛɨɪɵ

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Unit 9 Geometric Optics. Physics Optics

Lead-in

1. a) Which of the following objects are seen as: a) a source of light; b) by light reflected from it? The Moon, the Sun, a table lit by a torch in a dark room, a stage lit by several powerful spotlights, a lightbulb, a flame, a star.

b) Why is the sense of light extremely important to us? (Because it provides us with …). c) What phenomena caused by wave effects (particularly sound and light waves) are you aware of?

2. Read the following summary and fill in the gaps with the given words. Then read the text to see if you were right: equal – ɪɚɜɧɹɬɶɫɹ; reflection – ɨɬɪɚɠɟɧɢɟ; deviation – ɨɬɤɥɨɧɟɧɢɟ; angle of incidence – ɭɝɨɥ ɩɚɞɟɧɢɹ; surface – ɩɨɜɟɪɯɧɨɫɬɶ; dispersion – ɪɚɫɫɟɢɜɚɧɢɟ; interference – ɢɧɬɟɪɮɟɪɟɧɰɢɹ; convex – ɜɵɩɭɤɥɵɣ; concave – ɜɨɝɧɭɬɵɣ; medium – ɫɪɟɞɚ. Light can be carried from place to place by particles or by waves. When light strikes the 1) … of an object, it deviates from its original direction. This change in direction is called 2) …When a narrow beam of light strikes a flat surface, we define the 3) … … … The law of reflection states that the angle of incidence 4) … the angle of reflection. Reflecting surfaces do not have to be flat. Spherical mirrors can be 5) … when the centre of the mirror bulges toward the viewer or 6) … when the centre of the mirror sinks away from the viewer. Refraction takes place when light passes from one 7) … into another. 8) … is caused by the fact 3

that different frequencies are refracted at slightly different angles. The 9) … of light from a straight line is referred to as diffraction. Changes in wave motion produced by phase and amplitude relations of two or more waves are called 10) …

Reading

3. For each question (A–J) choose the part of the text (1–10) which contains an answer. A. What phenomenon is responsible for a number of common optical illusions? B. What happens when two or more waves have their displacement in the same direction? C. What does the law of reflection state? D. What happens to light when it strikes the surface of an object? E. What occurs when waves pass through a narrow slit? F. What causes the visible colour spectrum? G. What assumption has led to the ray model of light? H. What surfaces produce parallel rays on reflection? I. What phenomenon is called total internal reflection? J. How is light reflected from spherical mirrors?

(1;…) Light can be carried from place to place in basically two ways: by particles or by waves. This fact explains why some problems are explained using geometric optics while others can not be solved without the theory of wave motion. A great deal of evidence suggests that light travels in straight lines under a wide variety of circumstances. In fact, we infer the positions of objects in our environment by assuming that light moves from the object to our eyes in straight-line paths. This reasonable assumption has led to the ray model of 4

light. This model assumes that light travels in straight-line paths called light rays. When we see an object, according to the ray model, light reaches our eyes from each point on the object; although light rays leave each point in many different directions, normally only a small bundle of these rays can enter an observer’s eye, as shown in Fig. 1. If the person’s head moves to one side, a different bundle of rays will enter the eye from each point.

Figure 1. (2;…) Light travels in a straight line until it strikes the surface of an object and deviates from its original direction. A change in direction by this method is called reflection. Only some of the light is reflected. The rest is either absorbed by the object (and transformed to thermal energy) or, if the object is transparent like glass or water, part of it is transmitted through. For a very shiny object such as a silvered mirror, over 95 % of the light may be reflected.

(3;…) When a narrow beam of light strikes a flat surface (Fig. 2), we define the angle of incidence, Q1, to be the angle an incident ray makes with the normal to the surface (“normal” means perpendicular) and the angle of reflection, Qr, to be the angle the reflected ray makes with the normal. For flat surfaces, it is found that the incident and reflected rays lie in the same plane with the normal

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to the surface. The law of

reflection states that the angle of incidence

equals the angle of reflection.

Figure 2. (4;…) The reflection from very smooth or mirror surfaces is called regular or specular reflection (speculum is Latin for mirror). In regular reflection incident parallel rays are parallel on reflection (Fig. 3a). When light is incident on a rough surface, even microscopically rough such as this page, it is reflected in many directions. This is called diffuse reflection. Because of diffuse reflection in all directions, an ordinary object can be seen from many different angles (Fig. 3b). On the other hand, when a narrow beam of light is shone on a mirror, the light will not reach your eyes unless it is placed at just the right place where the law of reflection is satisfied. Galileo, using similar arguments, showed that the Moon must have a rough surface rather than a highly polished surface like a mirror, as some people thought.

Figure 3ɚ.

Figure 3b. 6

(5;...) Reflecting surfaces do not have to be flat. The most common curved mirrors are spherical, which means they form a section of a sphere. A spherical mirror is called convex if the reflection takes place on the outer surface of the spherical shape so that the centre of the mirror surface bulges out toward the viewer (Fig. 4a). A mirror is called concave if the reflecting surface is on the inner surface of the sphere so that the centre of the mirror sinks away from the viewer (like a “cave”) (Fig. 4b). Concave mirrors are used as shaving or makeup mirrors, and convex mirrors are sometimes used on cars and trucks (rearview mirrors) and in shops (to watch for thieves), because they take in a wide field of view. A concave mirror is commonly called a converging mirror because light rays parallel to the principal axis converge and pass through the focal point. A convex mirror is commonly called a diverging mirror. Parallel rays along the principal axis are reflected so that they appear to diverge from the focal point.

Figure 4a.

Figure 4b.

(6;…) When light passes from one medium into another, part of the incident light is reflected at the boundary. The remainder passes into the new medium. If a ray of light is incident at an angle to the surface (other than perpendicular), the ray is bent as it enters the new medium. This bending is called refraction. Fig. 5a shows a ray passing from air into water. The angle Q1 is the angle of incidence and Q2 is the angle of refraction. Notice that the ray bends toward the normal when entering the water. This is always the case when the ray enters a medium where the speed of light is less. If light travels from one medium into a second 7

where the speed is greater, the ray bends away from the normal; this is shown in Fig. 5b for a ray traveling from water to air. Refraction is responsible for a number of com-mon optical illusions. For example, a pencil put in water appears to be bent.

Figure 5a.

Figure 5b.

(7;…) An interesting thing happens as the angle of incidence becomes larger. The refracted ray is bent farther from the normal and at a particular critical angle Qc the refracted ray is along the boundary of the two media. For angles greater than Qc, the light is reflected and none is refracted. The phenomenon is called total internal reflection (Fig. 6). Internal reflection enhances the brilliance of cut diamonds. A diamond cut so that most of the light entering the diamond is internally reflected. The light then emerges from only certain portions with a brilliance far exceeding that of incoming light. This effect creates the diamond’s sparkle.

Figure 6. 8

(8;…) Light can be considered as an electromagnetic wave. The wave theory has explained a wide range of phenomena one of which is dispersion. The angle of refraction of light depends somewhat on the light’s frequency or wavelength. The fact that different frequencies are refracted at slightly different angles is called dispersion. When white light (electromagnetic radiation containing all wavelengths visible to the human eye) passes through a glass prism, the light rays are refracted on entering the glass. The amount of refraction is a function of the wavelength with the shortest wavelengths being deviated from their path by the greatest amount. Violet light has a shorter wavelength than red light. A prism used in this fashion produces the visible color spectrum, and we say the white light has been dispersed. A diamond is said to have “fire” because of colorful dispersion, in addition to having brilliance due to internal reflection.

(9;…) All waves – sound, light and so on deviate from a straight-line path when they pass through a narrow slit. The effect also occurs when light from a fairly bright source passes the edge of an opaque object. The deviation of light waves is referred to as diffraction. We are well aware that sound waves bend around everyday objects while light waves do not. If we hold a newspaper in front of our face and speak, the sound of our voice can be heard, but our face can not be seen. The phenomenon of diffraction and the ratio of Ȝld help to explain why. We know that audible sound waves have wavelengths of centimeters to meters, while visible light waves have wavelengths of around 10–6 m. Ordinary objects have dimensions of centimeters to meters. Thus we get §O · §O· | 106  1 ; ¨ ¸ t 1. ¨ ¸ visible © d ¹light © d ¹ audible sound

From these statements we see that diffraction readily occurs for audible sound but not for visible light. 9

(10;…) Interference effects are defined as changes in wave motion produced by phase and amplitude relations of two or more waves. When two or more waves have their displacement at all times in the same direction, they reinforce one another. They are in phase for constructive interference. If their displacements are in opposite directions, they may cancel each other. Then destructive interference occurs.

Vocabulary practice

4. Look at the words in bold and try to explain them.

5. Find the words in the text that mean: 1) a kind of natural radiation that makes things visible (1–9); 2) the outer part of an object (2, 3, 4, 5, 6); 3) a completely flat surface (3); 4) not level or smooth (4); 5) a solid figure that is entirely round (i. e. with every point on the surface at an equal distance from the centre) (5); 6)a line that mark a limit; a dividing line (6); 7) a transparent precious stone of pure carbon in crystallized form, the hardest substance known (7); 8) a solid geometric figure with a flat base and parallel upright edges (8); 9) a long narrow cut or opening (9).

6. Replace the underlined parts with the equivalent words and phrases from the text. 1. Only some of the light is thrown back from the surface which it reaches.

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2. Rays reflected from relatively uneven surfaces don’t run side by side having the same distance between each other at every point. 3. Mirrors whose surface is curved outwards are used on cars and trucks and in shops (to watch for thieves). 4. Refraction is responsible for false visual perception in a number of common cases. 5. Waves move away from a straight-line path when they pass through a narrow opening.

7. Match the words to their opposites. 1) enter

ɚ) diverge

2) reflect

b) smooth

3) rough

c) wide

4) convex

d) concave

5) converge

e) leave

6) bulge out

f) weaken

7) enhance

g) absorb

8) visible

h) invisible

9) narrow

i) destructive

10) constructive

j) sink

8. Fill in the necessary antonyms from exercise 7. 1. a) Distant stars are … to the naked eyes. b) They cut the trees down to make the lake … from the house. 2. a) A … mirror has a curved surface like the outside of a ball. b) A mirror is … if its surface is curved inwards like the inner surface of a sphere. 3. Light rays are refracted on a) …ing the glass and refracted again on b) …ing the glass. 11

4. a) Good secretarial skills should … your chances of getting a job. b) These internal disputes may … the government’s position. 5. a) The gate isn’t … enough to get the car through. b) The road was too … for cars to pass. 6. a) Our views … so greatly that it is impossible to agree. b) Our previously opposed views are beginning to … 7. a) A … surface produces a diffuse reflection. b) A … surface produces a regular reflection. 8. a) If you drop the box onto the snow, it will … b) If you put too many things into your pockets, they will … 9. a) Dry sand … water. b) The mirror … my face. 10. a) He tends to find faults with everything and point out what is wrong. His criticism is always … b) She is very helpful. She always suggests improvements. Her proposals are …

9. Use the nouns surface, reflection mirror and the adjectives from the list to translate the word combinations. Flat, rough, highly, polished, reflecting, outer, inner, very smooth, regular, specular, diffuse, internal, curved, convex, concave. 1) ɡɟɪɤɚɥɶɧɨɟ ɨɬɪɚɠɟɧɢɟ; 2) ɲɟɪɨɯɨɜɚɬɚɹ ɩɨɜɟɪɯɧɨɫɬɶ; 3) ɜɧɭɬɪɟɧɧɹɹ ɩɨɜɟɪɯɧɨɫɬɶ; 4) ɜɨɝɧɭɬɨɟ ɡɟɪɤɚɥɨ; 5) ɩɥɨɫɤɚɹ ɩɨɜɟɪɯɧɨɫɬɶ; 6) ɜɵɩɭɤɥɨɟ ɡɟɪɤɚɥɨ; 7) ɪɚɫɫɟɹɧɧɨɟ ɨɬɪɚɠɟɧɢɟ; 8) ɨɱɟɧɶ ɝɥɚɞɤɚɹ (ɢɞɟɚɥɶɧɚɹ) ɩɨɜɟɪɯɧɨɫɬɶ; 12

9) ɡɟɪɤɚɥɨ ɫ ɢɫɤɪɢɜɥɟɧɧɨɣ ɩɨɜɟɪɯɧɨɫɬɶɸ; 10) ɩɨɜɟɪɯɧɨɫɬɶ ɫ ɜɵɫɨɤɨɣ ɫɬɟɩɟɧɶɸ ɩɨɥɢɪɨɜɤɢ; 11) ɩɪɚɜɢɥɶɧɨɟ ɨɬɪɚɠɟɧɢɟ (ɜ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɡɚɤɨɧɨɦ ɨɬɪɚɠɟɧɢɹ); 12) ɨɬɪɚɠɚɸɳɚɹ ɩɨɜɟɪɯɧɨɫɬɶ; 13) ɜɧɟɲɧɹɹ ɩɨɜɟɪɯɧɨɫɬɶ; 14) ɜɧɭɬɪɟɧɧɟɟ ɨɬɪɚɠɟɧɢɟ.

10. Fill in the appropriate word from the list below. Deviate (2), transparent (2), normal, incidence, interference, diffuse (a), diffuse (v), property, medium, boundary, exceed, disperse, slit, strike. 1. The cost of the damage … (ɩɪɟɜɡɨɲɥɚ) our worst fears. 2. Direct light is better for reading than … (ɪɚɫɫɟɹɧɧɵɣ) light. 3. The plane … (ɨɬɤɥɨɧɢɥɫɹ) from its usual route. 4. People say that lightning never … (ɭɞɚɪɹɟɬ) twice in the same place. 5. The ray bends towards the … (ɩɟɪɩɟɧɞɢɤɭɥɹɪ) when entering the water. 6. If the object is … (ɩɪɨɡɪɚɱɧɵɣ), part of the light is transmitted through. 7. Oil has the … (ɫɜɨɣɫɬɜɨ) of floating on water. 8. The angle of … (ɩɚɞɟɧɢɟ) equals the angle of reflection. 9. I will never … (ɨɬɫɬɭɩɚɬɶ) from what I believe to be right. 10. A fish in water is in its natural … (ɫɪɟɞɚ). 11. The meaning of this passage seems quite … (ɹɫɧɵɣ, ɩɨɧɹɬɧɵɣ). 12. Police used tear gas to … (ɪɚɡɝɨɧɹɬɶ) the crowd. 13. The river forms the … (ɝɪɚɧɢɰɚ) between the two countries. 14. We put letters through the … (ɳɟɥɶ, ɨɬɜɟɪɫɬɢɟ) of the letter-box. 15. Clouds … (ɪɚɫɫɟɢɜɚɬɶ) light from the sun. 16. We apologize for the … (ɩɨɦɟɯɢ), which is due to bad weather conditions.

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11. Complete the sentences with one of the derivatives. A. Direct (ɧɚɩɪɚɜɥɹɬɶ, ɧɚɰɟɥɢɜɚɬɶ), direct (ɩɪɹɦɨɣ, ɧɟɩɨɫɪɟɞɫɬɜɟɧɧɵɣ), indirect (ɧɟɩɪɹɦɨɣ, ɨɤɨɥɶɧɵɣ), directly (ɩɪɹɦɨ, ɧɟɩɨɫɪɟɞɫɬɜɟɧɧɨ), indirectly (ɤɨɫɜɟɧɧɨ), direction (ɧɚɩɪɚɜɥɟɧɢɟ). 1. Light strikes the surface and deviates from its original … 2. We can’t blame him for what happened. He could be only …responsible for it. 3. We should … our efforts towards greater efficiency. 4. They were both going in the same … 5. We live … opposite the church. 6. Which is the most … route to London? 7. When he got up I understood that it was an … way of telling me to leave. 8. She has a good sense of … and never gets lost. 9. Please, … your complains to the manager. B. Assume (ɞɨɩɭɫɤɚɬɶ, ɩɪɟɞɩɨɥɚɝɚɬɶ), assumption (ɩɪɟɞɩɨɥɨɠɟɧɢɟ, ɞɨɩɭɳɟɧɢɟ), assumed (ɜɵɦɵɲɥɟɧɧɵɣ), assuming (ɩɪɟɞɩɨɥɨɠɢɜ). 1. Don’t rely on the information she gave you – it’s pure … 2. We must … him to be innocent until he is proved guilty. 3. … that you are right about this, what shall we do? 4. Now he is living under an … name. 5. This theory is base on a series of wrong …

12. Translate into English using the following words for the underlined parts: 1) it is ……, that allows us; 2) what you see in general is; 3) one or more sources; 4) in a lighted room; 5) windowpane; 6) serves; 7) yet; 8) transmitted; 9) masks. 1) ɂɦɟɧɧɨ ɨɬɪɚɠɟɧɢɟ ɫɜɟɬɚ ɩɨɡɜɨɥɹɟɬ ɧɚɦ ɜɢɞɟɬɶ ɜɟɳɢ. ɉɨɫɦɨɬɪɢɬɟ ɜɨɤɪɭɝ. 2) Ɍɨ, ɱɬɨ ɜɵ, ɜ ɨɫɧɨɜɧɨɦ, ɜɢɞɢɬɟ, ɷɬɨ ɫɜɟɬ, ɨɬɪɚɠɟɧɧɵɣ ɨɬ ɫɬɟɧ, 14

ɩɨɬɨɥɤɚ, ɩɨɥɚ ɢ ɞɪɭɝɢɯ ɩɪɟɞɦɟɬɨɜ. Ʉɨɧɟɱɧɨ, ɞɨɥɠɧɵ ɢɦɟɬɶɫɹ 3) ɨɞɢɧ ɢɥɢ ɛɨɥɟɟ ɢɫɬɨɱɧɢɤɨɜ ɫɜɟɬɚ. ɗɬɢɦɢ ɢɫɬɨɱɧɢɤɚɦɢ ɨɛɵɱɧɨ ɹɜɥɹɸɬɫɹ ɥɚɦɩɵ ɢɥɢ ɫɨɥɧɰɟ. ȿɫɥɢ ɜɵ ɧɚɯɨɞɢɬɟɫɶ ɜ ɬɟɦɧɨɣ ɤɨɦɧɚɬɟ, ɬɨ ɬɨɝɞɚ ɨɬɪɚɠɟɧɧɨɝɨ ɫɜɟɬɚ ɧɟɬ ɢ ɤɨɦɧɚɬɚ ɱɟɪɧɚɹ. ɇɨɱɶɸ 4) ɜ ɨɫɜɟɳɟɧɧɨɣ ɤɨɦɧɚɬɟ ɩɪɨɡɪɚɱɧɨɟ 5) ɨɤɨɧɧɨɟ ɫɬɟɤɥɨ ɞɨɜɨɥɶɧɨ ɯɨɪɨɲɨ 6) ɫɥɭɠɢɬ ɡɟɪɤɚɥɨɦ. 7) Ɍɟɦ ɧɟ ɦɟɧɟɟ, ɞɧɟɦ ɦɵ ɜɢɞɢɦ ɱɟɪɟɡ ɧɟɝɨ ɩɨɬɨɦɭ, ɱɬɨ 8) ɢɞɭɳɢɣ ɞɧɟɜɧɨɣ ɫɜɟɬ 9) ɫɤɪɵɜɚɟɬ ɨɬɪɚɠɟɧɧɵɣ ɫɜɟɬ. Ɇɵ ɱɚɫɬɨ ɜɢɞɢɦ ɤɪɚɫɢɜɵɟ ɨɬɪɚɠɟɧɢɹ ɜ ɩɪɢɪɨɞɟ.

13. Read the text again and do the following. 1. State the law of reflection and distinguish between regular and diffuse reflections. 2. Explain the principles of refraction and total internal reflection. 3. Explain how light is reflected from spherical mirrors. 4. Explain what is meant by dispersion of light and explain why it occurs. 5. Discuss the difference between sound waves and visible light waves.

Follow-up activities

14. Your friend, a girl 1.60 m tall wants to buy a mirror but she doesn’t know how tall it must be and how high its lower edge must be above the floor so as to be able to see her whole reflection. Assume her eyes are 10 cm below the top of her head. Explain to her how to find it out. Then use the words from the list to fill in the gaps in the given answer. Height, reflection, bottom, edge, to reach, ray, half, equals, to extend.

I’ve decided to diagram the situation for you to understand it better. First, consider the a) … from your foot, AB. Upon b) … it becomes BE and enters your eye E. The light from your foot (point A) enters your eye after reflecting at B; so the mirror needs c) … no lower than B. Because the angle of reflection 15

d) … the angle of incidence, the height BD is half of the height AE. Because AE = 1,60 m – 0,10 m = 1,50 m, then BD = 0,75 m. If you want to see the top of your head, the top e) … of the mirror only needs f) … point F, which is 5 cm below the top of your head (half of GE = 10 cm). Thus, DF = 1,55 m, and the mirror needs to have a vertical g) … of only (1,55 – 0,75 m) = 0,80 m. And the mirror’s h) … edge must be 0,75 m above the floor. In general, a mirror needs to be only i) … as tall as a person to see all of himself or herself and it does not depend upon the person’s distance from the mirror.

Figure 7.

15. Make the statements complete by matching the optical instruments (1–8) with their descriptions below (A–H). 1. The spectroscope …

5. The refracting telescope ….

2. Polarizing sunglasses …

6. The reflecting telescope ….

3. The magnifying glass …

7. The Hubble space telescope is a reflecting

4. The telescope …

telescope that … 8. The spectrometer ….

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A. … contains two converging lenses located at opposite ends of a long tube. The lens closest to the object is called the objective lens and forms a real image of the distant object. Although this image is smaller than the original object, it subtends a greater angle and is very close to the second lens, called the eyepiece, which acts as a magnifier.

B. … is used to produce magnified images of objects. The angle that an object subtends at the eye appears larger when it is used and more detail can be seen.

C. … is an instrument that separates a source of light into its respective frequencies or wavelengths.

D. … has been placed in orbit above the Earth’s atmosphere, so its resolution is not limited by turbulence in the atmosphere. Its objective diameter is 2,4 m.

E. … allow only the vertical component of the light to pass, and the horizontal component is blocked out, which reduces the glare.

F. … uses a concave mirror as the objective, since a mirror has only one surface to be ground (the construction and grinding of large lenses is very difficult). Normally, the eyepiece lens or mirror is removed so that the real image formed by the objective mirror can be recorded directly on film.

G. … is used to magnify objects that are very far away. In most cases, the object may be considered to be an infinity.

H. … is a device using a diffraction grating or a prism to separate different wavelengths and equipped with a scale for measuring them.

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16. Answer the following questions. Then check your answers by matching the numbers (1–3) with the letters (A, B, C). 1. Why does a person standing in waist-deep water appear to have shortened legs?

Figure 8. 2. How would a person looking up at the world from beneath the perfectly smooth surface of a lake of a swimming pool see the outside world?

Figure 9.

Figure 10.

3. What causes the colours when light is reflected from a thin film of oil on water? 18

Figure 11.

4. Why can motorists sometimes see on a hot day a mirage of water on the highway ahead of them, with distant vehicles seemingly reflected in it?

Figure 12.

A. The person would see the outside world compressed into a circle whose edge makes a 49° angle with the vertical sin Qc = 1,00 = 0,750 Therefore, Qc = 49°. Beyond this angle, the person would see reflections from the sides and bottom of the pool or lake.

B. When the reflected rays from the bottom and top surfaces of the oil film are in phase, constructive interference occurs and an observer sees only one colour of light for a certain angle and film thickness. If the reflected waves are out of 19

phase, destructive interference occurs, which means the light is transmitted at the bottom of the film surface rather than reflected. Because the film thickness varies, a colourful display is seen for the different wavelengths of light.

C. On a hot day, there can be a layer of very hot air next to the roadway (made hot by the Sun beating on the road). Hot air is less dense than cooler air, so the index of refraction is slightly lower in the hot air. In the picture we see a diagram of light coming from one point on a distant car (on the right) heading left toward the observer. Wave fronts and two rays are shown. Ray A heads directly at the observer and follows a straight-line path representing the normal view of the car. Ray B is a ray initially directed slightly downward. But it does not hit the ground. Instead, ray B is bent slightly as it moves through layers of air of different index of refraction. The wave fronts move slightly faster in the layers of air nearer the ground. Thus ray B is bent as shown and seems to the observer to be coming from below (dashed line) as if reflected off the road. Hence the mirage.

D. Because the path of light traveling from the bather’s foot to the observer’s eye bends at the water’s surface, and our brain interprets the light as having traveled in a straight line, from higher up (dashed line).

17. a) What work was Albert Einstein awarded a Nobel Prise for in 1921: 1. the development of a mathematical theory of Brownian motion, 2. his paper on ‘Special Theory of Relativity’, 3. the paper in which he explained the photoelectric effect by means of Planck’s quantum theory?

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b) Read the text quickly and match the words in bold with their Russian equivalents: 1) ɪɚɡɞɟɥɶɧɵɣ, ɫɨɫɬɨɹɳɢɣ ɢɡ ɪɚɡɪɨɡɧɟɧɧɵɯ ɱɚɫɬɟɣ;

6) ɨɛɨɫɧɨɜɚɧɧɵɣ;

2) ɦɝɧɨɜɟɧɧɨ;

7) ɩɪɟɜɪɚɳɟɧɢɟ, ɩɟɪɟɯɨɞ;

3) ɧɟɫɨɨɬɜɟɬɫɬɜɢɟ;

8) ɧɢɬɶ ɧɚɤɚɥɚ;

4) ɪɚɫɤɚɥɟɧɧɵɣ;

9) ɡɚɞɟɪɠɤɚ, ɨɬɫɪɨɱɤɚ;

5) ɡɧɚɱɢɬɟɥɶɧɵɣ, ɡɚɦɟɬɧɵɣ;

10) ɡɚɩɭɬɚɧɧɵɣ, ɧɟɹɫɧɵɣ.

c) Read the text carefully and do the following: 1) state Planck’s hypothesis, and explain why it was so radical; 2) explain what is meant by the dual nature of light; 3) describe the photoelectric effect and explain the quantum theory that describes it.

In the latter part of the nineteenth century light was shown to be an electromagnetic wave. However, the theory had some rough edges because of the discrepancies which were observed when the temperature of an incandescent solid such as the filament of a light bulb was increased and a hot solid went from a dull red to a bluish white. According to classical wave theory, the intensity of the emitted radiation was expected to be much greater than was actually observed. Actually it had to be proportional to the square of the frequency. This discrepancy was termed the ultraviolet catastrophe: “ultraviolet” because the difficulty occurred at high frequencies beyond the violet end of the visible spectrum, and “catastrophe” because the energy observed was much less than it was predicted. The dilemma was resolved in 1900 by German physicist Max Planck. Classically, an electron oscillator may vibrate with any frequency or have energy up to some maximum value. But Planck’s hypothesis states that the energy was quantized or that oscillators could have only discrete or certain

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amounts of energy. Thus Planck introduced the idea of a quantum, a discrete amount of energy. In 1905 Albert Einstein used Planck’s hypothesis to describe light in terms of particles rather than waves. He did so to describe the photoelectric effect. In this phenomenon, as scientists had observed before the turn of the nineteenth century, electrons are emitted when certain metallic materials are exposed to light. This direct conversion of light into electrical energy now forms the basis of photocells used in photographic light meters and solar energy applications. As we know, current flows from photocells almost immediately on being exposed to light. But according to classical theory, where light is a wave with a continuous flow of energy, it would take an appreciable time for an electron to be emitted. A wave supplies a flow of energy somewhat analogous to a stream of water. A stream of water would take a longer time to fill a bucket than dumping

water

from

another

bucket

which

fills

the

other

almost

instantaneously. A quantum also supplies energy in a packet or bundle, analogous to a bucket of water.

Wave nature

Quantum nature

Figure 13. By considering light to be composed of photons or quanta of energy, Einstein was able to successfully explain the photoelectric effect. The classical time delay to get enough energy to free an electron is not a problem with quanta of energy. The quanta or packets of energy provide a given amount of energy all at once. 22

Einstein’s photoelectric theory satisfied the scientific method by being experimentally valid. We have a confused situation. Is light a wave or a particle? The answer to this could be in the term “the dual nature of light”, which simply means that light acts sometimes like a wave and sometimes like a particle. Grammar in use The infinitive and the -ing forms 18. Use the verbs in brackets to supply the appropriate forms of the infinitive (the to-infinitive or the bare infinitive). 1. Refraction makes a pencil put in water … bent (look). 2. Gas explosions caused the carbon … fire (catch). 3. A telescope is used … objects that are very far away (magnify). 4. Large radioactive doses can … mutation in genes (cause). 5. Radioactive isotopes allow researchers … the flow of blood in biological organisms (monitor). 6. A tornado warning made people … shelter (seek). 7. We were made … indoor shoes inside the school building (wear). 8. You’d better … what you think (say). 9. I’d rather … for a walk in the rain than … nothing at all (go, do). 10. Let’s … the speed of light in diamond (calculate). 11. I felt the house … with the explosion (shake). 12. I heard the door … and saw a shadow … across the floor (open, move). 19. Rewrite the sentences using a to-infinitive instead of that. 1. People know that she is a very generous woman. People know her to be a very generous woman. 2. I hope that I will succeed. I hope to succeed. 3. I believe that they are guilty. 4. I found that he was very lazy. 23

5. She pretended that she didn’t recognize him. 6. He expects that they will come to the party. 7. He clams that he was abroad at the time of the robbery. 8. He expects that he will inherit a large house when his grandfather dies. 9. We discovered that the agreement was false. 10. I agreed that I would come. 20. Choose the prompts from the list to answer the following questions: a) to settle my financial problems; b) to smoke; c) not to let it discourage; d) to work harder; e) not to put a knife in your mouth; f) to make fun of you; g) to put a napkin on the lap and not to use it as a tie; h) to cross the street at a red light; i) to talk to each other during exams. 1. What do some parents force their children to do? They force them to work harder. 2. What do you hate other people to do? I hate them … 3. What don’t you trust dishonest people to do? I don’t trust them … 4. What do traffic rules forbid you to do? They forbid us … 5. What can you advise your friend to do after he has failed his exam? I can advise him … 6. What don’t your teachers allow you to do? They don’t allow us … 7. What does the notice on the entrance forbid people to do? It forbids them … 8. What do rules of etiquette warn you not to do when you are at table? They warn us … 9. What do rules of etiquette recommend you to do when you are at table? They recommend us … 24

21. Rewrite the sentences using too. 1. It is very cold. You can’t swim. It is too cold (for you) to swim. 2. The soup is very salty. I can’t eat it. 3. The tea is very hot. I can’t drink it. 4. He was furious. He couldn’t speak. 5. The shoes are very small. I can’t wear them. 6. I’m very busy. I can’t make dinner tonight. 7. I was terrified. I couldn’t move. 8. She is very short. She can’t be in the basketball team. 9. He is lazy. He won’t get up early. 10. He was very drunk. He couldn’t answer my questions.

22. Rewrite the sentences using enough. 1. The room is spacious. We can have a party. The room is spacious enough to have a party. 2. The ladder isn’t very long. It can’t reach the window. The ladder isn’t long enough to reach the window. 3. The coffee isn’t strong. It can’t keep us awake. 4. He is clever. He can solve the problem. 5. He is rich. He can buy a mansion. 6. You aren’t very old. You can’t understand these things. 7. He was foolish. He told lies to the police. 8. She isn’t patient. She can’t look after the children. 9. She is old. She can make her own decisions. 10. He isn’t strong. He can’t carry the bag. 11. The dog is big. It could harm you.

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23. Look at the table and name the form of the gerund in the sentences. Translate the sentences. Active

Passive

Simple

reading

being read

Perfect

having read

having been read

1. They are blamed for refusing to cooperate. 2. He turned quickly away embarrassed at having been noticed. 3. He didn’t want to admit having stolen the car. 4. The child is in danger of being spoilt. 5. Wearing glasses seemed to increase her shyness. 6. Would you have any objections to our examining your package? 7. He didn’t want to admit his having been deported. 8. People can’t stand not being forgiven. 9. I regret having prevented her doing what she wanted.

24. Put the verbs in brackets into the correct infinitive form or the -ing form. 1. He refused … the bribe (accept). 2. You can’t help … him (like). 3. He was fined for … without help (drive). 4. He pretended … ill (be). 5. Imagine … with someone who never stops … (live, talk). 6. He tried … but she refused … (explain, listen). 7. Would you mind … the window (open)? 8. I hope he will give up … (smoke). 9. There is not much point in … that old car (repair). 10. She denies … my money (take). 11. I expect … her soon (see). 12. It’s no use … over spilt milk (cry). 26

13. People used … fire by rubbing two sticks together (make). 14. He suggested … research into the effects of pollution on fish breeding (do). 15. He threatened … the children when they disobeyed him (punish). 16. They continued … over this point for two hours (argue).

25. Consider which verb form is more likely and why. 1. I saw him cut/cutting his finger. 2. I heard the baby cry/crying for most of the night. 3. I saw the plane crash/crashing into the hill and burst/bursting into flames. 4. I felt the bee bite/biting me. 5. As we passed his house we heard him practice/practicing the violin. 6. I noticed her quickly slip/slipping something into her pocket and leave the shop. 7. When I came out of the café I noticed some children play/playing football across the street.

26. Put the verbs in brackets into the correct infinitive form or the -ing form. 1) a. She answered the doorbell and went on … the meat (cook). b. Please go on … I don’t want to interrupt you (write). 2) a. He got annoyed because his wife stopped … in every shop window (look). b. Just stop … and listen for a moment (talk). 3) a. I like … to the dentist every six months (go). b. She likes … stamps. It’s her hobby (collect). 4) a. The two sides will probably try … an agreement during the talks (reach). b. You should try … more fruit. It’s good for your health (eat). 5) a. I meant … you a postcard but I forgot to take my address book (send). b. She is determined to lose weight even if it means … sweet things (give up). 6) a. I distinctly remember … the front door in the morning (lock). b. I must remember … him the medicine after dinner (give). 27

7) a. I’ll never forget … my favorite film star (meet). b. I forgot … some bread for dinner on my way home (buy).

Revision Exercises

27. Choose the correct answer. 1. ‘Sorry I’m late. … very long?’ ‘No, only five minutes.’ a) Are you waiting;

b) Do you wait;

c) Have you been waiting.

2. ‘Pete is playing music very loud!’ ‘Again! He … that.’ a) always does;

b) always did;

c) is always doing.

3. ‘The restaurant was packed last night.’ ‘Yes, luckily I … a table in advance.’ a) had booked;

b) booked;

c) had been booking.

4. ‘You look exhausted.’ ‘Yes, I …’ a) was shopping;

b) have been shopping;

c) had been shopping.

5. I … a party tonight. Do you want to come? a) have;

b) will have;

c) am having.

b) will the play start;

c) is the play starting.

6. What time … tonight? a) does the play start;

7. The new house … at the moment. a) is decorated;

b) has been decorated;

28. Correct the mistakes. 1. I forgot posting your letter yesterday. 2. Ann’s mother made her to tidy her room. 3. I saw her to talk to the manager. 28

c) is being decorated.

4. I can’t afford going on holiday this year. 5. Tom suggested to drive to the seaside. 6. You shouldn’t to get angry with him. It’s not his fault. 7. This book is too expensive for me to buy it. 8. She is enough old to drive a car. 9. I’d like going for a walk tonight. 10. It’s no use to ask Paul. He won’t be able to help you.

29. Express the ideas using the right form of the infinitive. 1. He can’t find the key. It seems he has lost it. He seems to have lost it. 2. I was disappointed that I had missed the party. I was disappointed … 3. It is expected that she will break the world record. She is expected … 4. It seems that they are arguing. They seem … 5. The table is scratched. I think it was scratched when it was being moved. The table must … 6. It is said that he has been waiting for the opportunity in ages. He is said … 7. It’s a pity that you have been working without a break for such a long time. You shouldn’t …

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Unit 10 Special Theory of Relativity Lead-in 1. Look at the list of theories and say which of them were the product of classical physics (physics as it was known at the end of the nineteenth century) and which ones can be referred to modern physics (the new physics that grew out of the great revolution at the turn of the twentieth century): a) Newtonian mechanics; b) The theory of relativity; c) Kinetic theory; d) Maxwell’s theory of electromagnetism; e) Quantum theory.

2. What is the significance of the revolutionary theories of the twentieth century?

3. Read the following summary and fill in the gaps with the given words. Then read the text to see if you were right. Independently of – ɧɟɡɚɜɢɫɢɦɨ ɨɬ; resolved (resolve – ɪɟɲɚɬɶ); inertial reference frames – ɢɧɟɪɰɢɚɥɶɧɵɟ ɫɢɫɬɟɦɵ ɨɬɱɟɬɚ; quantities – ɜɟɥɢɱɢɧɵ; extension – ɪɚɫɲɢɪɟɧɢɟ, ɩɪɨɞɨɥɠɟɧɢɟ; though – ɧɟɫɦɨɬɪɹ ɧɚ ɬɨ, ɱɬɨ; speed – ɫɤɨɪɨɫɬɶ; constancy – ɩɨɫɬɨɹɧɫɬɜɨ, ɧɟɢɡɦɟɧɧɨɫɬɶ; accurate – ɬɨɱɧɵɣ, ɩɪɚɜɢɥɶɧɵɣ; aware – ɡɧɚɸɳɢɣ, ɨɫɜɟɞɨɦɥɟɧɧɵɣ; consequences – ɩɨɫɥɟɞɫɬɜɢɹ, ɡɧɚɱɟɧɢɟ, ɜɚɠɧɨɫɬɶ; arose (arise – ɜɨɡɧɢɤɚɬɶ, ɩɨɹɜɥɹɬɶɫɹ). Einstein’s special theory of relativity analyzes events when they are observed and measured from 1) … We can consider Earth an inertial frame 30

2) … it rotates. Both Galileo and Newton were 3) … of the relativity principle which states that the laws of physics are the same in all inertial frames. At the turn of the century there 4) … some problems with regard to electronic theory and Newtonian mechanics. Nineteenth century physicists assumed that light would have a different 5) … in different frames of reference. The problems were 6) … by Einstein’s introduction of the theory of relativity. Its first postulate is an 7) … of the Newtonian relativity. It states that the laws of physics have the same form in all inertial reference frames. The second postulate refers to the 8) … of the speed of light 9) … the speed of the source or observer. Some important 10) … of the theory of relativity are that it has changed the way we view the world. It gives more 11) … results, especially at very high speeds. We can no longer regard time and space as absolute 12) … even our concepts of matter and energy have changed.

Reading

4. Choose the most suitable heading from the list A – G for each part (1–6) of the text. There is one extra heading which you do not need to use. A. Resolution of the complications with regard to electromagnetic theory. B. Relativistic additions of velocities. C. Description of mechanical phenomena in inertial reference frames. D. New properties of the basic mechanical quantities discovered by relativity. E. The impact of special relativity. F. Presentation of the theory which did not seem to obey the relativity principle. G. Observation and measurement of events from inertial and noninertial frames.

(1;…) Einstein’s special theory of relativity deals with events that are observed and measured from so-called inertial reference frames. A reference frame is a 31

set of coordinate axes fixed to some body such as the Earth, a train, the Moon and so on. When we say that we observe or make measurements from a certain reference frame, it means that we are at rest in that reference frame. It is easiest to analyze events when they are observed and measured from inertial frames. The Earth, though not quite an inertial frame (it rotates), is close enough and for most purposes we can consider it an inertial frame. Rotating or otherwise accelerating frames of reference are noninertial frames. On a rotating platform (say a merry-go-round), for example, an object at rest starts moving outward even though no body exerts a force on it. This is therefore not an inertial frame. Einstein dealt with such complicated frames of reference in his general theory of relativity.

(2;…) Both Galileo and Newton were aware of what we now call the relativity principle applied to mechanics: that the basic laws of physics are the same in all internal frames. You may have recognized its validity in everyday life. For example, objects move in the same way in a smoothly moving (constant velocity) train or airplane as they do on Earth. (This assumes no vibrations or rocking – for they would make the reference frame noninertial.) When you walk, drink a cup of soup, play Ping-Pong, or drop a pencil on the floor while traveling in a train, airplane, or ship moving at constant velocity, the bodies move just as they do when you are at rest on Earth. Galilean-Newtonian relativity involves certain unprovable assumptions that make sense from everyday experience. It is assumed that the lengths of objects are the same in one reference frame as in another, and that time passes at the same rate in different reference frame. In classical mechanics, then, space and time are considered to be absolute: their measurement doesn’t change from one reference frame to another. The mass of an object, as well as all forces, are assumed to be unchanged by a change in inertial reference frame. That the laws of mechanics 32

are the same in all reference frames implies that all inertial reference frames are equivalent for the description of mechanical phenomena.

(3;…) In the last half of the nineteenth century there arose a complication. When Maxwell presented his comprehensive and very successful theory of electromagnetism, he showed that light can be considered an electromagnetic wave. Maxwell’s equations predicted that the velocity of light c would be 3 · 108 m/s. The question then arose: in what reference frame does light have precisely the value predicted by Maxwell’s theory? It was assumed that light would have a different speed in different frames of reference. For example, if observers were traveling on a rocket ship at a speed of 1 · 108 m/s away from a source of light, we might expect them to measure the speed of light reaching them to be 3 · 108 m/s – 1 · 108 m/s = 2 · 108 m/s. Nineteenth-century physicists viewed the material world in terms of the laws of mechanics, so it was natural for them to assume that light too must travel in some medium. They called this transparent medium the ether and assumed it permeated all space. It was therefore assumed that the velocity of light given by Maxwell’s equation must be with respect to the ether. However, it appeared that Maxwell’s equations did not satisfy the relativity principle. They were not the same in all inertial frames. They were simplest in a reference frames at rest in the ether. Thus, although most of the laws of physics obeyed the relativity principle, the laws of electricity and magnetism apparently did not. Instead, they seemed to single out one reference frame that was better than any other – a reference frame that could be considered absolutely at rest.

(4;…) The problems that existed at the turn of the century with regard to electromagnetic theory and Newtonian mechanics were beautifully resolved by 33

Einstein’s introduction of the theory of relativity in 1905. Einstein concluded that the inconsistencies he found in electromagnetic theory were due to the assumption that an absolute space exists. In his famous 1905 paper he proposed doing away completely with the idea of ether and the accompanying assumption of an absolute reference frame at rest. This proposal was embodied in two postulates. The first postulate was an extension of the Newtonian relativity principle to include not only the laws of mechanics but also those of the rest of physics, including electricity and magnetism. First postulate (the relativity principle): The laws of physics have the same form in all inertial reference frames. The second postulate is consistent with the first. Second postulate (constancy of the speed of light): Light propagates through empty space with a definite speed c independent of the speed or the source of observer. These two postulates form the foundation of Einstein’s special theory of relativity.

(5;…) One of the important consequences of the theory of relativity is that we can no longer regard time as an absolute quantity. No one doubts that time flows onward and never turns back. But the time interval between two events, even if two events are simultaneous, depends on the observer’s reference frame. If the two events occur at widely separated places, it is more difficult to know whether the events are simultaneous since we have to take into account the time it takes for the light from them to reach us. In other words events which are simultaneous to one observer are not necessarily simultaneous to a second observer. This fact suggests that time itself is not absolute. Einstein’s theory of relativity predicts that it may pass differently in one reference frame than in another. A general result of the theory is known as time dilation. The time 34

dilation effect states that clocks moving relative to an observer are measured by that observer to run more slowly (as compared to clocks at rest). Not only time intervals are different in different reference frames. Space intervals – lengths and distances – are different as well: the length of an object is measured to be shorter when it is moving relative to the observer than when it is at rest. Not only length and time intervals have shown to be relative. Mass, another basic mechanical quantity, is measured to increase as its speed increases. Another basic result of the special relativity is that the speed of an object cannot equal or exceed the speed of light. It is perhaps easiest to see it from the mass-increase formula, m = m0 / ¥1 – v2 / c2. As an object is accelerated to greater and greater speeds, its mass becomes larger and larger. Indeed, if v were to equal c, the denominator in this equation would be zero and the mass m would become infinite. To accelerate an object up to v = c would thus require infinite energy, and so is not possible. The fact that a steady net force applied to an object contributes to increasing its speed, mass and energy has led to a crucial part of Einstein’s theory, to the idea that mass is a form of energy. The relation E = mc2 (energy equals mass times the square of the speed of light) is now believed to apply to all processes, although the changes are often too small to measure.

(6;…) A great many experiments have been performed to test the predictions of the special theory of relativity. Within experimental error, no contradictions have been found. Scientists have therefore accepted relativity as an accurate description of nature. At speeds much less than the speed of light (v