The Correspondence Principle

The only reason we don't usually notice diffraction of light in everyday life is that we don't normally deal with objects that are comparable in size to a wavelength of visible light, which is about a millionth of a meter. Does this mean that wave optics contradicts ray optics, or that wave optics sometimes gives wrong results? No. If you hold three fingers out in the sunlight and cast a shadow with them, either wave optics or ray optics can be used to predict the straightforward result: a shadow pattern with two bright lines where the light has gone through the gaps between your fingers. Wave optics is a more general theory than ray optics, so in any case where ray optics is valid, the two theories will agree. This is an example of a general idea enunciated by the physicist Niels Bohr, called the correspondence principle: when flaws in a physical theory lead to the creation of a new and more general theory, the new theory must still agree with the old theory within its more restricted area of applicability. After all, a theory is only created as a way of describing experimental observations. If the original theory had not worked in any cases at all, it would never have become accepted.

In the case of optics, the correspondence principle tells us that when λ /d is small, both the ray and the wave model of light must give approximately the same result. Suppose you spread your fingers and cast a shadow with them using a coherent light source. The quantity λ /d is about 10 - 4, so the two models will agree very closely. (To be specific, the shadows of your fingers will be outlined by a series of light and dark fringes, but the angle subtended by a fringe will be on the order of 10^-4 radians, so they will be invisible and washed out by the natural fuzziness of the edges of sun-shadows caused by the finite size of the sun.)

Task2 Rearrange the paragraphs below in a logical way:

Huygens’ Principle

1) Thomas Young (1773-1829) was the person who finally, a hundred years later, did a careful search for wave interference effects with light and analyzed the results correctly. He observed double-slit diffraction of light as well as a variety of other diffraction effects, all of which showed that light exhibited wave interference effects, and that the wavelengths of visible light waves were extremely short. The crowning achievement was the demonstration by the experimentalist Heinrich Hertz and the theorist James Clerk Maxwell that light was an electromagnetic wave. Maxwell is said to have related his discovery to his wife one starry evening and told her that she was the only person in the world who knew what starlight was.	2) The history is interesting. Isaac Newton loved the atomic theory of matter so much that he searched enthusiastically for evidence that light was also made of tiny particles. The paths of his light particles would correspond to rays in our description; the only significant difference between a ray model and a particle model of light would occur if one could isolate individual particles and show that light had “graininess” to it. Newton never did this, so although he thought of his model as a particle model, it is more accurate to say he was one of the builders of the ray model.
3) Almost all that was known about reflection and refraction of light could be interpreted equally well in terms of a particle model or a wave model, but Newton had one reason for strongly opposing Huygens' wave theory. Newton knew that waves exhibited diffraction, but diffraction of light is difficult to observe, so Newton believed that light did not exhibit diffraction, and therefore must not be a wave. Although Newton's criticisms were fair enough, the debate also took on the overtones of a nationalistic dispute between England and continental Europe, fueled by English resentment over Leibniz's supposed plagiarism of Newton's calculus. Newton wrote a book on optics, and his prestige and political prominence tended to discourage questioning of his model.	4) Returning to the example of double-slit diffraction, f, note the strong visual impression of two overlapping sets of concentric semicircles. This is an example of Huygens' principle, named after a Dutch physicist and astronomer. (The first syllable rhymes with “boy.”) Huygens' principle states that any wavefront can be broken down into many small side-by-side wave peaks, g, which then spread out as circular ripples, h, and by the principle of superposition, the result of adding up these sets of ripples must give the same result as allowing the wave to propagate forward, i. In the case of sound or light waves, which propagate in three dimensions, the “ripples" are actually spherical rather than circular, but we can often imagine things in two dimensions for simplicity.
5) Since Huygens' principle is equivalent to the principle of superposition, and superposition is a property of waves, what Huygens had created was essentially the first wave theory of light. However, he imagined light as a series of pulses, like hand claps, rather than as a sinusoidal wave.	6) In double-slit diffraction the application of Huygens' principle is visually convincing: it is as though all the sets of ripples have been blocked except for two. It is a rather surprising mathematical fact, however, that Huygens' principle gives the right result in the case of an unobstructed linear wave, h and i. A theoretically infinite number of circular wave patterns somehow conspire to add together and produce the simple linear wave motion with which we are familiar.

(from Optics by Benjamin Crowell, Fullerton, California, ed. 2.2, 2007, ISBN 0-9704670-5-2)

Task 3 Match the words and expressions (underlined in the text) with their definitions:

1) a theorist	a) the material that everything in the universe is made of, including solids, liquids, and gases
2) to relate to	b) the part of mathematics that deals with changing quantities, such as the speed of a falling stone or the slope of a curved line
3) made of	c) a shape or pattern that looks like a wave
4) (the atomic theory of) matter	d) if two or more things do this, part of one thing covers part of another thing:
5) tiny	e) produced, for example by putting the different parts together
6) in terms of	f) half a circle
7) to exhibit (diffraction)	g) to secretly plan with someone else to do something illegal
8) calculus	h) to show how two different things are connected
9) to question smth	i) to separate something into smaller parts so that it is easier to do or understand
10) to overlap	j) used to say that lots of small amounts gradually make a large total
11) a (concentric) semicircle	k) to have or express doubts about whether something is true, good, necessary etc
12) to break smth down into	l) a quality or power that a substance, plant etc has [= quality, characteristic]
13) ripples	m) someone who develops ideas within a particular subject that explain why particular things happen or are true
14) (the principle of) superposition	n) used to show that you are describing or considering a subject in a particular way or from a particular point of view
15) to add up	o) to spread
16) to propagate (forward)	p) to clearly show a particular quality, emotion, or ability
17) a property (of waves)	q) putting one picture, image, or photograph on top of another so that both can be partly seen
18) to conspire	r) extremely small

Task 4 Compare what you have learn about diffraction and Huygens’ Principle from the above text with what you found out from Text 2A.

MODULE 3 POLARIZATION Texts: A. Polarization of Light Waves B. A Polarizing Microscope C. Wiener’s Method Grammar revision: the Infinitive, complexes with the Infinitive

Terminology

1. polarization – поляризация, linear polarization – линейная поляризация;

2. polarizing filter – поляризационный фильтр (поляризатор); sheet polarizer – пленочный (листовой) поляризатор;

3. analyzer – анализатор, дисперсионная призма;

4. to oscillate - колебаться, вибрировать, oscillation - колебание, качание, oscillating function – функция колебаний;

5. transparency – прозрачность, transparent – прозрачный, просвечивающий;

6. incandescent lamp – лампа накаливания;

7. transverse – поперечный;

8. to absorb – поглощать, впитывать; absorption –поглощение;

9. axis (pl. axes) – ось; transmission axis – ось пропускания;

10. incident light – падающий свет;

11. optical vector – электрический вектор;

12. to emerge from – появляться, выходить из....

Preliminary exercises

1. Read and translate the following words without a dictionary:

function, position, vector, component, plastic, detail, vibration; scalar, parallel, physical, equivalent, microscopic, ordinary, isotropic, approximate.

2. Read and translate the adjectives below, pay attention to their affixes:

   1. finite – infinite; regular – irregular;

   2. coherent – incoherent; polarized – unpolarized;

   3. distinguishable, appreciable, incandescent, resultant, angular, perpendicular.

3. Read and translate the word-combinations below:

direction – preferred direction, intermediate direction, direction of propagation; quantity – vector quantity, scalar quantity; plane – vibration plane, plane polarization, plane-polarized light, plane light wave.

4. Find equivalent phrases either in Text 3A or in the right-hand column:

1) в определённых случаях	a) in more detail
2) исследовать природу...	b) to keep in a fixed position
3) с другой стороны	c) some distinctive property
4) некоторые отличительные особенности	d) from the above considera­tions
5) изготовление солнцезащитных очков	e) to inquire into the character of...
6) держать неподвижно	f) closely obeys a law
7) строго подчиняется закону	g) the manufacture of sunglasses
8) направление которого не совпадает с...	h) on the other hand
9) более подробно	i) in certain cases
10) из вышесказанного	j) whose direction does not coincide with…

5. Read Text 3A ‘Polarization of Light Waves’ and answer the following questions: 1) На каком примере объясняется явление поляризации света? 2) В чём сущность закона Малюса? 3) Какой свет называется линейно-поляризованным?

TEXT 3A POLARIZATION OF LIGHT WAVES

By the study of interference and diffraction we have learned that the optical disturbance is a rapidly oscillating function of time whose form, in certain cases, appro­ximates that of a sinusoidal function. However, we have not yet inquired into the character of the optical disturbance.

It is clear that, if optical disturbance is a scalar qu­antity, or if it is a vector parallel to the direction of propa­gation, all planes through the same light ray are physically equivalent. If, on the other hand, the disturbance is a vec­tor pointing in a direction different from the direction of propagation, the plane combining this vector might be expec­ted to possess some distinctive property.

The question thus arises whether the infinite numbers of planes passing through the same light ray are physically distinguishable. This question can be answered by a simple ex­periment with a sheet polarizer, which is a sheet of transpa­rent plastic widely used, e.g., in the manufacture of sunglas­ses. Let us hold a sheet polarizer before our eyes and look through it at a light source such as an incandescent lamp. If we rotate the sheet in its own plane we notice no change in the light intensity. We now place a second sheet polarizer between the light source and the eye. If we rotate the second sheet in its own plane, keeping the first in a fixed position, we find the light intensity to change periodically. The inten­sity is practically zero at two angular positions⁸of the se­cond sheet 180° apart, and it is a maximum at angular posi­tions half-way between⁹. If we actually measure the intensity I of the light that emerges from the second sheet polarizer, we find that it closely obeys, a law of the following type:

I () =I0 cos2­ () (3-1)

where I­0 is the maximum intensity and  is the angle of rotation of the second sheet, measured from the position at which the intensity is a maximum. The law expressed by (3-1) is called the Law of Malus.

The very fact that the transmitted intensity depends on the angular position of the second sheet proves that the opti­cal disturbance is a vector quantity, whose direction does not coincide with the direction of propagation. We shall call this vector the optical vector. To explain in a natural way the details of the above experiment, as well as many other obser­vations, it is necessary to assume that the optical vector of a plane light wave propagating in an isotropic medium is perpendicular to the direction of propagation.

From the above considerations, there develops the following picture. Light waves are transverse waves. In the light coming from an ordinary light source, the optical vector changes direction rapidly and irregularly with time, while it always remains perpendicular to the direction of propagation. As we shall discus later in more detail, this behavior is due to the incoherent superposition of the optical disturbances coming from the many microscopic sources that form any ordinary light source. The light under such conditions is called natural or unpolarized light.

Consider a light wave incident perpendicularly upon a sheet polarizer. The sheet transmits the light wave without appreciably absorption if the optical vector is parallel to a certain preferred direction (the "transmission axis"), while (it absorbs completely) if the optical vector is perpen­dicular to this preferred direction. If the optical vector has an intermediate direction, it may be regarded as the resultant of two vectors, one being parallel and he other perpendicular to the transmission axis of the sheet polarizer. The sheet transmits the first component and absorbs the second so that, in all cases, the optical vector of the light wave emerging from the filter is parallel to the transmission axis. We shall call this wave linearly polarized or plane polarized. We shall call the plane containing the direction of propagation and the optical vector the plane of vibration. Any optical device capable of transmitting only linearly polarized light will be called a polarization filter.

2500 п. зн.

Words and word-combinations to be learnt:

actually - действительно, в самом деле

to obey a law - подчиняться закону

to coincide with - совпадать с чем-либо

to assume - предполагать

as well as - a так же

so that - так, что

by means of - посредством, с помощью