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Файл:English for Optics Students. Английский для студентов, изучающих оптику. Учебное пособие
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Task 3. Read the text and define its main idea.
Interference
1. In physics, interference is a phenomenon in
which two waves superpose to form a resultant
wave of greater or lower amplitude. Interference
usually refers to the interaction of waves that are
correlated or coherent with each other, either because they come from the same source or because
they have the same or nearly the same frequency.
Interference effects can be observed with all types of waves, for example,
light, radio, acoustic, surface water waves or matter waves.
2. The principle of superposition of waves states that when two or more
propagating waves of same type are incident on the same point, the total
displacement at that point is equal to the pointwise sum of the displacements
of the individual waves. If a crest of a wave meets a crest of another wave
of the same frequency at the same point, then the magnitude of the displacement is the sum of the individual magnitudes – this is constructive interference. If a crest of one wave meets a trough of another wave then the
magnitude of the displacements is equal to the difference in the individual
magnitudes – this is known as destructive interference.
3. Constructive interference occurs when the phase difference between
the waves is a multiple of 2π, whereas destructive interference occurs when
the difference is an odd multiple of π. If the difference between the phases is
intermediate between these two extremes, then the magnitude of the displacement of the summed waves lies between the minimum and maximum
values.
Task 4. Match the paragraphs 1 – 3 to their subtitles A–D. One is extra.
A. Conditions for positive interference.
B. The essence of the phenomenon of interference.
C. The formula of interference.
D. Conditions for crests and troughs.
Task 5. Answer the questions.
1. Which of the graphs below shows Constructive interference and
which Destructive interference?
2. What does the upper/middle/bottom line demonstrate?
3. Why are the resultant waves different in both graphs?
4. What does constructive/destructive interference cause?
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Resultant wave
Wave 1
Wave 2
Task 6. Match the words to their explanations.
1 fringes
2 overlap
3 intersect
4 essentially
5 redistribution
6 regain
7 throughout
8 occur
A in every part of a place
B cross, divide something by lines etc.
C happen, especially unexpectedly; exist
D fit over the edge of the other object
E the outer edge of something
F at the end of a process or period of time
G get something back
H the process or action of separating or dividing
Task 7. Work in pairs. Discuss what a plane wave is. Is it possible in
practice? Why? Give reasons for your opinion.
Task 8. Answer the questions.
1. What do the letters (A, B, x, θ, d) in the scheme mean?
2. What does the figure on the left show?
Task 9. Read the following formulas.
E.g. The phase difference at the point A is given by
22sindx
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We can read this formula as follows:
f
Increment of phi [fi:] equals/is equal to/is two pi [pi] times/multiplied by
d over/divided by lambda [læmbdə] equals two pi times sine [sain] theta
[θeitə]/[θi:tə] divided by lambda.
–sub
ddf
f
sin
1.
x
0, 1, 2, ...
sin 1 3
2.
x
,,...
22
3.
d
f
sin
Task 10. To answer the following questions use the formulas from
Task 10 and possible variants A-F below.
1. How is fringe spacing denoted?
2. When does the fringe spacing increase?
3. When can the fringes be observed?
4. When are two waves half a cycle out of phase?
5. When does constructive interference occur?
6. When does destructive interference occur?
A. The fringe spacing increases with increase in wavelength, and with
decreasing angle θ.
d is known as the fringe spacing.
B.
C. Two waves are half a cycle out of phase when …
D. The fringes are observed wherever the two waves overlap and the
fringe spacing is uniform throughout.
E. Destructive interference occurs when waves are half a cycle out of
phase.
F. Constructive interference occurs when the waves are in phase.
Thus, an interference fringe pattern is produced, where the separation of
the maxima is …
53
Task 11. Look at the picture of different patterns of interference and
answer the questions.
1. What kind of source produces a spherical
wave?
2. Which of the rows (upper or lower) presents
the bigger wavelength?
3. Which of the rows (left or right) presents the
bigger distance between the sources?
4. What does the interference pattern depend on?
Task 12. Discuss with your partner the meaning of the terms superpo-
sition and interference, the main notions of the field and their applica-
tions.
Task 13. One of you is Student A and the other is Student B. Read the
corresponding task and talk to your partner.
Student A: You are a teacher at university. Discuss with a colleague of
yours some experiments demonstrating phenomenon of superposition and
interference that you want to show to your students.
Student B: You are a professor teaching optics at university. Listen to
your colleague and ask him/her why they believe those experiments would
be useful for students. Disagree with your colleague, express your own
opinion and prove it.
Task 14. Write an essay of 150 words on the topic Superposition and
interference. Read your essay to your group mates and share your ideas
with them.
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Additional tasks to Unit Superposition and Interference
Terminology
luminous gap path lengths
double-slit path difference fringe
Task 1. Match the words to their meanings.
1 edge
2 reject
3 apparent
4 despite
5 nonetheless
6 eminent
7 partition
A несмотря на, вопреки
B тем не менее
C выдающийся
D не признавать, отвергать
E край, кромка
F зд. перегородка, переборка
G очевидный
Task 2. Answer the questions.
1. What scientists contributed to the development of the theories of
light?
2. What natural light phenomena caused people search for their physical
explanation?
3. Why was the wave theory of light rejected for a long time?
Task 3. Read and entitle the text.
In the 17th and 18th centuries some scientists proposed a wave theory of
light based on experimental observations, including Robert Hooke, Christiaan Huygens and Leonhard Euler. However, Isaac Newton, who did many
experimental investigations of light, had rejected the wave theory of light
and developed his corpuscular theory of light according to which light is
emitted from a luminous body in the form of tiny particles. This theory was
accepted until the beginning of the nineteenth century despite the fact that
many phenomena, including diffraction effects at edges or in narrow apertures, colours in thin films and insect wings, and the apparent failure of light
particles to crash into one another when two light beams crossed, could not
be adequately explained by the corpuscular theory which, nonetheless, had
many eminent supporters, including Pierre-Simon Laplace and JeanBaptiste Biot.
Young's interference experiment, also called Young's double-slit interferometer, was the original version of the modern double-slit experiment,
55
performed at the beginning of the nineteenth century by Thomas Young.
This experiment played a major role in the general acceptance of the wave
theory of light. In Young's own judgment, this was the most important of his
many achievements.
Interference can also occur for particles, because of the duality introduced by quantum mechanics. A famous example is the so-called two-slit
experiment.
Path of Single
Photon
Consider a partition with two narrow parallel slits in it. On one side of
the partition one places a source of light of a particular color (that is, of a
particular wavelength). Most of the light will hit the partition, but a small
amount will go through the slits. Now suppose one places a screen on the
far side of the partition from the light. Any point on the screen will receive
waves from the two slits. However, in general, the distance the light has to
travel from the source to the screen via the two slits will be different. This
will mean that the waves from the slits will not be in phase with each other
when they arrive at the screen: in some places the waves will cancel each
other out, and in others they will reinforce each other. The result is a characteristic pattern of light and dark fringes.
Task 4. What famous scientists are mentioned in the text of Task 3?
What do you know about them? What did they do for science? If necessary search the Internet to learn more about them.
Task 5. Find the following words in the text of Task 3. Read and
translate the sentences where they are used. Make your own sentences
about light theories using these words.
according to, despite, nonetheless, via, when
56
Task 6. Work with a partner to complete the word families in the table
below. Translate them into Russian.
Noun Adjective Adverb Verb
acceptance
judgment
partition
…
…
…
failure
…
…
–
…
…
apparent
…
–
–
–
…
–
…
–
…
…
…
consider
cancel
–
…
Task 7. Work in pairs. Choose any 7 words from the table above and
write down 7 questions about light theories using the words chosen.
Ask the questions to your partner.
Task 8. Work in pairs. Describe Young’s experiment to your partner.
Task 9. Answer the questions.
1. What is the difference between original Young’s experiment and its
modern version?
2. What would happen if there were two or three partitions?
3. What would happen if the source of light were a laser?
Task 10. Work on these words and word combinations. Look up their
meanings in the dictionary, find these words families. Translate each word
of the family. Find these words in the text of Task 11 and translate them.
optical flat, currently, mean, even,
band, odd, multiple
Task 11. Read the text and entitle
each paragraph and the whole text.
Write those titles down.
Creation of interference fringes by an
optical flat on a reflective surface. Light
rays from a monochromatic source pass
through the glass and reflect off both the
bottom surface of the flat and the supporting surface. The tiny gap between the surfaces mean the two reflected rays
have different path lengths and interfere when they combine. At locations
57
(b) where the path difference is an even multiple of λ/2, the waves reinforce.
At locations (a) where the path difference is an odd multiple of λ/2 the
waves cancel. Since the gap between the surfaces varies slightly in width at
different points, a series of alternating bright and dark bands are seen.
Because the frequency of light waves (~10
14
Hz) is too high to be
detected by currently available detectors, it is possible to observe only the
intensity of an optical interference pattern. The intensity of the light at a
given point is proportional to the square of the average amplitude of the
wave. This can be expressed mathematically.
The interference pattern maps out the difference in phase between the
two waves, with maxima occurring when the phase difference is a multiple
of 2π. If the two beams are of equal intensity, the maxima are four times as
bright as the individual beams, and the minima have zero intensity.
The two waves must have the same polarization to give rise to interference fringes since it is not possible for waves of different polarizations to
cancel one another out or add together. Instead, when waves of different
polarization are added together, they give rise to a wave of a different polarization state.
(https://en.wikipedia.org/wiki/Interference_%28wave_propagation%29)
Task 12. Why are there dark and light “stripes” on the surface in the
Figure illustrating the text of Task 11?
Task 13. Give the explanations to the following words:
point, beam, square, state, time, case, cause
Task 14. Use the titles to the paragraphs you gave in Task 11 as a plan
to describe the nature of interference in thin films.
Task 15. Find the following words in the texts of Tasks 11 and 16.
Translate the sentences where they are used.
instead, since, therefore
Task 16. What grammar phenomenon is there in the sentence below?
Pay attention to the underlined words. (You may use grammar reference
of unit Physical Optics, Task 12.)
The colors corresponding to these wavelengths are absent from the reflected light, which therefore appears to be colored.
58
Task 17. Why are transparent soap bubbles
colored? Read the information and then give
your explanation of the phenomenon without
looking into the text.
A familiar example of interference in the
case of light is the colors that are often seen in
soap bubbles. These are caused by reflection of
light from the two sides of the thin film of water forming the bubble. White
light consists of light waves of all different wavelengths, or colors. For certain wavelengths the crests of the waves reflected from one side of the soap
film coincide with the troughs reflected from the other side. The colors corresponding to these wavelengths are absent from the reflected light, which
therefore appears to be colored.
Task 18. Discuss with your partner the examples of superposition and
interference and their explanations. You may use the information you
have learned in the unit.
Task 19. Write an essay of 150 words on the topic Superposition and
interference. Read your essay to share your ideas with the class.
Additional texts to Unit Superposition and Interference
Text 1
Light source requirements
The discussion above assumes that the waves which interfere with one
another are monochromatic, i.e. have a single frequency–this requires that
they are infinite in time. This is not, however, either practical or necessary.
Two identical waves of finite duration whose frequency is fixed over
that period will give rise to an interference pattern while they overlap. Two
identical waves which consist of a narrow spectrum of frequency waves of
finite duration, will give a series of fringe patterns of slightly differing
spacings, and provided the spread of spacings is significantly less than the
average fringe spacing, a fringe pattern will again be observed during the
time when the two waves overlap.
Conventional light sources emit waves of differing frequencies and at
different times from different points in the source. If the light is split into
two waves and then re-combined, each individual light wave may generate
an interference pattern with its other half, but the individual fringe patterns
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generated will have different phases and spacings, and normally no overall
fringe pattern will be observable. However, single-element light sources,
such as sodium- or mercury-vapor lamps have emission lines with quite
narrow frequency spectra. When these are spatially and colour filtered, and
then split into two waves, they can be superimposed to generate interference
fringes. All interferometry prior to the invention of the laser was done using
such sources and had a wide range of successful applications.
A laser beam generally approximates much more closely to a monochromatic source, and it is much more straightforward to generate interference fringes using a laser. The ease with which interference fringes can be
observed with a laser beam can sometimes cause problems in that stray
reflections may give spurious interference fringes which can result in errors.
Normally, a single laser beam is used in interferometry, though interference has been observed using two independent lasers whose frequencies
were sufficiently matched to satisfy the phase requirements.
Text 2
Optical arrangements
To generate interference fringes, light from the source has to be divided
into two waves which have then to be re-combined. Traditionally, interferometers have been classified as either amplitude-division or wavefrontdivision systems.
In an amplitude-division system, a beam splitter is used to divide the
light into two beams travelling in different directions, which are then superimposed to produce the interference pattern. The Michelson interferometer
and the Mach-Zehnder interferometer are examples of amplitude-division
systems.
In wavefront-division systems, the wave is divided in space—examples
are Young's double slit interferometer and Lloyd's mirror.
Interference can also be seen in everyday phenomena such as iridescence and structural coloration. For example, the colours seen in a soap
bubble arise from interference of light reflecting off the front and back surfaces of the thin soap film. Depending on the thickness of the film, different
colours interfere constructively and destructively.
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