The photographic material can be used in physics lessons in grades 9 and 11, section “Wave Optics”.
Interference in thin films
Iridescent colors are produced by the interference of light waves. When light passes through a thin film, some of it is reflected from outer surface, while the other part penetrates the film and is reflected from the inner surface.
Interference is observed in all thin, light-transmitting films on any surfaces; in the case of a knife blade, a thin film (tarnish) is formed during the oxidation process environment on the metal surface. 
Diffraction of light
The surface of a compact disc is a relief spiral track on the surface of the polymer, the pitch of which is commensurate with the wavelength of visible light. On such an ordered and finely structured surface, diffraction and interference phenomena appeared, which is the reason for the iridescent color of the CD highlights observed in white light. 
Let's look at an incandescent lamp through small diameter holes. An obstacle appears in the path of the light wave, and it bends around it; the smaller the diameter, the stronger the diffraction (light circles are visible). The smaller the hole in the cardboard, the fewer rays pass through the hole, thereby the image of the incandescent lamp filament is clearer, and the decomposition of light is more intense.
Let's look at an incandescent lamp and the Sun through the nylon. Nylon acts as a diffraction grating. The more layers there are, the more intense the diffraction occurs.
LABORATORY WORK No. 4
STUDYING THE PHENOMENON OF LIGHT DIFFRACTION.
Learning goal of the lesson: The phenomenon of light diffraction on a diffraction grating is used in spectral instruments and allows one to determine wavelengths in the visible range of the spectrum. In addition, knowledge of the laws of diffraction allows one to determine the resolving power of optical instruments. X-ray diffraction makes it possible to determine the structure of bodies with a regular arrangement of atoms and to determine defects caused by violation of the regularity of the structure of bodies without destruction.
Base material: To successfully complete and pass the work, you need to know the laws of wave optics.
Preparation for the lesson:
Physics course: 2nd ed., 2004, ch. 22, pp., 431-453.
, “Course of General Physics”, 1974, §19-24, pp.113-147.
Physics course. 8th ed., 2005, §54-58, pp.470-484.
Optics and atomic physics, 2000,: chapter 3, pp. 74-121.
Incoming control: Preparation for laboratory work is controlled according to the prepared laboratory work form, according to general requirements and answers to questions:
1.Why does a diffraction grating split the light from an incandescent lamp into a spectrum?
2. At what distance from the diffraction grating is it best to observe diffraction?
3.What will the spectrum look like if the incandescent lamp is covered with green glass?
4.Why do measurements need to be taken at least three times?
5.How is the order of the spectrum determined?
6.Which color of the spectrum is located closer to the slit and why?
Devices and accessories: Diffraction grating,
Theoretical introduction and background:
Any wave propagating in an isotropic (homogeneous) medium, the properties of which do not change from point to point, maintains the direction of its propagation. In an anisotropic (inhomogeneous) medium, where as waves pass through they experience unequal changes in amplitude and phase on the surface of the wave front, the initial direction of propagation changes. This phenomenon is called diffraction. Diffraction is inherent in waves of any nature, and practically manifests itself in the deviation of the direction of light propagation from rectilinear.
Diffraction occurs with any local change in the wavefront, amplitude or phase. Such changes can be caused by the presence of opaque or partially transparent barriers in the path of the wave (screens), or sections of the medium with a different refractive index (phase plates).
Summarizing what has been said, we can formulate the following:
The phenomenon of deviation of light waves from rectilinear propagation when passing through holes and near the edges of screens is called diffraction.
This property is inherent in all waves, regardless of nature. In essence, diffraction is no different from interference. When there are few sources, the result of their joint action is called interference, and if there are many sources, then they talk about diffraction. Depending on the distance from which the wave is observed behind the object at which diffraction occurs, diffraction is distinguished Fraunhofer or Fresnel:
· if the diffraction pattern is observed at a finite distance from the object causing diffraction and the curvature of the wave front must be taken into account, then we speak of Fresnel diffraction. With Fresnel diffraction, a diffraction image of an obstacle is observed on the screen;
· if the wave fronts are flat (parallel rays) and the diffraction pattern is observed at an infinitely large distance (lenses are used for this), then we are talking about Fraunhofer diffraction.
In this work, the phenomenon of diffraction is used to determine the wavelength of light.
A". When the wave front reaches the slit and takes position AB (Fig. 1), then according to Figure 2 Huygens' principle all points of this wave front will be coherent sources of spherical secondary waves propagating in the direction of movement of the wave front.
Let us consider waves propagating from points of the AB plane in a direction making a certain angle with the original one (Fig. 2). If a lens parallel to plane AB is placed in the path of these rays, then the rays, after refraction, will converge at some point M of the screen located in the focal plane of the lens and will interfere with each other (point O is the main focus of the lens). Let us lower a perpendicular AC from point A to the direction of the selected beam of rays. Then, from the AC plane and further to the focal plane of the lens, the parallel rays do not change their path difference.
The path difference, which determines the interference conditions, occurs only on the path from the initial front AB to the plane AC and is different for different rays. To calculate the interference of these rays, we use the Fresnel zone method. To do this, mentally divide the line BC into a number of segments of length l/2. At a distance BC = a sin j will fit z = a×sin j/(0.5l) of such segments. Drawing lines parallel to AC from the ends of these segments until they meet AB, we will divide the slit wave front into a number of strips of the same width, these strips will appear in in this case Fresnel zones.
From the above construction it follows that waves coming from each two adjacent Fresnel zones arrive at point M in opposite phases and cancel each other. If with this construction number of zones it turns out even, then each pair of adjacent zones will cancel each other out and at a given angle on the screen will minimum illumination
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Thus, if the difference in the path of the rays coming from the edges of the slit is equal to an even number of half-waves, we will observe dark stripes on the screen. In the intervals between them, maximum illumination will be observed. They will correspond to the angles for which the wave front breaks into odd number Fresnel zones https://pandia.ru/text/80/353/images/image007_9.gif" width="143" height="43 src="> , (2)
where k = 1, 2, 3, … ,https://pandia.ru/text/80/353/images/image008_7.gif" align="left" width="330" height="219">Formulas (1 ) and (2) can be obtained, and if we directly use the interference conditions from laboratory work No. 66. Indeed, if we take two beams from adjacent Fresnel zones ( even number of zones), then the path difference between them is equal to half the wavelength, that is odd number of half waves. Consequently, by interfering, these rays provide a minimum of illumination on the screen, that is, condition (1) is obtained. Doing the same for rays from the extreme Fresnel zones, with odd number of zones we obtain formula (2).
https://pandia.ru/text/80/353/images/image010_7.gif" width="54" height="55 src=">.
· If the gap is very narrow (<< l), то вся поверхность щели является лишь небольшой частью зоны Френеля, и колебания от всех точек ее будут по любому направлению распространяться почти в одинаковой фазе. В результате во всех точках экран будет очень слабо равномерно освещен. Можно сказать, что свет через щель практически не проходит.
· 
If the gap is very wide ( a>> l), then the first minimum will already correspond to a very small deviation from rectilinear propagation at an angle. Therefore, on the screen we get a geometric image of the slit, bordered at the edges by thin alternating dark and light stripes.
Clear diffraction highs And minimums will be observed only in the intermediate case, when at the slit width a several Fresnel zones will fit.
When illuminating the slit with non-monochromatic ( white) with light, the diffraction maxima for different colors will diverge. The smaller l, the smaller the angles at which diffraction maxima are observed. Rays of all colors arrive at the center of the screen with a path difference equal to zero, so the image in the center will be white. Right And left diffraction patterns will be observed from the central maximum spectra first, second And etc.. order.
Diffraction grating
To increase the intensity of diffraction maxima, they use not one slit, but a diffraction grating.
A diffraction grating is a series of parallel slits of equal width a, separated by opaque intervals of width b. Sum a+ b = d called period or constant diffraction grating.
Diffraction gratings are made on glass or metal (in the latter case the grating is called reflective). With the thinnest diamond tip, using a dividing machine, a series of thin parallel strokes of the same width and located at equal distances from each other is applied. In this case, the strokes that scatter light in all directions play the role of opaque spaces, and the untouched areas of the plate play the role of slits. The number of lines per 1 mm in some gratings reaches 2000.
Let us consider diffraction from N slits. When light passes through a system of identical slits, the diffraction pattern becomes significantly more complicated. In this case, the rays diffracting from different slits, overlap each other in the focal plane of the lens and interfere among themselves. If the number of slits is N, then N beams interfere with each other. As a result of diffraction, the formation condition diffraction maxima will take the form
https://pandia.ru/text/80/353/images/image014_4.gif" width="31" height="14 src=">. (3)
Compared to single-slit diffraction, the condition has changed to the opposite:
Maxima satisfying condition (3) are called main. The position of the minima does not change, since those directions in which none of the slits sends light do not receive it even with N slits.
In addition, there are possible directions in which the light sent by different slits is extinguished (mutually destroyed). In general, diffraction from N slits produces:
1) main highs
https://pandia.ru/text/80/353/images/image017_4.gif" width="223" height="25">;
3) additionalminimums.
Here, as before, a– slot width;
d = a + b– period of the diffraction grating.
Between the two main maxima there are N–1 additional minima, separated by secondary maxima (Fig. 5), the intensity of which is significantly less intensity main maxima.
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The resolution l/Dl of a diffraction grating characterizes the ability of the grating to separate illumination maxima for two wavelengths l1 and l2 close to each other in a given spectrum. Here Dl = l2 – l1. If l/Dl > kN, then the illumination maxima for l1 and l2 are not resolved in the kth order spectrum.
Work order:
Exercise 1. Determining the wavelength of light using a diffraction grating.
1. By moving the scale with the slit, set the diffraction grating at a given distance “y” from the slit.
2. Find spectra of 1st, 2nd, 3rd orders on both sides of the zero maximum.
3. Measure the distance between the zero maximum and the first maximum located along right side from zero - x1, between the zero maximum and the first maximum located along left side from Figure 6 zero - x2. Find and determine the angle j corresponding to this maximum intensity. Measurements should be made for the maxima of violet, green and red colors, in spectra of 1st, 2nd and 3rd orders for three values of “y”. For example, for y 1 = 15, y 2 = 20 and y 3 = 30 cm.
4. 
Knowing the lattice constant ( d= 0.01 mm) and the angle j at which the maximum intensity of a given color and order is observed, find the wavelength l using the formula:
Here k taken modulo.
5. Calculate the absolute error for the found wavelengths corresponding to the violet, green and red regions of the spectrum.
6. Enter the results of measurements and calculations into the table.
Colors | y,m | k | x 1 ,m | x 2 , m | m | l, nm | , nm | D l, nm |
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
Red | 1 | |||||||
2 | ||||||||
1 | ||||||||
2 | ||||||||
1 | ||||||||
2 |
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
Green | 1 | |||||||
2 | ||||||||
1 | ||||||||
2 | ||||||||
1 | ||||||||
2 | ||||||||
Violet | 1 | |||||||
2 | ||||||||
1 | ||||||||
2 | ||||||||
1 | ||||||||
2 |
Test questions and assignments.
1. What is the phenomenon of diffraction?
2. How does Fresnel diffraction differ from Fraunhofer diffraction?
3. Formulate the Huygens-Fresnel principle.
4. How can we explain diffraction using the Huygens-Fresnel principle?
5. What are Fresnel zones?
6. What conditions must be met in order for diffraction to be observed?
7. Describe diffraction from a single slit.
8. Diffraction by a diffraction grating. What is the fundamental difference between this case and single-slit diffraction?
9. How to determine the maximum number of diffraction spectra for a given diffraction grating?
10. Why are such characteristics as angular dispersion and resolution introduced?
Laboratory work No. 1 3
Topic: Observation of the phenomena of interference and diffraction of light
Goal: during the experiment, prove the existence of diffraction and inter-
interference, and also be able to explain the reasons for the formation of interference
tion and diffraction patterns
If light is a stream of waves, then the phenomenon should be observed interference, i.e., the addition of two or more waves. However, it is impossible to obtain an interference pattern (alternating maxima and minima of illumination) using two independent light sources.
To obtain a stable interference pattern, consistent (coherent) waves are needed. They must have the same frequency and a constant phase difference (or path difference) at any point in space.
A stable interference pattern is observed on thin films of kerosene or oil on the surface of water, on the surface of a soap bubble.
Newton obtained a simple interference pattern by observing the behavior of light in a thin layer of air between a glass plate and a flat-convex lens superimposed on it.
Diffraction– waves bending around the edges of obstacles is inherent in any wave phenomenon. Waves deviate from rectilinear propagation at noticeable angles only at obstacles whose dimensions are comparable to the wavelength, and the light wavelength is very short (4 10 -7 m - 8 10 -7 m).
In this lab we will be able to observe interference and
diffraction, as well as explain these phenomena on the basis of theory.
Equipment: - glass plates – 2 pcs.;
Shreds of nylon or cambric;
Straight filament lamp, candle;
Calipers
Work order:
Note : a report on the implementation of each experiment must be prepared according to
the following diagram: 1) drawing;
2) explanation of the experience.
I . Observation of the phenomenon of light interference.
1. Wipe the glass plates thoroughly, place them together and squeeze them with your fingers.
2. Examine the plates in reflected light , on a dark background (place them
it is necessary so that too bright reflections do not form on the surface of the glass
from windows or white walls).
3. In some places where the plates touch, bright rainbow colors are observed
ring-shaped or irregularly shaped stripes.
4. Draw the observed interference pattern.
II . Observation of the diffraction phenomenon.
a) 1. Install a 0.05 mm wide gap between the jaws of the caliper.
2. Place the slit close to the eye, positioning it vertically.
3. Looking through the slit at a vertically located luminous thread
lamp, candle, watch, there are rainbow stripes on both sides of the thread
(diffraction spectra).
4. By increasing the slit width, notice how this change affects the diffraction
tion picture.
5. Draw and explain the diffraction spectra obtained from the slit
calipers for the lamp and for the candle.
b) 1. Observe diffraction spectra using shreds of nylon or
2. Sketch and explain the diffraction pattern obtained on the patch
III . After conducting the experiments, draw a general conclusion based on the results of observations.
Security questions:
1. Why is it not observed in an ordinary room where there are many light sources?
interference? What condition must these sources satisfy?
State this condition.
2. What phenomenon is observed on the surface of soap bubbles?
Who explained this phenomenon and how?
3. What is Jung's experience? What are its results?
4. What obstacles can a light wave bend around?
5. What phenomenon, along with interference and diffraction, took place in the observation?
experiences you have had? How did this manifest itself?
Laboratory work on topic : "Observation of interference and diffraction of light"
Purpose of the work: experimentally study the phenomenon of interference and diffraction.
Equipment: electric lamp with a straight filament, two glass plates, a glass tube, a glass with a soap solution, a wire ring with a handle 30 mm in diameter, a CD, nylon fabric, a light filter.
Theory: Interference is a phenomenon characteristic of waves of any nature: mechanical, electromagnetic.
Wave interference – addition in space of two (or several) waves, in which at different points the resultant wave is strengthened or weakened .
Interference is usually observed when waves emitted by the same light source, arriving at a given point in different ways, overlap. It is impossible to obtain an interference pattern from two independent sources, because molecules or atoms emit light in separate trains of waves, independently of each other. Atoms emit fragments of light waves (trains), in which the oscillation phases are random. The trains are about 1 meter long. Wave trains of different atoms overlap each other. The amplitude of the resulting oscillations changes chaotically over time so quickly that the eye does not have time to sense this change in patterns. Therefore, a person sees the space uniformly illuminated. To form a stable interference pattern, coherent (matched) wave sources are required.
Coherent waves that have the same frequency and a constant phase difference are called.
The amplitude of the resulting displacement at point C depends on the difference in the wave paths at a distance d2 – d1.
Maximum condition
, (Δd=d 2 -d 1 )
Where k=0; ± 1; ± 2; ± 3 ;…
(the difference in wave path is equal to an even number of half-waves)
Waves from sources A and B will arrive at point C in the same phases and “reinforce each other.”
φ A =φ B - oscillation phases
Δφ=0 - phase difference
A=2X max
Minimum condition
, (Δd=d
2
-d
1
)
Where k=0; ± 1; ± 2; ± 3;…
(the difference in wave path is equal to an odd number of half-waves)
Waves from sources A and B will arrive at point C in antiphase and “cancel each other.”
φ A ≠φ B - oscillation phases
Δφ=π - phase difference
A=0 – amplitude of the resulting wave.
Interference pattern – regular alternation of areas of increased and decreased light intensity.
Interference of light – spatial redistribution of the energy of light radiation when two or more light waves are superimposed.
Due to diffraction, light is deviated from its linear propagation (for example, near the edges of obstacles).
Diffraction – the phenomenon of wave deviation from rectilinear propagation when passing through small holes and the wave bending around small obstacles .
Diffraction condition : d< λ , Where d – size of the obstacle,λ - wavelength. The dimensions of obstacles (holes) must be smaller or comparable to the wavelength.
The existence of this phenomenon (diffraction) limits the scope of application of the laws of geometric optics and is the reason for the limit of the resolution of optical instruments.
Diffraction grating – an optical device that is a periodic structure of large number regularly arranged elements on which light diffraction occurs. Strokes with a specific and constant profile for a given diffraction grating are repeated at the same intervald (lattice period). The ability of a diffraction grating to separate a beam of light incident on it according to wavelengths is its main property. There are reflective and transparent diffraction gratings.Modern devices mainly use reflective diffraction gratings. .
Condition for observing the diffraction maximum :
d·sinφ=k·λ, Where k=0; ± 1; ± 2; ± 3; d - lattice period , φ - the angle at which the maximum is observed, and λ - wavelength.
From the maximum condition it followssinφ=(k λ)/d .
Let k=1, then sinφ cr =λ cr /d And sinφ f =λ f /d.
It is known that λ cr >λ f , hence sinφ cr >sinφ f . Because y=sinφ f - function is increasing, thenφ cr >φ f
That's why purple in the diffraction spectrum is located closer to the center.
In the phenomena of interference and diffraction of light, the law of conservation of energy is observed . In the interference region, light energy is only redistributed without being converted into other types of energy. The increase in energy at some points of the interference pattern relative to the total light energy is compensated by its decrease at other points (total light energy is the light energy of two light beams from independent sources). Light stripes correspond to energy maxima, dark stripes correspond to energy minima.
Work progress:
Experience 1. Dip the wire ring into the soapy solution. A soap film is formed on the wire ring.
Place it vertically. We observe light and dark horizontal stripes that change in width as the film thickness changes.
Explanation. The appearance of light and dark stripes is explained by the interference of light waves reflected from the surface of the film. triangle d = 2h.The difference in the path of light waves is equal to twice the thickness of the film. When positioned vertically, the film has a wedge-shaped shape. The difference in the path of light waves in its upper part will be less than in the lower part. In those places of the film where the path difference is equal to an even number of half-waves, light stripes are observed. And when odd number half-waves are dark stripes. The horizontal arrangement of the stripes is explained by the horizontal arrangement of lines of equal film thickness.
We illuminate the soap film with white light (from a lamp). We observe that the light stripes are colored in spectral colors: blue at the top, red at the bottom.
Explanation. This coloring is explained by the dependence of the position of the light stripes on the wavelength of the incident color.
We also observe that the stripes, expanding and maintaining their shape, move downward.
If you use light filters and illuminate with monochromatic light, the interference pattern changes (the alternation of dark and light stripes changes)
Explanation. This is explained by a decrease in film thickness, as the soap solution flows down under the influence of gravity.
Experience 2. Using a glass tube, blow a soap bubble and examine it carefully. When illuminated with white light, observe the formation of colored interference rings, colored in spectral colors. The upper edge of each light ring has blue, the bottom one is red. As the film thickness decreases, the rings, also expanding, slowly move downward. Their ring-shaped form is explained by the ring-shaped lines of equal thickness.
Answer the questions:
Why are soap bubbles rainbow-colored?
What shape do rainbow stripes have?
Why does the color of the bubble change all the time?
Experience 3. Wipe the two glass plates thoroughly, place them together and press together with your fingers. Due to the imperfect shape of the contacting surfaces, thin air voids are formed between the plates.
Explanation: The surfaces of the plates cannot be completely flat, so they only touch in a few places. The thinnest air wedges form around these places various shapes, giving the interference pattern. In transmitted light the maximum condition is 2h=kl
Answer the questions:
Why are bright rainbow ring-shaped or irregularly shaped stripes observed at the places where the plates touch?
Why do the shape and location of the interference fringes change with a change in pressure?
Experience 4. Look carefully underneath different angles surface of the CD (on which recording is made).
Explanation : The brightness of the diffraction spectra depends on the frequency of the grooves applied to the disk and on the angle of incidence of the rays. Almost parallel rays incident from the lamp filament are reflected from adjacent convexities between the grooves at points A and B. Rays reflected at an angle equal to the angle fall, form an image of the lamp filament in the form of a white line. Rays reflected at other angles have a certain path difference, as a result of which wave addition occurs.
What are you observing? Explain the observed phenomena. Describe the interference pattern.
The surface of a CD is a spiral track with a pitch commensurate with the wavelength of visible light. Diffraction and interference phenomena appear on a fine-structured surface. The glare of CDs has a rainbow coloration.
Experience 5. Look through the nylon fabric at the filament of the burning lamp. By rotating the fabric around its axis, achieve a clear diffraction pattern in the form of two diffraction stripes crossed at right angles.
Explanation : A diffraction maximum is visible in the center of the cross white. At k=0, the difference in the wave paths is zero, so the central maximum is white. The cross is formed because the threads of the fabric are two diffraction gratings folded together with mutually perpendicular slits. The appearance of spectral colors is explained by the fact that white light consists of waves of different lengths. The diffraction maximum of light for different wavelengths is obtained in different places.
Sketch the observed diffraction cross. Explain the observed phenomena.
Experience 6.
Small aperture diffraction
To observe such diffraction, we need a thick sheet of paper and a pin. Using a pin, make a small hole in the sheet. Then we bring the hole close to the eye and observe a bright light source. In this case, diffraction of light is visible
Record the conclusion. Indicate in which of the experiments you performed the phenomenon of interference was observed, and in which diffraction . Give examples of interference and diffraction that you have encountered.
Security questions ( Each student prepares answers to questions ):
What is light?
Who proved that light is an electromagnetic wave?
What is the speed of light in a vacuum?
Who discovered the interference of light?
What explains the rainbow coloration of thin interference films?
Can light waves coming from two incandescent electric lamps interfere? Why?
Why is a thick layer of oil not rainbow colored?
Does the position of the main diffraction maxima depend on the number of grating slits?
Why does the visible rainbow color of soap film change all the time?