Stagnation of light interference. Interference in thin layers: a revelation and understanding for your guilt How to detect interference in thin layers
Light needles with two light point jets. But we often find ourselves on the right side with long shafts of light in cases of interference, like in natural minds, if the shaft of light is used to serve as a plot of the palate, then. The Russians are bright during the day. The most common and significant episode of this kind occurs when thin transparent layers are lightened, when it is necessary for two coherent bundles of splitting of the light fiber to occur This is due to the lightness of the front and rear surfaces of the cast.
This is the phenomenon visible under the name colors of thin swimsuits It is easy to be careful on large bulbs, on thin flotsam of oil or oil that floats on the surface of the water, etc.
Let the plane-parallel scarf fall into view, and a flat light-colored thread falls, so that you can see it as a parallel bundle of threads.
The plate displays two parallel beams of light, one of which emerges from the upper surface of the plate, the other, which emerges from the lower surface of the skin from these bundles of representations in one exchange).
Malyunok 2. Interference in thin swimmers.
When entering and exiting the plate, another bundle becomes bent. In addition to these two beams, the scarf displays the beams that emerge as a result of three, five, etc. multiple imaging of the surface of the plate. However, due to its low intensity, we will not be able to bring these beams to your respects. The difference in progress is added by exchanging 1 and 2 until they converge at point C, the old one, (8) where S 1- Dovzhina vidrezka PS; S 2- total deposit of AT and OS components; n- display of a crumpled scarf.
A sign of a broken middle, too much of a scarf, respectfully equal to one, b- It's a bad record. The little one can see that:
;
Having substituted the values in expression (8) and carried out simple calculations, it is easy to bring formula (9) for the difference in the move Δ to the form
. (9)
However, when calculating the difference between phases in exchanges 1 and 2, it is necessary, in addition to the optical difference in the course of Δ, to consider the possibility of changing the phase of the circuit at the point where the image corresponds to the difference between the optical parameters w of a slick middle. Therefore, the hvyli phase signifies a change to π. The result between 1 and 2 is an additional phase difference that is equal to π. They can be sealed by adding half of the liquid in a vacuum to Δ (or above it). As a result, we reject
(10)
The intensity depends on the value of the optical difference in the course (10). Apparently, minds (5) and (6) when there are maximums, and when there are minimums in intensity ( m- whole number).
So the maximum intensity looks like this:
, (11)
and for a minimum of lightening we can
. (12)
With a light-colored flat-parallel scarf ( b= const) the results of the interference lie below the tails of the falling spittle. The interference picture looks like curvilinear dark and light browns that alternate. The skin darkening of these is consistent with the greater significance of the fall. That's why they call it stink dark colors and lines of smooth nakhil. Since the entire lens L is optically perpendicular to the surface of the film, the dark of the same naked mother appears as concentric rings centered at the head focus of the lens. This phenomenon is used in practice for precise control of the degree of plane-parallelism of thin clear plates; A change in the thickness of the plates by an amount of approximately 10 -8 m can be detected by the change in the shape of the ring of the equal nail.
Interference darks on the surface of the melt with a wedge-like appearance show equal lightness at all points on the surface, which corresponds to the quality of the melt. Interference darks are parallel to the edge of the wedge. They're called Interferential shadows of equal comradeship
Formula (10) was developed to prevent interference in a broken light. Since interference darks are carefully avoided in thin plates or flots that are exposed to light (in the light that passes), then there will be no difference In the course of the process, Δ will appear in formula (9). Also, the optical differences in the course for passing through and the broken light are divided by λ/2, then. The maximums of interference in the switched light are indicated by the minimums in the light that passes through and in the end.
Newton's ring.
The dark spots of equal tyranny can be removed by placing a flat-convex lens with a great radius of curvature R on a flat-convex plate. A wedge is created between them. In whose dark of equal comradeship the appearance of a circle, which is called Newton's rings; The difference in the course of interfering exchanges, and in the first instance, is determined by formula (10).
The radius of Newton's kth ring is significant: from the tricutaneous ABC 
, stars, nechtuyuchi b 2 so as R>> b, omitted.
Figure 3. Newton's coil
We represent this expression in formula (10):
Since this difference in motion is equal to the whole number of dovzhin hvil (minus the maximum interference), then for the radius of the kth light Newton ring in the light or dark circle:
. (14)
Having completed similar awkward calculations, we derive the formula for calculating the radii of the dark rings in the light (or light rings):
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When light passes through the lenses or prisms of the skin, the light flow is often knocked out from the surface. In folding optical systems, with many lenses and prisms, the flow of light that passes through significantly changes, in addition, glare appears. Thus, it was established that in the periscopes of underwater ships up to 50% of the light that enters them is displayed. To eliminate these defects, use a technique called enlightenment of optics. The essence of this technique is that the optical surfaces are covered with thin fluffs, creating interference phenomena. The purpose of the melt lies at the extinguisher of the broken light.
Nutrition for self-control
1) What is called interference and interference of flat panels?
2) What kinds of things are called coherent?
3) Explain the concepts of time-hour and spatial coherence.
4) What is interference in thin layers.
5) Explain why there is a lot of interference.
REFERENCES
Main
1. Detlaf, A.A. Physics course in basic sciences. Pos_bnik/A.A. Detlaff, B.M. Yavorsky. - 7th view. Erase. - M: IC "Academy". – 2008.-720 p.
2. Savelyev, I.V.. Physics course: 3 volumes: Volume 1: Mechanics. Molecular physics: textbook/I.V. Savelyev. - 4 types. erased - St. Petersburg; M. Krasnodar: Lan.-2008.-352 p.
3. Trofimova, T.I. physics course: navch. Pos_bnik/T.I. Trofimova.- 15th edition, erased. - M: IC "Academy", 2007.-560 p.
Dodatkova
1. Feynman, R. Feynman lectures on physics/R. Feynman, R. Layton, M. Sands. - M: Peace.
T.1. Such is the science about nature. Laws of mechanics – 1965. –232 p.
T. 2. Prostir, chas, ruh. – 1965. – 168 p.
T. 3. Viprominyuvannya. Khvili. Quanti. – 1965. – 240 p.
2. Berkeley course of physics. T.1,2,3. - M: Science, 1984
T. 1. Kitel, Ch. Mechanics / Ch. Kitel, W. Knight, M. Ruderman. – 480 s.
T. 2. Purcell, Ege. Electrics and magnetism / E. Purcell. – 448 p.
T. 3. Crawford, F. Khvili/F. Crawford – 512 p.
3. Frish, S.E. Course of advanced physics: 3 volumes: navch. / S.E. Frish, A.V. Timorova. - St. Petersburg: M.; Krasnodar: Lan.-2009.
T. 1. Physical ambushes of mechanics. Molecular physics Kolivannya and hvili: podruchnik – 480 p.
T.2: Electrical and electromagnetic boxes: handy. – 518 p.
T. 3. Optics. Atomic physics: handbook – 656 p.
Powered 1.
Basic laws of geometric optics
Geometric optics- a branch of optics that includes the laws of broadening the light of clear media and the principles of depicting the passage of light in optical systems not in accordance with the medical authorities.
The basic laws of geometric optics were known long before the physical nature of light was established.
Law of linear light broadening: in an optically homogeneous middle, the light broadens linearly. Conclusive proof of this law can be sharp shades that appear as opaque bodies when illuminated with light dzherel to reach small sizes (point dzherel). Another proof may be the passage of light from a distant jet through a small opening, resulting in the creation of a narrow beam of light. This leads to the understanding of the light exchange as a geometric line, from which the light expands. It means that the law of linear expansion of light is violated and the concept of light exchange loses the sense that light can pass through small openings, the dimensions of which can be equalized by a long time. Thus, geometric optics, which revolves around the phenomena of light exchange, is the borderline fall of light optics at? > 0. The differences between geometric optics will be discussed in the section on light diffraction.
At the intersection of two clear midpoints, light can often appear so that part of the light energy expands after being reflected in a new direction, and part of it passes through the cordon and continues to expand at the other middle.
The law of light reflection: falling and breaking the exchange, and direct a perpendicular to the intersection of the two middles, ending at the point of the fall of the exchange, lying at the same plane (flatness of the fall). Kut image γ ancient Kutu fall α
The law of broken light: the falling and bending part, as well as the perpendicular to the intersection of the two middles, at the point of the falling part, lie in the same plane. The ratio of the sine of the cut to the sinus of the bend is a value that is constant for two given media:
The constant value n is called a clear indicator of the fracture of another middle before the first. The display of a broken middle is called, in a vacuum, an absolute display of brokenness.
The average indicator of the fracture of two midpoints is the traditional relationship between their absolute indicators of fracture:
The laws of imagination and distortion can be explained by the Hwyllian physics. Often with symptoms of the spine, it is broken and changes the fluidity of the spine when moving from one medium to another. The physical replacement of the indicator of bending is the difference between the fluidity of the widening of the spine in the first middle?1 to the fluidity of their widening in the other middle?2:
An absolute indicator of the broken state of the light fluidity from the vacuum of the light fluidity? at the middle:
Laws of reflection and bending: γ = α; n 1 sin α = n 2 sin β.
A centerpiece with a smaller absolute display of bending is called optically smaller.
When light transitions from an optically larger center to an optically smaller center n 2< n 1 (например, из стекла в воздух) можно наблюдать явление полного отражения, то есть исчезновение преломленного луча. Это явление наблюдается при углах падения, превышающих некоторый критический угол α пр, который называется предельным углом полного внутреннего отражения (см. рис. 3.1.2).
For kuta padinya α = α pr sin β = 1; value sin α pr = n 2 / n 1< 1.
If the other midpoint is the surface (n 2 ≈ 1), then the formula can be easily rewritten from the view
sin α pr = 1/n,
where n = n 1 > 1 is an absolute indicator of the brokenness of the first middle.
For the border section of the slope-surface (n = 1.5), the critical cut is αpr = 42°, for the water-surface cordon (n = 1.33) αpr = 48.7°.
On the outside there is a mirror light between the water and the surface; S – dot dzherelo light
FOOD 2
Light interference
Light interference is a redistribution of light intensity due to the superposition (superposition) of several coherent light strands. This is accompanied by a range of intensity maxima and minima. This division is called an interference pattern.
Monochromatic hvilya
Monochromatic wave is a strictly harmonic (sinusoidal) wave with constant frequency, amplitude and cob phase.
Coherent ideas
Coherent vibrations are vibrations that sound at the same frequency and the difference in phases of their vibration is constant.
Interference of light fibers
Interference is one of the brightest manifestations of the chylous nature of light. This effect is clearly avoided when two or several light beams are applied. The intensity of light in the area of overlap of beams determines the nature of light and dark darks that are distinguished, and at maximums the intensity is greater, and at minimums less than the sum of the intensities of the beams. When the white light is low, the interference lines appear blurred in different color ranges. We often encounter interference phenomena: the colors of oil stains on the asphalt, the contamination of bugs, the chimera-colored babies on the wings of various snowstorms and beetles - all of which exhibit light interference.
The first experiment to prevent light interference in laboratory minds is due to I. Newton. This creates an interference pattern that occurs when light is reflected in a thin wind tunnel between a flat glass plate and a flat-convex lens with a large radius of curvature (Fig. 3.7.1). The interference pattern is small in appearance of concentric rings, which are called Newton's rings
Newton could not, from the perspective of the corpuscular theory, explain why the rings appear, which is connected with some periodicity of light processes
The first interference evidence, which removed the explanations from the explanations of the Holy Light theory, became the evidence of Jung (1802). Before Jung, the light from the dzherel, in the frame of which served as a thin slit S, fell on the screen with two closely spaced slit S 1 and S 2 (Fig. 3.7.3). Passing through the skin from the crevices, the light beam widened due to diffraction, and on the white screen E the light beams that passed through the gaps S 1 and S 2 overlapped. In the area of overlap of light beams, an interference pattern was observed in the appearance of light and dark browns that alternated.
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| Malyunok 3.7.3. Young's Interference Evidence Scheme |
Jung is the first to realize that it is impossible to prevent interference when the arms are folded into two independent arms. Therefore, in this case, the gaps S 1 and S 2, which are consistent with Huygens’ principle, can be seen as the cores of the secondary cores, illuminated by the light of one core S. With a symmetrical arrangement of the gaps, the secondary cores i, which are released by the sockets S 1 and S 2, are located in the phase, otherwise You must go to the guarding point P at different points r1 and r2. So, the phases of the kolivan, the folding of the needles S 1 and S 2 at point P, seem to be different. Thus, the problem of interference is reduced to the task of combining the same frequency, but with different phases. Statements about those that consist of elements S 1 and S 2 are expanding independently from one another, and in terms of caution, they simply add up, and it is an established fact that they are called the principle of superposition.
A monochromatic (or sinusoidal) wave, which runs directly throughout the radius vector, is recorded in the view
There are no adjustments that could be made to follow the rapid changes in the light field in the optical range; Beware of the magnitude of the flow of energy, which is directly proportional to the square of the amplitude of the electric field of the coil. The physical quantity that is equal to the square of the amplitude of the electric field is usually called intensity: I = A 2 .
Uncomplicated trigonometric transformations are brought to the desired value for the intensity of the resulting vibration at point P:
de Δ = r 2 - r 1 - this is the name of the difference in the move.
This shows that the interference maximum (light dark) is reached at these points in space, at which Δ = mλ (m = 0, ±1, ±2, ...). In Tsyomu I max = (a 1 + a 2) 2 > I 1 + I 2. The interference minimum (dark brown) is reached at Δ = mλ + λ / 2. Minimum intensity value I min = (a 1 – a 2) 2< I 1 + I 2 . На рис. 3.7.4 показано распределение интенсивности света в интерференционной картине в зависимости от разности хода Δ.
Zokrema, since I 1 = I 2 = I 0, then the intensities of both values interact, however, the expression (*) looks like:
When the coordinate axis y is displaced to a distance equal to the width of the interference zone Δl, then when shifted from one interference maximum to the reference one, the difference in stroke Δ changes There is one dovzhina hvili λ. Otje,
de ψ - Where the convergence of “exchanges” is at the point of guarding P. It is acceptable that the distance between the cracks S 1 and S 2 is 1 mm, and the distance from the gaps to screen E becomes L = 1 m, then = d / L = 0.001 rad. For green light (λ = 500 nm), Δl = λ / ψ = 5 10 5 nm = 0.5 mm. For red light (λ = 600 nm) Δl = 0.6 mm. In this way, Jung first died out for a long time in the light years, although the accuracy of these extinctions was low.
It should be noted that in Hvilov optics, instead of geometric optics, the concept of light takes physical place. The term “promin” is used here to indicate the thickness of the spine. Let’s get used to this term without paws.
In Newton's experiment (Fig. 3.7.1), with a normal fall on the flat surface of the lens, the difference in movement is approximately the same as the sub-war 2h of the winding gap between the lens and the plane. For example, if the radius of curvature R of the lens is large at the same level as h, you can approximate:
At r = 0, then at the center (point to the point) Δ = λ/2; Therefore, in the center of Newton's ring, there is always an interference minimum - a dark flame. The radii r m of the advancing dark circles are indicated by the viraz
This formula allows you to experimentally determine the light intensity based on the radius of curvature R of the lens.
Interferometry
Interferometer- a vimirual device, the principle of action of which is based on obvious interference. The operating principle of the interferometer is the same: a beam of electromagnetic interference (light, radio waves, etc.), with the help of another device, is spatially divided into two or more coherent beams. The skin from the beams passes through various optical paths and rotates onto the screen, creating an interference pattern, behind which you can set the phase shift of the beams.
Nutrition 3
Diffraction hvil(Lat. diffractus- Literally breaking, breaking, bending over the spine) - a phenomenon that reveals itself as an evolution from the laws of geometric optics with wide spines. It is a universal phenomenon and is characterized by the same laws for the protection of fields of various natures. 
Diffraction of the first and second order is like the interference of waves created when a flat panel falls onto an impenetrable screen with a pair of slits. Arrows show lines that pass through the lines of interference maxima
Huygens–Fresnel principle- the main postulate of the hvil theory, which describes and explains the mechanism of widening of the hyl, zokrem, light.
The Huygens-Fresnel principle is a recipe for a near solution to diffraction problems. This is based on the assumption that the skin element on the surface of the spine can be seen as a core of secondary spines that are found everywhere (Fig. 2.1). These hulls are coherent, the fragments of the stench are awakened by one and the same primordial hull. The resulting field at the guard point P can be found as a result of the interference of secondary inputs. As the surface of the secondary cores may be covered not only with the surface of the leather front, but also with another closed surface. In this case, the phase and amplitude of the secondary convolutions are determined by the values of the phase and amplitude of the primary convolution.
Consistent with the Huygens-Fresnel principle, the complex amplitude of the field at the point of control P is formed by the action of secondary cores that populate a small element of the surface ds, which can be written in the form
Here is the complex amplitude of the field of the primary spine of the dzherel on the ds element, - the dove of the hvilya (the dzherel is transferred to monochromatic), - so is the coefficient of the nahil, which lies between the normal to the element of the surface ds and the radius - vector. Theoretically, Fresnel is given to a specific type of storage; Much of the theory of light diffraction can be taken into account in this regard. It is important to take into account that the function kuta changes significantly, which takes the value K = 1 at . The type of function was determined by the theory of Kirchhoff (b. 1883), which was explained by the analysis of the decision of the Khvilian Rivne. Also, the propagation of the secondary jets is not isotropic, although the spine fronts (the surfaces of the stationary phase) are spherical.
With a more precise formulation of the Huygens-Fresnel principle, it would be possible to interpret in (2.1) the phase relationship between the vibrations of the secondary engines and the primary engine. In many cases, the exact significance of the colivan phase does not become interesting, so there is no sense in complicating the relationship (2.1). The outside field at point P can be found by the integration path (2.1) behind all the secondary gates.
At the highest diffraction conditions, if there is a widening of light lines near the crossing point, the Huygens-Fresnel principle should be supplemented with the Fresnel postulate about boundary zones.
Let a piece of wood fall onto the screen behind the opening (Fig. 2.2). Fresnel's postulate is based on the possibility of populating the secondary geraniums of only a part of the surface of the vine front, which is not shaded by a screen. Integration of virus (2.1) follows the viscosity on surface S, shown in Fig. 2.2 with a dotted line. When the surface S is shaded by a screen, the amplitude of the secondary signals remains zero. On the open parts of the screen, the field of the primary fluid is transferred undamaged. Fresnel's postulate means that, with integration (2.1), the complex amplitude of the primary line is replaced by , and is written as follows:
Fresnel's postulate, like the Huygens-Fresnel principle, has a similar character. This stagnation will greatly simplify the diffraction task and produce enough practical results for the mind, so that the size of the distortion on which the light diffracts, as well as to stand between the transition and the caution point and the great ones in the same time hvili.
Based on the Huygens-Fresnel principle, it is possible to derive simple solutions to certain diffraction problems (axis symmetry problems, diffraction at one-dimensional transitions). Finally, the diffraction problem is reduced to calculating the integral (2.2)
Fresnel zone method
Fresnel using the original method of breaking the quill surface S on the zone, which made it possible to greatly simplify the assignment of tasks ( Fresnel zone method ).
The cordon of the first (central) zone is the surface point S, what is located at the distance from the point M(Fig. 9.2). Krapki sferi S, what is available at the stations, etc. type of speck M, Do 2, 3, etc. Fresnel zone.
Kolivannya, what will happen at the point M between two vessel zones, the length of the phase, the difference in the course of these zones to the point M .
Therefore, when adding these stench, the stench is mutually responsible for weakening one another:
de A– amplitude of the resulting vibration, – amplitude of the vibration that is generated i th Fresnel zone.
The value lies in the flat zone between the normal to the surface and the straight line, straight to the point M.
Area of one zone
The star shows that the Fresnel area does not lie with the zone number i. Tse means that with small and flat vascular zones, however.
At the same time, as the zone number increases, the zone grows and, therefore, the intensity of the zone’s propagation to the point directly changes. M, then. the amplitude changes. The won also changes through increasing distance to the point M:
There are a large number of Fresnel zones that fit on a part of a sphere formed at a point M, is even greater: with , , the number of zones is , and the radius of the first zone is .
The star is shining, which goes between the normal to the zone and straight to the point M The adjacent zones are approximately equal, then. what amplitudes of the hvil that come from the corner M type of court zones ,approximately equal.
The light spine widens straight. The phases of colivan, which are aroused by the joint zones, are differentiated by π. Therefore, as permissible proximity can be taken into account, the amplitude of the oscillating action m The th zone is equal to the arithmetic mean of the amplitudes of the zones that adjoin it, then.
.
Todi Viraz (9.2.1) can be written as
| . | (9.2.2) |
Since the surface areas of the joint zones are the same, the expressions in the arms reach zero, which means the resulting amplitude.
Intensity of vibration.
In such a manner the resulting amplitude that is created at any point M by the entire spherical surface , more than half the amplitude, which creates one more central zone, and intensity .
So, since the radius of the central zone is small, you can take into account that there is light in front of the point P to the point M expands linearly .
If you put an impenetrable screen with an opening on the road, which deprives the central Fresnel zone of the open area, then the amplitude is exactly M I'll be equal. Apparently, the intensity at the point M will be four times larger, less for the width of the screen (since ). The intensity of the light increases as all the zones are covered.
Thus, the Huygens-Fresnel principle allows us to explain the linear broadening of light in a homogeneous middle.
The validity of the subcutaneous front on the Fresnel zone has been confirmed experimentally. For what purpose are zone plates formed - a system of clear and non-clear rings that are marked.
Evidence confirms that using additional zone scarves you can increase the lightening of the point M, similar to a retractable lens.
Nutrition 4
Diffraction particles
Diffraction particles- an optical device that operates on the principle of light diffraction, i.e. the combination of a large number of regularly spaced strokes (cracks, protrusions) applied to the surface of the glass. The first description of the box was made by James Gregory, who was vikorystuvuv as a thief for the bird.
Nutrition 5
Light polarization
Inheritance of Maxwell's theory (div. § 162) - the cross-section of light coils: vectors of electric stress E and magnetic N The fields of the needles are mutually perpendicular and oscillate perpendicular to the vector of fluidity v the width of the needles (perpendicular to the change). To describe the patterns of light polarization, it is enough to know the behavior of at least one of the vectors. Make sure all the merchandising is carried out well light vector- Tension vector E electric field (this name is due to the fact that when light is applied to the flux, the main significance is the electric storage field of the flue, which is the action of electrons in the atoms of the flux).
Light is the total electromagnetic reflection of the impersonality of atoms. At the same time, the light strands are invariably one type, so the light strands that are promoted by the body as a whole are characterized by all sorts of constant vibrations of the light vector (Fig. 272, a; ін perpendicular to the plane of the baby). Which type has an even distribution of vectors? E is explained by the great number of atomic
viprominyuvachiv, and the equality of the amplitude values of the vectors E- however (in the middle) the intensity of the stimulation of the skin's atoms. Svitlo with all equal vector orientations E(and, father, N) is called natural
The light in which the light vector is directly ordered is called polarized. Thus, as a result of any external inflows there appears to be an important (and not blaming!) direct colivan of the vector E(Fig. 272, b), then on the right partially polarized light. Svetlo, v yakoma vector E(and, father, N) only oscillates in one straight line, perpendicular to the area (Fig. 272, c), is called plane polarized (linearly polarized).
The area that passes through the direct line of the light vector of a plane-polarized coil and the direct width of this coil is called plane of polarization. Plane-polarized light with a boundary drop elliptical polarized light- light, for some vector E(Vector N) changes over time so that its end describes an ellipse that lies near the plane perpendicular to the change. Since the polarization ellipse virtuates (div. § 145) in the direct direction (with a difference in phases j, which is equal to zero or p), then we can look to the right at a more plane-polarized light, as in the colo (at j=±p/2 equal hvil amplitudes, what is being added up), then we can on the right circularly polarized (collar polarized) with light.
Podviyne promenezalomlennya
All crystal openings (including crystals of the cubic system, which are optically isotropic) may be dated undergrowth, i.e. bifurcation of the skin falling light bundle. Tse, 1669 First discovered by the Danish scientist E. Bartholin (1625-1698) for Iceland spar (a type of calcite CaCO 3), it is explained by the peculiarities of the broadening of light in anisotropic middles and directly follows from Maxwell’s level.
If you direct a narrow beam of light onto a solid Icelandic spar crystal, then two spaciously separated channels will emerge from the crystal, one parallel to the other and the falling channel (Fig. 277). In this case, if the first beam falls on the crystal normally, the broken beam is divided into two, and one of them is a continuation of the first one, and the other dies (Fig. 278). Another of these changes, having removed the name non-primary(f) , and the first one - secondary(O).
The Icelandic spar crystal has a single direction, making sure that there is no danger of any kind of submergence. Directly in an optically anisotropic crystal, in which the light channel expands without being subject to bending, is called optically all crystal. Who's going to have to go to hell on her own? about directly, and not about a straight line that passes through any point of the crystal. Even if it is straight, if it runs parallel to this straight line, it will be optical throughout the crystal. Crystals in storage according to the type of their symmetry occur one-spring and two-spring, To wash one or two optical axes (before the first ones are washed with Iceland spar).
The area that passes straight through the light and optical crystal is called head flat(or head cap crystal). Analysis of light polarization (for example, with tourmaline or a glass mirror) shows that what came out of the crystal is plane polarized at mutually perpendicular planes: the change of the light vector (voltage vector E electric field)
Small 11.13
Vipromіnyuvannya of the accurate jerel s, pushed through the polarizer p, the plate q, yak is the serpent of polarizers with polarizas, izhnterphydrofychy smears: ї turn the vector to 2α; To avoid interference smudges through analyzer A, then when rotated by π/2, the picture seen on screen E is inverted: through an additional difference in phases, the darks of the smudges become light and . An analyzer is also necessary here in order to combine two polarized exchanges into one area.
When polarized light passes through a crystalline plate, the difference in the movement between the two components of polarization lies in the thickness of the plate, the middle cut and the difference in the indicators. Obviously, the phase difference is responsible for this
Wrapping the polarization plane.
Wrapping the polarization area transverse spine - a physical phenomenon that lies at the turn of the polarization vector of the linearly polarized transverse spine near the spine vector when the spine passes through the anisotropic middle. The sound can be electromagnetic, acoustic, gravitational, etc.
A linearly polarized transverse coil can be described as a superposition of two circularly polarized coils with the same vector and amplitude. In the isotropic median projection of the field vector, these two tails on the polarization plane fluctuate in phase, their sum is equal to the field vector of the total linearly polarized tail. There is a difference in the phase fluidity of circularly polarized fibers in the midsection (circular anisotropy of the midsection, as well as Podviyne promenezalomlennya), then one of them appears in front of the other, which leads to the appearance of a phase difference between the values of the projections on the selected area. This difference in phases changes with wider growth (in the same middle – linear growth). If you rotate the plane of polarization around the field vector to the point where the same half of the phase difference is present, then the projection of the field vectors onto it will be again in phase - the rotated plane will be the plane of polarization at that moment.
Wrapping of the polarization area of the electromagnetic coil in plasma under an applied magnetic field (Faraday effect).
Thus, the primary reason for the rotation of the polarization plane is the increase in the difference of phases between the circularly polarized warehouses of the linearly polarized coil with its expansion in the circularly anisotropic middle. For electromagnetic radiation, such a middle is called optically active (or gyrotropic.
), for spring transverse hulls - acoustically active. Vidomy also rotates the polarization plane at imaged type of anisotropic middle (div., for example, magneto-optical Kerr effect).
Circular anisotropy of the midsection (and, apparently, the rotation of the plane of polarization of the spine, which expands in it) may lie due to the effects on the midsection of external fields (electric, magnetic) and types of mechanical tension (div. Photospring
). In addition, the stage of anisotropy and the onset of phases, which appear to have started, may lie under the influence of the last phase (dispersion). Where the rotation of the plane of polarization is linear, it is necessary to follow other equal minds until the end of the journey in the active medium. The optically active medium, which consists of a mixture of active and inactive molecules, rotates the polarization area in proportion to the concentration of the optically active substance, which is the basis for the polarimetric method of vibrating the concentration of such substances in different regions; The proportionality coefficient, which relates the rotation of the polarization plane to the increase in the concentration of the speech, is called the petty wrapper of this speech.
In times of acoustics colivans, the turn of the explosion of the polariza, the deprivation of the liche for the cross -shaped bells of the hwille (the okolki for the posdizhnіkh hwil Plaariza Polyarizov) I, the way, can be lichen in hard, the Ale is not in the abstains of the gas.
The general theory of aqueousness transfers the wrapping of the polarization area of the light line in an empty space with an expanded light line in space with various types of metrics due to the parallel transfer of the polarization vector along the zeros Its geodetic trajectory of the light exchange (gravitational Faraday effect or Ritov-Skrotsky effect)
The effect of wrapping the plane of polarization of light is distorted
§ for determining the concentration of optically active substances in different regions (div., for example, Saccharimetry
§ to investigate mechanical stresses in clear bodies;
§ for keruvannaya insight rare crystalline ball in rare crystal indicators(circular anisotropy of the DC lies under the applied electric field).
Schrödinger's Rivne. Zavdannya is a microparticle station, a hvilian function, and a statistical substitution. Superposition of positions in quantum theory. Amplitude of virality. Schrödinger stationary station, stationary stations. Part in a single straight pit. Walking through the area above and below the bar. Harmony oscillator. Elements of quantum electronics. Khvil's functions of stationary stations.
Light interference in thin layers.
Light interference can be prevented in laboratory minds with the help of special installations and devices, and in natural minds. Thus, it is easy to prevent the formation of long-lasting smelts, thin smelts of naphtha and mineral oil on the surface of water, and oxide smelts on the surface of hardened steel parts (no matter the color). All these phenomena are caused by the interference of light in thin transparent layers, which arises as a result of the superimposition of coherent elements that appear when the upper and lower surfaces of the layer are displayed.
Optical difference in the course of exchanges 1 and 2
(6)
De p – indicator of the folded lining; n0 – indicator of bending of the surface, n0 = 1; λ 0 /2 – the last half of the drink spent during the image of exchange 1 at the point between the section with an optically larger core (n >n 0,).
. (7)
The darks of equal weariness and equal comradeship.
The darks of equal strength and equal impudence are avoided by the interference of the forks, broken from two cordons of clear molten material or a plane-parallel plate.
Smogs of equal strength are localized on inconsistency.
The smudges of equal fat are localized in the flat area that deflates the spittle. Between the width of the float, you can take into account that the interference pattern is localized where it is most convenient for you.
To prevent the smoothness of the surfaces that are being beaten, they must be perfectly plane-parallel. A couple of flats that are beaten can create a thin wedge. There may be other surfaces, one or another spherical (Newton rings).
Moreover, the two surfaces that are knocked down can be moved in different places, as in Michelson interferometer (Fig. 28). Here s is the light source, p is the screen to prevent interference from the damaged parts of mirrors 1 and 2, 3 is the display plate. If the mirror 2 thoughts are displayed in the mirror plate 3, the image will take position 2". Together with the mirror, 2 thoughts are displayed in the mirror plate and all the changes, so go right-handed from it to the mirror 2 and go back to the video recorder and go to the screen p. The light will come, the sky will rise from two surfaces 1 and 2". If you add two lenses to the interferometer, which means it will work (Fig. 29), then, by carefully positioning the lens l 2 and the screen p, you can prevent the same compatibility (1/a 1 + 1/a 2 = 1/f 2) or smugi of equal nakhil (a 2 = f 2).
Newton's ring.
Before 
Newton's rings and interference stains that appear when the needles are applied, beaten from the upper and lower surfaces of a thin windscreen, placed between a glass plate and a large lens placed on it th radius of curvature (Fig. 2).
The width of the windshield increases from point n to the edges of the lens. At points p 1 and p 2 equally distant from point n, the size of the ball is the same. On the entire surface of the plate, the uniform ball is rotated along concentric circles centered at point n. If you illuminate the plate-lens system with a parallel beam of monochromatic light, then the illuminated light will have a large number of light and dark concentric rings that alternate with a dark flame in the area points n. These circles of equal comradeship are called Newton's rings. The dark spot in the center of the ring (with caution at the broken light) is explained by the fact that the geometric difference in the path between the forks that interfere in the area of point n is practically equal to zero and is less likely to be lost when good surface of the lens.
The difference in the course of the interfering 1 and 2 D = 2d×n. For a wind ball n = 1. In addition to the indicated difference in the stroke, there is an additional difference in the stroke in the air as a result of the impact of the exchange at the point of the optically larger middle:
In this manner, the difference between the movements 1 and 2 will be:
1). For the dark ones 
(9)
2). For light people, rings 
(10)
De m = 1,2,3…
We expand the radius of Newton's ring r m, which is guarded against the broken light.
From Fig. 3 there is a trace from the rings in order m:
Oskolki d m<<2r, то 2r-d m 2r следовательно:
Substituting formulas (9) and (10) for d m can be eliminated:
1). For dark ringlets (12)
2). For light people, rings 
(13)
These formulas could be calculated by knowing the radius of the ring, the radius of curvature of the lens, and the order of the minimum (or maximum). However, due to the spring deformation of the glass, it is impossible to achieve the ideal thickness of the lens and plate at the point. Therefore, the result will be more accurate if we calculate l by the difference in the diameters of two rings in the order of d k and d m. For dark rings we can:
(14)
In this way, knowing the radius of curvature of the lens and the diameter of the dark interference rings, we can use formula (14) to calculate the dovzhin of the light ring l.
Practical implementation of interference.
Vicious interference in technology. The phenomenon of interference is known to be widely used in modern technology. One of these problems is the use of “coated” optics. The polished glass surface reflects approximately 4% of the light falling on it. Modern optical devices are made up of a large number of parts manufactured from warehouses. Passing through the skin of these parts, the light weakens by 4%. The total light loss in the camera lens is approximately 25%, in stationary binoculars and microscopes - 50% then.
To reduce light losses in optical devices, all glass parts through which light passes are covered with melt, the shape of which is less than that of a broken glass. The thickness of the spit is the last quarter of a century.
Other conditions of interference include the removal of the coatings, which are good for displaying, which are necessary for large optics. For this type of material, a thin spit of l/4 thickness is used, the breaking factor of which is n 2, which is greater than the breaking factor of n 3. In which type of deformation in the anterior boundary is caused by the loss of pvcv, fragments n 1< n 2 , а отражение от задней границы происходит без потери полволны (n 2 >n 3). As a result, the difference between the moves d = l/4+l/4+l/2=l and the vibrations will be equal to each other.
I. C. Widely used in spectral analysis for accurate measurement of parts and cuts, in refractometry, in surface quality control tasks, for the creation of light filters, mirrors, translucent coatings, etc.; on the boxes. S. Holography was founded. An important idiot. S. – interference of polarized exchanges.
Light diffraction. Huygens-Fresnel principle. Fresnel zone. Fresnel diffraction on a small circular opening. Fraunhofer diffraction by one slit. Fraunhofer diffraction on a diffraction grid. Dispersion and separate properties of a diffraction grating.
Lecture No. 8
When light passes through thin melts or through beaten light, bundles of coherent fibers are created on the surface of the thin melts, which can interfere with each other (Fig. 8.1).
Like the spit of tovshchina and the showmanship of the broken a parallel beam of light falls under the cut, then after a series of last beats and breaks at points A, B, C and E, two beams 1" and 1"" are created, broken, and two beams 2" and 2"" have passed through exchange spit . Since the flow is thin, all changes preserve coherence and interference.
Optical difference in the progress of the 1" and 1"" replacements:
.
To remove the residual damage, it is necessary to twist the light strands, as well as other strands that emerge from an optically thicker center (line 1 at point A), to remove the additional The difference between the phases is equal, then. The additional difference is due to the course of the same. Vaughn is avoided at point A for the exchange of 1" after the image of the cordon with an optically larger middle, lower and lower. C, and also when the exchanges are broken, such additives are not required.
From the ABF and FBC trikulets we can remove:
, 
from the tricube ADC:
Doctors who are broken by law
omitable:
,
,
,
,
.
As soon as you come to the bottom of the valley,
Todi with cheers
, ,
negated
,
residual
.
The results of the maximums and minimums of interference in the melted light will be written down as follows:
, .
2. Set the minimum light intensity
, .
Optical difference between 2" and 2"" exchanges, which passed through the old age:
,
.
Don't be afraid to spend your breath in the light that you need to pass through.
The level of maximum or minimum interference in the light that passes through the flow will be recorded as the upcoming order
1. Set the maximum light intensity
, .
2. Set the minimum light intensity
, .
In this way, if in the light that passes through, the mental strength of the light ends (the maximum intensity is established), then in the light that is turned off for the same purpose, the mental weakening ends (the minimum intensity is established) intensity) and in general. This means that in the first phase the spitting is visible in the exchanges, but the passage is not visible in the knocked-out ones, and in the other it is not visible. In this case, the energy of the light veins is overdistributed between the damaged and exchanged exchanges.
As soon as the spittle appears white, the wash is maximally condensed to exchange the last of the liquid, then. The spit is being prepared. The butt is a rainbow of colors of thin spittle that sit on the surface of water, covered with a thin ball of petroleum products, spittle of oxides, the surface of mile spittle, etc.
If bundles of exchanges (which diverge or converge) fall on the same plane-parallel flow, then after the formation or bending of the exchanges, which fall under one and the same coil, they will interfere.
For some values the mind is equal to the maximum, for other values the mind is equal to the minimum. In this case, there is an interference pattern on the screen, which was called the dark of equal nahil. For different darks, there is a difference. Darkness of equal weakness is localized in inconsistency and can be avoided with a simple eye, adapted to inconsistency.
If a parallel beam of light () falls on a single flot of a variable material, then after emitting from the upper and lower edges of the flot, they move near the upper surface of the float and interfere. On the surface of the melt there is an interference pattern that is called the dark of equal comradeship.
The configuration of the smudge is indicated by the shape of the spittle; the smudge represents the geometric location of the points at which the spittle has the same thickness. The darks of equal weariness are localized on the surface.
Smudges of equal nakhil (interference from a plane-parallel plate)
In nature, it is often possible to observe a rainbow formation of thin spilts (oil spilts on water, small bulbs, oxide spilts on metals), which results from the interference of light that appears on the two surfaces of the spilt.
Place a plate with a folded display on a plane parallel to the view n those bosses d under the bush q(Fig. 4.4) a flat monochromatic hvil falls 1 .
On the surface of the spit, at point A, the groove will split into two: it will often ripple past the upper surface of the spit, and will often break. The fractures that have reached point B often break in the wind ( n = 1), and often appears and goes to the point Z. Khvilya (promin) 2 , what falls under the same pile that is washed away 1 , exactly Z, also appear. Please remember that you are out of the woods 1 and beaten 2 go in one direction and are coherent, since their optical difference in the course is small, equal with the great coherence of the falling tail. If you put a lens on their side that collects, then it will go to one point of the focal plane of the lens and give an interference pattern on the screen, which is indicated by optical difference.
There is an optical difference in the course that occurs between the two exchanges that interfere, with the preservation of the energy consumption when the light is displayed in the form of an optically larger center at the point Z more expensive:
.
The minds of the interference maxima and minima will be remarkably equal:
max 
min 
.
On the screen there is a system of light and dark rings that are drawn from the dark center. Descriptions of the interferential dark sound like a dark skin of equal nahila, the fragments of the skin dark are created in exchange with the new coats of the fall. When the scarf is illuminated with solar light, interference is avoided only in the event that the thickness of the scarf does not exceed several hundredths of a millimeter. When bleaching light with a higher degree of coherence (for example, laser propagation), interference is avoided when imaging solid plates or melts.
Smudges of equal commerce (interference from the payment of equal commerce).
Newton's ring
When the melt (plate) is lightened with a parallel beam of light on its surface, a system of interference darks appears on its surface. The skin is dark due to the size of the scarf, which is suitable for wearing clothes (the thickness of the plate can be changed quite a bit). Interference problems that arise as a result of interference in the world of the new society are called the darks of equal comradeship. Butt of the dark of equal comradeship
is Newton's ring. Newton's rings are protected by the reflection of light from a plane-parallel solid glass plate that sticks one after another, and a flat-convex lens with a large radius of curvature (Fig. 4.5). The role of the thin lining, on the surface of which coherent strands are beaten, is played by the winding gap (with the lining that changes) b
) between the plate and the lens. With a normal fall, the dark of the dark of equal tyranny has the appearance of concentric rings, with a weak fall - ellipses.
The radii of Newton's light and dark rings can be found using the following formula:
, m =
1, 2, 3
Paired m are represented by the radii of light rings, and unpaired m are represented by the radius of dark rings. significance m= 1 confirms r= 0, then. point in the place of torning of the plate and lenses. At this point, a minimum intensity is avoided, as a result of a phase change to p with a light colored tail visible as a scarf.
The darks of equal comradeship can also be avoided by a wedge-shaped plate. These interferential darks are parallel to the edge of the wedge.
Enlightened optics
Interference during the reflection of thin layers is the basis for the brightening of optics. The passage of light through the skin surface of the lens, which breaks, is accompanied by the reflection of approximately 4% of the incident light. In folding lenses, such images are generated abundantly, and the total loss of light flux reaches a noticeable value. Vibration on the surface of the lenses leads to the appearance of glare. In the case of enlightened optics, the appearance of light has been reduced to the skin surface of the lens by applying a thin liquid of speech with a folded surface underneath the lens. The thickness of the spittle is selected so that the spittle from both surfaces extinguishes one another. A particularly good result is achieved if the angle of the fused sliver is equal to the square root of the squared axis of the lens. However, the intensity of both battered surfaces of the melt is the same.