If the light coming from one source is divided in a certain way, for example, into two beams, and then they are superimposed on each other, then the intensity in the region of superposition of the beams will change from one point to another. In this case, at some points, an intensity maximum is reached, which is greater than the sum of the intensities of these two beams, and a minimum, where the intensity is equal to zero. This phenomenon is called light interference. If the creeping beams of light are strictly monochromatic, then interference always occurs. This, of course, cannot apply to real light sources, since they are not strictly monochromatic. The amplitude and phase of a natural light source is subject to continuous fluctuations, and they occur very quickly so that the human eye or a primitive physical detector cannot detect these changes. In beams of light that come from different sources, the fluctuations are absolutely independent; such beams are said to be mutually incoherent. When such sources of interference are superimposed, no interference is observed; the total intensity is equal to the sum of the intensities of individual light beams.
Methods for obtaining interfering light beams
There are two common method receive beams of light that can interfere. These methods underlie the classification of devices that are used in interferometry.
In the first of them, the beam of light is divided when passing through holes that are located close to each other. This method is called the wavefront division method. It is only applicable if small light sources are used.
The first experimental setup to demonstrate the interference of light was made by Jung. In his experiment, light from a point monochromatic source fell on two small holes in an opaque screen, which were located close to each other at equal distances from the light source. These holes in the screen became secondary sources of light, light beams, emanating from which could be considered coherent. Beams of light from these secondary sources overlap, an interference pattern is observed in the region of their overlap. The interference pattern consists of a combination of light and dark bands, which are called interference fringes. They are at equal distances from each other and directed at right angles to the line that connects the secondary light sources. Interference fringes can be observed in any plane of the overlap region of divergent beams from secondary sources. Such interference fringes are called non-localized.
In the second method, the light beam is divided by one or more surfaces that partly reflect and partly transmit light. This method is called the amplitude division method. It can be used for extended sources. Its plus is that with its help a greater intensity is obtained than the method of dividing the front.
An interference pattern, which is obtained by dividing the amplitude, can be obtained if a plane-parallel plate of a transparent material is illuminated with light from a point source of quasi-monochromatic light. At the same time, two beams come to any point that is on the same side as the light source. One of them was reflected from the upper surface of the plate, the other was reflected from its lower surface. The reflected rays interfere and form an interference pattern. In this case, the stripes in planes that are parallel to the plate have the form of rings, with an axis normal to the plate. The visibility of such rings decreases as the size of the light source increases. If the observation point is at infinity, then the observation is carried out with an eye that is adapted to infinity or in the focal plane of the telescope objective. The rays reflected from the upper and lower surfaces of the plate are parallel. The bands resulting from the interference of rays incident on the film at the same angles are called bands of equal slope. (For more information about interference in a plane-parallel plate, see the section "Interference in thin films")
Examples of problem solving
EXAMPLE 1
| Exercise | What is the position of the second light band in Young's experiment, if the distance between the slits is b, the distance from the slits to the screen is l. The slits are illuminated with monochromatic light with a won length equal to . |
| Solution | Let us depict the situation of light passing from holes ( and ) to the screen in Young's experiment (Fig. 1). The screen is parallel to the plane in which the holes are located. We find the difference in the path of the rays, based on Fig. 1:
The maximum condition for interfering light rays (see the "Light Interference" section): According to the condition of the problem, we are interested in the position of the second interference fringe, therefore: . Applying expressions (1.1) and (1.2), we obtain:
Let us express from formula (1.3):
|
| Answer |  m |
EXAMPLE 2
| Exercise | In Young's experiment, on the path of one of the rays emanating from the secondary source, a thin glass plate with a refractive index n was placed perpendicular to this beam. In this case, the central maximum shifted to the position previously occupied by maximum number m. What is the thickness of the plate if the wavelength of light is ? |
| Solution | The difference in the path of the rays in the presence of a plate, given that the beam falls on the plate along the normal, we write as: |
Of the same frequency, then at the meeting point arises interference pattern. However, if we try to set up the same experiment using two independent light sources emitting the same light, then no interference pattern will arise - at the meeting point of both waves, we will simply observe the summation of the light intensities.
In 1675, Newton created a special installation " Newton's rings which allowed him to observe interference, but he did not find an explanation for the origin of light maxima and minima.
In 1801, Thomas Young was able to observe the interference of light using the installation:
.
Bright Light source C enters the slot S. When the light wave goes around the edges of this slot, i.e. there is a phenomenon diffraction, it illuminates two narrow slits S 1 and S 2 . Due to the phenomenon of diffraction, two waves emerge from both slits, which partially overlap each other. Interference occurs in this region, and on screen M one can see a system of interference maxima and minima, which appear in the form of fringes. Thomas Young explained the origin of these fringes as a phenomenon of wave interference and calculated wavelength, having received the value λ ≈ 5 10 -7 m.
In addition to the Young installation, a number of other devices have been developed that make it possible to see the occurrence of light interference.
If the screen with slit S is removed in Young's setup, then the light source will directly illuminate the slits S 1 and S 2 . In this case, the interference pattern will disappear. But removing the slot S does not change frequency response of light, and both slots - S 1 and S 2 - transmit light waves with the same frequency.
It can be seen that in the case when the condition of frequency equality is sufficient for the occurrence of interference from the addition of sinusoidal waves, and for light waves this condition is not enough. The reason lies in the non-sinusoidality of light waves, which plays a decisive role in the case of interference.
When added incoherent waves no interference; the average intensity of the wave at any point is equal to the sum of the intensities of the terms of the incoherent waves.
The interference pattern appears only in the case of addition coherent light waves. This makes it possible to explain the presence of slot S in Young's experiment. In this setup, both slots S 1 and S 2 lie on the same wave front and are excited by one common train(by a number of perturbations with breaks between them) emanating from the slit S. Therefore, light waves with the same phase emanate from both slits, i.e., coherent waves that give an interference pattern on the screen.
If the slot S is removed, then the slots S 1 and S 2 will be excited by different trains that originate from different sections Sveta. The waves coming from both slits will be incoherent and the interference pattern will disappear.
At each point, two waves propagating in space give the geometric sum of their oscillations. This principle is called superposition of waves. This law is observed with incredible accuracy. However, in rare cases it may be ignored. This applies to situations in which waves propagate in complex media, when their intensity (amplitude) becomes very large. This principle means that for some electromagnetic waves propagating in a certain medium, the medium itself responds in a very specific way - it reacts to only one wave, as if there were no others nearby. Mathematically, this means that at any point in the selected medium, the strength and induction of the electromagnetic field will be equal to the vector sum of the magnetic inductions and strengths of all the combined fields. Due to the principle of superposition of electromagnetic waves, phenomena such as diffraction and interference of light arise. They are interesting from a physical point of view, in addition, they amaze with their beauty.
What is interference?
This phenomenon can be considered only in compliance with special conditions. Light interference is the formation of attenuation and amplification bands that alternate with each other. One of the important conditions is the imposition of electromagnetic waves (beams of light) on top of each other, and their number should be from two or more. The standing wave is a special case. It should be noted that interference is a purely wave effect, applicable not only to light. In a standing wave, which is formed due to superimposition on a reflected or incident wave, intensity maxima (antinodes) and minima (nodes) of intensity are observed, which alternate with each other.
Basic conditions
Wave interference is due to their coherence. What does this term mean? Coherence is the consistency of waves in phase. If two waves that come from different sources are superimposed on each other, then their phases will change randomly. Light waves are a consequence of the radiation of atoms, so each of them is the result of the superposition of a huge number of components.
Lows and Highs
For the appearance of "correct" amplifications and attenuations of the total waves in space, it is necessary that the added components at the selected point cancel each other out. That is, for a long time, electromagnetic waves would have to be in antiphase so that the phase difference would always remain the same. The maximum appears at the moment when the component waves are in the same phase, that is, when they are amplified. Light interference is observed under the condition of a constant phase difference at a given point. And such waves are called coherent.
natural sources
When can one observe such a phenomenon as light interference? Radiated electromagnetic waves from natural sources are incoherent because they are generated randomly by different atoms, usually completely inconsistent with each other. Each individual wave released by an atom is a segment of a sinusoid, absolutely coherent with itself. Thus, it is necessary to divide into two or more beams one stream of light that comes from the source, and then superimpose the resulting beams on top of each other. In this case, we will be able to observe the minima and maxima of such a phenomenon as light interference.
Watching Overlapping Waves
As mentioned above, light interference is a very broad concept in which the result of adding light beams in intensity is not equal to the intensity of individual beams. As a result of this phenomenon, there is a redistribution of energy in space - the same minima and maxima are formed. That is why the interference pattern is just an alternation of dark and light bands. If you use white light, then the stripes will be painted in a variety of colors. But when in ordinary life do we encounter light interference? This happens quite often. Its manifestations include oil stains on asphalt, soap bubbles with their iridescent tints, the play of light on the surface of hardened metal, drawings on the wings of a dragonfly. This is all the interference of light in thin films. In fact, observing this effect is not as easy as it might seem. If two identical lamps are lit, their intensities add up. But why is there no interference effect? The answer to this question lies in the absence of such an overlay of the most important condition - the coherence of the waves.
Fresnel biprism
To obtain an interference pattern, let's take a source, which is a narrow illuminated slit installed parallel to the edge of the biprism itself. The wave coming from it will split in two due to refraction in the halves of the biprism and reach the screen in two different ways, that is, have a path difference. On the screen, in that part of it where the beams of light from the halves of the biprism overlap, alternating dark and light stripes appear. The stroke difference is limited for some reasons. In each act of radiation, an atom releases a so-called wave train (systems of electromagnetic waves), which propagates in space and time, maintaining its sinusoidality. The duration of this train is limited by the damping of the natural vibrations of a particle (electron) in the atom and the collisions of this atom with others. If white light is passed through a biprism, then color interference can be seen, as was the case with thin films. If the light is monochromatic (from an arc discharge in some gas), then the interference pattern will simply be light and dark stripes. This means that the wavelengths of different colors are different, that is, light is of different colors and is characterized by a difference in wavelengths.
Getting superimposed waves
An ideal light source is a laser (quantum generator), which is by its nature a coherent source of stimulated radiation. The length of a coherent laser train can reach thousands of kilometers. It is thanks to quantum generators that scientists have created a whole area of modern optics, which they called coherent. This branch of physics is incredibly promising in terms of technical and theoretical advances.
Areas of application of the effect
In a broad sense, the concept of "light interference" is a modulation in space of the energy flow and its state of radiation (polarization) in the area of intersection of several electromagnetic waves (two or more). But where is this effect used? The use of light interference is possible in various fields of technology and industry. For example, this phenomenon is used to carry out precision control of the surfaces of machined products, as well as mechanical and thermal stresses in parts, to measure the volumes of various objects. Also, the interference of light has found application in microscopy, in the spectroscopy of infrared and optical radiation. This phenomenon underlies modern three-dimensional holography and active Raman spectroscopy. Basically, interference, as can be seen from the examples, is used for high-precision measurements and calculation of refractive indices in different media.
17.2. Methods for obtaining interference patterns.
There are a number of ways to obtain interference patterns: Young method, Fresnel mirrors, Fresnel biprism etc. Let us consider Young's method in detail.
The source of the set is a brightly lit gap S(Fig. 17.3), from which the light wave falls on two narrow equidistant slots and 
, parallel slots S. Thus, the slits play the role of coherent sources. The interference pattern is observed on the screen ( E) located at some distance from the slots 
and 
. In this setting, Jung made the first observation of interference.
17.3. Interference in thin films.
Plate of constant thickness. When a light wave falls on a thin transparent plate (or film), reflection occurs from both surfaces of the plate. As a result, two light waves arise, which, under certain conditions, can interfere.
Let a plane light wave (a parallel beam of light) fall on a transparent plane-parallel plate (Fig. 17.4). As a result of reflections from the surfaces of the plate, part of the light returns to the original medium.
Two rays come to any point P located on the same side of the plate as the source. These rays form an interference pattern.
To determine the type of stripes, one can imagine that the rays come out of imaginary images S 1 and S 2 sources S created by the surfaces of the plate. On a remote screen located parallel to the plate, the interference fringes look like concentric rings centered on a perpendicular to the plate passing through the source. S. This experience imposes less stringent requirements on the size of the source S than the experiments discussed above. Therefore, it is possible as S use a mercury lamp without an auxiliary screen with a small hole, which provides a significant luminous flux. Using a piece of mica (0.03 - 0.05 mm thick) you can get a bright interference pattern directly on the ceiling and on the walls of the auditorium. The thinner the plate, the larger the scale of the interference pattern, i.e. more distance between the stripes.
Stripes of equal slope. Particularly important is the special case of interference of light reflected by two surfaces of a plane-parallel plate, when the observation point P is at infinity, i.e. observation is carried out either with an eye accommodated to infinity, or on a screen located in the focal plane of a converging lens (Fig. 17.5).
In this case, both beams coming from S To P, are generated by one incident beam and after reflection from the front and back surfaces of the plate are parallel to each other. The optical path difference between them at a point P same as line DC:
Here n is the refractive index of the plate material. It is assumed that there is air above the plate; . Because 
,
(h is the thickness of the plate, 
and 
are the angles of incidence and refraction on the upper face; 
), then for the path difference we obtain
It should also be taken into account that when a wave is reflected from the upper surface of the plate, in accordance with the Fresnel formulas, its phase changes by π. Therefore, the phase difference δ of the added waves at the point P is equal to:
,
where 
is the wavelength in vacuum.
In accordance with the last formula, the light stripes are located in places for which 
, where m
– interference order. The band corresponding to a given order of interference is due to light falling on the plate at a well-defined angle α. Therefore, these bands are called interferencestripes of equal slope.
If the objective axis is perpendicular to the plate, the fringes look like concentric rings centered at the focus, with the maximum order of interference in the center of the picture.
Stripes of equal slope can be obtained not only in reflected light, but also in light transmitted through the plate. In this case, one of the rays passes directly, and the other after two reflections on the inside of the plate. However, the visibility of the bands is low.
To observe bands of equal slope, instead of a plane-parallel plate, it is convenient to use michelson interferometer (fig.17.6). Consider the scheme of the Michelson interferometer: z1 and z2 are mirrors. The translucent mirror is silver-plated and divides the beam into two parts - beam 1 and 2. Beam 1, reflected from z1 and passing, gives, and beam 2, reflected from z2 and further from, gives. The plates are the same in size. It is placed to compensate for the difference in the path of the second beam. Rays are coherent and interfere.
Stripes of equal thickness (wedge interference). We have considered interference experiments in which the division of the amplitude of a light wave from a source occurred as a result of partial reflection on the surfaces of a plane-parallel plate. Localized bands with an extended source can also be observed under other conditions. It turns out that for a sufficiently thin plate or film (whose surfaces do not have to be parallel and generally flat), one can observe an interference pattern localized near the reflecting surface. The bands that appear under these conditions are called stripes of equal thickness . In white light, the interference fringes are colored. Therefore, this phenomenon is called colors of thin films. It is easy to observe on soap bubbles, on thin films of oil or gasoline floating on the surface of water, on oxide films that appear on the surface of metals during quenching, etc.
Consider the interference pattern obtained from plates of variable thickness (from a wedge).
The directions of propagation of the light wave reflected from the upper and lower boundaries of the wedge do not coincide (Fig. 17.7). The reflected and refracted rays meet, so the interference pattern when reflected from the wedge can be observed without using a lens if the screen is placed in the plane of the points of intersection of the rays (the lens of the eye is placed in the desired plane).
Interference will be observed only in the 2nd region of the wedge, since in the 1st region the optical path difference will be greater than the coherence length.
Point interference result 
and the screen is determined by the well-known formula 
,
substituting into it the thickness of the film at the point of incidence of the beam ( 
or 
). The light must be parallel (): if two parameters change simultaneously b and α, then there will be no stable interference pattern.
Since the difference in the path of the rays reflected from different parts of the wedge will not be the same, the illumination of the screen will be uneven, there will be dark and light stripes on the screen (or colored stripes when illuminated with white light, as shown in Fig. 17.8). Each of these bands arises as a result of reflection from sections of the wedge with the same thickness, therefore they are called stripes of equal thickness .
Newton's rings. Figure 17.9 shows a frame in which two glass plates are clamped. One of them is slightly convex, so that the plates touch each other at some point. And at this point, something strange is observed: rings appear around it. In the center they are almost uncolored, a little further they shimmer with all the colors of the rainbow, and towards the edge they lose their color saturation, fade and disappear.
This is how the experiment that in the 17th century laid the foundation for modern optics looks like. Newton studied this phenomenon in detail, discovered patterns in the arrangement and color of the rings, and also explained them on the basis of the corpuscular theory of light.
Ringstripes of equal thickness observed in the air gap between the contacting convex spherical surface of a lens of small curvature and a flat glass surface are calledNewton's rings .
|
|
The common center of the rings is located at the point of contact. In reflected light, the center is dark, since when the thickness of the air gap is much smaller than the wavelength , the phase difference of the interfering waves is due to the difference in the conditions of reflection on two surfaces and is close to π. Thickness h air gap is related to distance r to touch point:
.
Here the condition is used 
. When observed along the normal, the dark bands, as already noted, correspond to the thickness 
, so for the radius 
m th dark ring we get
(m
= 0, 1, 2, …).
If the lens is gradually moved away from the glass surface, then the interference rings will shrink towards the center. As the distance increases, the picture takes on its former form, since the place of each ring will be occupied by a ring of the next order. With the help of Newton's rings, as in Young's experiment, one can approximately determine the wavelength of light by relatively simple means.
So, stripes of equal slope obtained by illuminating a plate of constant thickness scattered light, which contains rays of different directions. Stripes of equal thickness observed when illuminating a plate of variable thickness(wedge) parallel beam of light. Bands of equal thickness are localized near the plate.
| " |
Interference patterns are light or dark bands that are caused by beams that are in phase or out of phase with each other. When superimposed, light and similar waves add up if their phases coincide (both in the direction of increase and decrease), or they compensate each other if they are in antiphase. These phenomena are called constructive and destructive interference, respectively. If a beam of monochromatic radiation, all of which have the same wavelength, passes through two narrow slits (the experiment was first carried out in 1801 by Thomas Young, an English scientist who, thanks to him, came to the conclusion about the wave nature of light), the two resulting beams can be directed on a flat screen, on which, instead of two overlapping spots, interference fringes are formed - a pattern of evenly alternating light and dark areas. This phenomenon is used, for example, in all optical interferometers.
Superposition
The defining characteristic of all waves is superposition, which describes the behavior of superimposed waves. Its principle is that when more than two waves are superimposed in space, the resulting perturbation is equal to the algebraic sum of the individual perturbations. Sometimes this rule is violated for large perturbations. This simple behavior leads to a number of effects, which are called interference phenomena.
The phenomenon of interference is characterized by two extreme cases. In the constructive maxima of the two waves coincide, and they are in phase with each other. The result of their superposition is an increase in the perturbing effect. The amplitude of the resulting mixed wave is equal to the sum of the individual amplitudes. And, conversely, in destructive interference, the maximum of one wave coincides with the minimum of the second - they are in antiphase. The amplitude of the combined wave is equal to the difference between the amplitudes of its constituent parts. In the case when they are equal, the destructive interference is complete, and the total perturbation of the medium is equal to zero.
Young's experiment
The interference pattern from two sources clearly indicates the presence of overlapping waves. suggested that light is a wave that obeys the principle of superposition. His famous experimental achievement was the demonstration of constructive and destructive in 1801. The modern version of Young's experiment differs essentially only in that it uses coherent light sources. The laser uniformly illuminates two parallel slits in an opaque surface. Light passing through them is observed on a remote screen. When the width between the slits significantly exceeds the wavelength, the rules of geometric optics are followed - two illuminated areas are visible on the screen. However, as the slits approach each other, the light diffracts, and the waves on the screen overlap each other. Diffraction itself is a consequence of the wave nature of light and is another example of this effect.
interference pattern
Determines the resulting intensity distribution on the illuminated screen. An interference pattern occurs when the path difference from the slit to the screen is equal to an integer number of wavelengths (0, λ, 2λ, ...). This difference ensures that the highs arrive at the same time. Destructive interference occurs when the path difference is an integer number of wavelengths shifted by half (λ/2, 3λ/2, ...). Jung used geometric arguments to show that superposition results in a series of evenly spaced fringes or patches of high intensity corresponding to areas of constructive interference separated by dark patches of full destructive interference.
Distance between holes
An important parameter of the double-slit geometry is the ratio of the light wavelength λ to the distance between the holes d. If λ/d is much less than 1, then the distance between the fringes will be small and no overlap effects will be observed. By using closely spaced slits, Jung was able to separate the dark and light areas. Thus, he determined the wavelengths of the colors of visible light. Their extremely small magnitude explains why these effects are observed only under certain conditions. To separate areas of constructive and destructive interference, the distances between the sources of light waves must be very small.
Wavelength
Observing interference effects is challenging for two other reasons. Most light sources emit a continuous spectrum of wavelengths, resulting in multiple interference patterns superimposed on each other, each with its own spacing between fringes. This cancels out the most pronounced effects, such as areas of complete darkness.
coherence
In order for interference to be observed over an extended period of time, coherent light sources must be used. This means that the radiation sources must maintain a constant phase relationship. For example, two harmonic waves of the same frequency always have a fixed phase relationship at every point in space - either in phase, or in antiphase, or in some intermediate state. However, most light sources do not emit true harmonic waves. Instead, they emit light in which random phase changes occur millions of times per second. Such radiation is called incoherent.
Ideal source - laser
Interference is still observed when waves of two incoherent sources are superimposed in space, but the interference patterns change randomly, along with a random phase shift. including the eyes, cannot register a rapidly changing image, but only a time-averaged intensity. The laser beam is almost monochromatic (i.e., consists of one wavelength) and highly coherent. It is an ideal light source for observing interference effects.
Frequency detection
After 1802, the wavelengths of visible light measured by Jung could be related to the insufficiently precise speed of light available at the time to approximate its frequency. For example, for green light it is about 6×10 14 Hz. This is many orders of magnitude higher than the frequency. For comparison, a person can hear sound with frequencies up to 2×10 4 Hz. What exactly fluctuated at such a rate remained a mystery for the next 60 years.
Interference in thin films
The observed effects are not limited to the double slit geometry used by Thomas Young. When rays are reflected and refracted from two surfaces separated by a distance comparable to the wavelength, interference occurs in thin films. The role of the film between the surfaces can be played by vacuum, air, any transparent liquids or solids. In visible light, interference effects are limited to dimensions of the order of a few micrometers. A well-known example of a film is a soap bubble. The light reflected from it is a superposition of two waves - one is reflected from the front surface, and the second - from the back. They overlap in space and stack with each other. Depending on the thickness of the soap film, the two waves can interact constructively or destructively. A complete calculation of the interference pattern shows that for light with one wavelength λ, constructive interference is observed for a film thickness of λ/4, 3λ/4, 5λ/4, etc., and destructive interference is observed for λ/2, λ, 3λ/ 2, ...
Formulas for calculation
The phenomenon of interference has found many applications, so it is important to understand the basic equations related to it. The following formulas allow you to calculate various quantities associated with interference for the two most common interference cases.
The location of light bands in ie areas with constructive interference can be calculated using the expression: y bright. =(λL/d)m, where λ is the wavelength; m=1, 2, 3, ...; d - distance between slots; L is the distance to the target.
The location of dark bands, i.e., areas of destructive interaction, is determined by the formula: y dark. =(λL/d)(m+1/2).
For another type of interference - in thin films - the presence of a constructive or destructive superposition determines the phase shift of the reflected waves, which depends on the thickness of the film and its refractive index. The first equation describes the case where there is no such shift, and the second describes the half-wavelength shift:
Here λ is the wavelength; m=1, 2, 3, ...; t is the path traveled in the film; n is the refractive index.
observation in nature
When the sun shines on the soap bubble, bright bands of color can be seen as the different wavelengths are subject to destructive interference and are removed from the reflection. The remaining reflected light appears as complementary to distant colors. For example, if there is no red component as a result of destructive interference, then the reflection will be blue. Thin films of oil on water produce a similar effect. In nature, the feathers of some birds, including peacocks and hummingbirds, and the shells of some beetles appear iridescent, but change color as the viewing angle changes. The physics of optics here is the interference of reflected light waves from thin layered structures or arrays of reflective rods. Similarly, pearls and shells have an iris, thanks to the superposition of reflections from several layers of mother-of-pearl. Gemstones such as opal exhibit beautiful interference patterns due to the scattering of light from regular patterns formed by microscopic spherical particles.
Application
There are many technological applications of light interference phenomena in Everyday life. The physics of camera optics is based on them. The usual anti-reflective coating of lenses is a thin film. Its thickness and refraction are chosen to produce destructive interference of reflected visible light. More specialized coatings, consisting of several layers of thin films, are designed to transmit radiation only in a narrow range of wavelengths and, therefore, are used as light filters. Multilayer coatings are also used to increase the reflectivity of astronomical telescope mirrors, as well as laser optical cavities. Interferometry - precise measurement methods used to record small changes in relative distances - is based on the observation of shifts in dark and light bands created by reflected light. For example, measuring how the interference pattern will change allows you to set the curvature of the surfaces of optical components in fractions of the optical wavelength.
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