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 in spaceIf more than two waves are superimposed, then 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 series of effects 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 component parts. In the case when they are equal, the destructive interference is complete, and the total perturbation of the medium is zero.
Jung's experiment
The interference pattern from two sources clearly indicates the presence of overlapping waves. Thomas Jung suggested that light is a wave that obeys the principle of superposition. His famous experimental achievement was the demonstration of constructive and destructive interference of light in 1801. The modern version of Young's experiment is essentially different 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 slots is much greater thanwavelength, the rules of geometric optics are observed - 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
The principle of superposition 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 total 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 onlyunder 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 total 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 each 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.
The ideal source is a 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. Light sensors, including eyes, cannot register quicklychanging image, but only the 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, Jung's measured wavelengths of visible light 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 6×1014 Hz. This is many orders of magnitude higher than the frequency of mechanical vibrations. In comparison, a human can hear sound with frequencies up to 2×104 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 soapfilm, 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 bright fringes in Young's experiment, i.e. areas with constructive interference, can be calculated using the expression: ybright.=(λL/d)m, where λ is the wavelength; m=1, 2, 3, …; d is the 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: ydark.=(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 of the absence of such a shift, and the second describes a half-wavelength shift:
2nt=mλ;
2nt=(m+1/2) λ.
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 a soap bubble, bright colored bands can be seen as 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, due 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 ofseveral layers of thin films are designed to transmit radiation only in a narrow wavelength range 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, a precise measurement technique used to detect 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 determine the curvature of the surfaces of optical components in fractions of the optical wavelength.
