interference

View more Science videos

For more information on interference, visit Britannica.com.

Concept

When two or more waves interact and combine, they interfere with one another. But interference is not necessarily bad: waves may interfere constructively, resulting in a wave larger than the original waves. Or, they may interfere destructively, combining in such a way that they form a wave smaller than the original ones. Even so, destructive interference may have positive effects: without the application of destructive interference to the muffler on an automobile exhaust system, for instance, noise pollution from cars would be far worse than it is. Other examples of interference, both constructive and destructive, can be found wherever there are waves: in water, in sound, in light.

How It Works

Waves

Whenever energy ripples through space, there is a wave. In fact, wave motion can be defined as a type of harmonic motion (repeated movement of a particle about a position of equilibrium, or balance) that carries energy from one place to another without actually moving any matter. A wave on the ocean is an example of a mechanical wave, or one that involves matter; but though the matter moves in place, it is only the energy in the wave that experiences net movement.

Wave motion is related to oscillation, a type of harmonic motion in one or more dimensions. There is one critical difference, however: oscillation involves no net movement, only movement in place, whereas the harmonic motion of waves carries energy from one place to another. Yet, individual waves themselves are oscillating even as the overall wave pattern moves.

A transverse wave forms a regular up-and-down pattern in which the oscillation is perpendicular to the direction the wave is moving. Ocean waves are transverse, though they also have properties of longitudinal waves. In a longitudinal wave, of which a sound wave is the best example, oscillation occurs in the same direction as the wave itself.

Parameters of Wave Motion

Some waves, composed of pulses, do not follow regular patterns. However, the waves of principal concern in the present context are periodic waves, ones in which a uniform series of crests and troughs follow each other in regular succession. Periodic motion is movement repeated at regular intervals called periods. In the case of wave motion, a period (represented by the symbol T) is the amount of time required to complete one full cycle of the wave, from trough to crest and back to trough.

Period can be mathematically related to several other aspects of wave motion, including wave speed, frequency, and wavelength. Frequency (abbreviated f) is the number of waves passing through a given point during the interval of one second. It is measured in Hertz (Hz), named after nineteenth-century German physicist Heinrich Rudolf Hertz (1857-1894), and a Hertz is equal to one cycle of oscillation per second. Higher frequencies are expressed in terms of kilohertz (kHz; 10³ or 1,000 cycles per second) or megahertz (MHz; 10⁶ or 1 million cycles per second.) Wavelength (represented by the symbol abbreviated λ, the Greek letter lambda) is the distance between a crest and the adjacent crest, or a trough and an adjacent trough, of a wave. The higher the frequency, the shorter the wavelength.

Another parameter for describing wave motion—one that is mathematically independent from the quantities so far described—is amplitude, or the maximum displacement of particles from a position of stable equilibrium. For an ocean wave, amplitude is the distance from either the crest or the trough to the level that the ocean would maintain if it were perfectly still.

Superposition and Interference

Superposition

The principle of superposition holds that when several individual but similar physical events occur in close proximity, the resulting effect is the sum of the magnitude of the separate events. This is akin to the popular expression, "The whole is greater than the sum of the parts," and it has numerous applications in physics.

Where the strength of a gravitational field is being measured, for instance, superposition dictates that the strength of that field at any given point is the sum of the mass of the individual particles in that field. In the realm of electromagnetic force, the same statement applies, though the units being added are electrical charges or magnetic poles, rather than quantities of mass. Likewise, in an electrical circuit, the total current or voltage is the sum of the individual currents and voltages in that circuit.

Superposition applies only in equations for linear events—that is, phenomena that involve movement along a straight line. Waves are linear phenomena, and, thus, the principle describes the behavior of all waves when they come into contact with one another. If two or more waves enter the same region of space at the same time, then, at any instant, the total disturbance produced by the waves at any point is equal to the sum of the disturbances produced by the individual waves.

Interference

The principle of superposition does not require that waves actually combine; rather, the net effect is as though they were combined. The actual combination or joining of two or more waves at a given point in space is called interference, and, as a result, the waves produce a single wave whose properties are determined by the properties of the individual waves.

If two waves of the same wavelength occupy the same space in such a way that their crests and troughs align, the wave they produce will have an amplitude greater than that possessed by either wave initially. This is known as constructive interference. The more closely the waves are in phase—that is, perfectly aligned—the more constructive the interference.

It is also possible that two or more waves can come together such that the trough of one meets the crest of the other, or vice versa. In this case, what happens is destructive interference, and the resulting amplitude is the difference between the values for the individual waves. If the waves are perfectly unaligned—in other words, if the trough of one exactly meets the crest of the other—their amplitudes cancel out, and the result is no wave at all.

Resonance

It is easy to confuse interference with resonance, and, therefore, a word should be said about the latter phenomenon. The term resonance describes a situation in which force is applied to an oscillator at the point of maximum amplitude. In this way, the motion of the outside force is perfectly matched to that of the oscillator, making possible a transfer of energy. As with interference, resonance implies alignment between two physical entities; however, there are several important differences.

Resonance can involve waves, as, for instance, when sound waves resonate with the vibrations of an oscillator, causing a transfer of energy that sometimes produces dramatic results. (See essay on Resonance.) But in these cases, a wave is interacting with an oscillator, not a wave with a wave, as in situations of interference. Furthermore, whereas resonance entails a transfer of energy, interference involves a combination of energy.

Transfer Vs. Combination

The importance of this distinction is easy to see if one substitutes money for energy, and people for objects. If one passes on a sum of money to another person, a business, or an institution—as a loan, repayment of a loan, a purchase, or a gift—this is an example of a transfer. On the other hand, when married spouses each earn paychecks, their cash is combined.

Transfer thus indicates that the original holder of the cash (or energy) no longer has it. Yet, if the holder of the cash combines funds with those of another, both share rights to an amount of money greater than the amount each originally owned. This is analogous to constructive interference.

On the other hand, a husband and wife (or any other group of people who pool their cash) also share liabilities, and, thus, a married person may be subject to debt incurred by his or her spouse. If one spouse creates debt so great that the other spouse cannot earn enough to maintain the payments, this painful situation is analogous to destructive interference.

Real-Life Applications

Mechanical Waves

One of the easiest ways to observe interference is by watching the behavior of mechanical waves. Drop a stone into a still pond, and watch how its waves ripple: this, as with most waveforms in water, is an example of a surface wave, or one that displays aspects of both transverse and longitudinal wave motion. Thus, as the concentric circles of a longitudinal wave ripple outward in one dimension, there are also transverse movements along a plane perpendicular to that of the longitudinal wave.

While the first wave is still rippling across the water, drop another stone close to the place where the first one was dropped. Now, there are two surface waves, crests and troughs colliding and interfering. In some places, they will interfere constructively, producing a wave—or rather, a portion of a wave—that is greater in amplitude than either of the original waves. At other places, there will be destructive interference, with some waves so perfectly out of phase that at one instant in time, a given spot on the water may look as though it had not been disturbed at all.

One of the interesting aspects of this interaction is the lack of uniformity in the instances of interference. As suggested in the preceding paragraph, it is usually not entire waves, but merely portions of waves, that interfere constructively or destructively. The result is that a seemingly simple event—dropping two stones into a still pond—produces a dazzling array of colliding circles, broken by outwardly undisturbed areas of destructive interference.

A similar phenomenon, though manifested by the interaction of geometric lines rather than concentric circles, occurs when two power boats pass each other on a lake. The first boat chops up the water, creating a wake that widens behind it: when seen from the air, the boat appears to be at the apex of a triangle whose sides are formed by rippling eddies of water.

Now, another boat passes through the wake of the first, only it is going in the opposite direction and producing its own ever-widening wake as it goes. As the waves from the two boats meet, some are in phase, but, more often than not, they are only partly in phase, or they possess differing wavelengths. Therefore, the waves at least partially cancel out one another in places, and in other places, reinforce one another. The result is an interesting patchwork of patterns when seen from the air.

Sound Waves

In Tune and Out of Tune

The relationships between musical notes can be intriguing, and though tastes in music vary, most people know when music is harmonious and when it is discordant. As discussed in the essay on frequency, this harmony or discord can be equated to the mathematical relationships between the frequencies of specific notes: the lower the numbers involved in the ratio, the more pleasing the sound.

The ratio between the frequency of middle C and that of its first harmonic—that is, the C note exactly one octave above it—is a nice, clean 1:2. If one were to play a song in the key of C-which, on a piano, involves only the "white notes" C-D-E-F-G-A-B—everything should be perfectly harmonious and (presumably) pleasant to the ear. But what if the piano itself is out of tune? Or what if one key is out of tune with the others?

The result, for anyone who is not tone-deaf, produces an overall impression of unpleasantness: it might be a bit hard to identify the source of this discomfort, but it is clear that something is amiss. At best, an out-of-tune piano might sound like something that belonged in a saloon from an old Western; at worst, the sound of notes that do not match their accustomed frequencies can be positively grating.

How a Tuning Fork Works

To rectify the situation, a professional piano tuner uses a tuning fork, an instrument that produces a single frequency—say, 264 Hz, which is the frequency of middle C. The piano tuner strikes the tuning fork, and at the same time strikes the appropriate key on the piano. If their frequencies are perfectly aligned, so is the sound of both; but, more likely, there will be interference, both constructive and destructive.

As time passes—measured in seconds or even fractions of seconds—the sounds of the tuning fork and that of the piano key will alternate between constructive and destructive interference. In the case of constructive interference, their combined sound will become louder than the individual sounds of either; and when the interference is destructive, the sound of both together will be softer than that produced by either the fork or the key.

The piano tuner listens for these fluctuations of loudness, which are called beats, and adjusts the tension in the appropriate piano string until the beats disappear completely. As long as there are beats, the piano string and the tuning fork will produce together a frequency that is the average of the two: if, for instance, the out-of-tune middle C string vibrates at 262 Hz, the resulting frequency will be 263 Hz.

Difference Tones

Another interesting aspect of the interaction between notes is the "difference tone," created by discord, which the human ear perceives as a third tone. Though E and F are both part of the C scale, when struck together, the sound is highly discordant. In light of what was said above about ratios between frequencies, this dissonance is fitting, as the ratio here involves relatively high numbers—15:16.

When two notes are struck together, they produce a combination tone, perceived by the human ear as a third tone. If the two notes are harmonious, the "third tone" is known as a summation tone, and is equal to the combined frequencies of the two notes. But if the combination is dissonant, as in the case of E and F, the third tone is known as a difference tone, equal to the difference in frequencies. Since an E note vibrates at 330 Hz, and an F note at 352 Hz, the resulting difference tone is equal to 22 Hz.

Destructive Interference in Sound Waves

When music is played in a concert hall, it reverberates off the walls of the auditorium. Assuming the place is well designed acoustically, these bouncing sound waves will interfere constructively, and the auditorium comes alive with the sound of the music. In other situations, however, the sound waves may interfere destructively, and the result is a certain muffled deadness to the sound.

Clearly, in a music hall, destructive interference is a problem; but there are cases in which it can be a benefit—situations, that is, in which the purpose, indeed, is to deaden the sound. One example is an automobile muffler. A car's exhaust system makes a great deal of noise, and, thus, if a car does not have a proper muffler, it creates a great deal of noise pollution. A muffler counteracts this by producing a sound wave out of phase with that of the exhaust system; hence, it cancels out most of the noise.

Destructive interference can also be used to reduce sound in a room. Once again, a machine is calibrated to generate sound waves that are perfectly out of phase with the offending noise—say, the hum of another machine. The resulting effect conveys the impression that there is no noise in the room, though, in fact, the sound waves are still there; they have merely canceled each other out.

Electromagnetic Waves

In 1801, English physicist Thomas Young (1773-1829), known for Young's modulus of elasticity became the first scientist to identify interference in light waves. Challenging the corpuscular theory of light put forward by Sir Isaac Newton (1642-1727), Young set up an experiment in which a beam of light passed through two closely spaced pinholes onto a screen. If light was truly made of particles, he said, the beams would project two distinct points onto the screen. Instead, what he saw was a pattern of interference.

In fact, Newton was partly right, but Young's discovery helped advance the view of light as a wave, which is also partly right. (According to quantum theory, developed in the twentieth century, light behaves both as waves and as particles.) The interference in the visible spectrum that Young witnessed was manifested as bright and dark bands. These bands are known as fringes—variations in intensity not unlike the beats created in some instances of sound interference, described above.

Oily Films and Rainbows

Many people have noticed the strangely beautiful pattern of colors generated when light interacts with an oily substance, as when light reflected on a soap bubble produces an astonishing array of shades. Sometimes, this can happen in situations not otherwise aesthetically pleasing: an oily film in a parking lot, left there by a car's leaky crankcase, can produce a rainbow of colors if the sunlight hits it just right.

This happens because the thickness of the oil causes a delay in reflection of the light beam. Some colors pass through the film, becoming delayed and, thus, getting out of phase with the reflected light on the surface of the film. These shades destructively interfere to such an extent that the waves are cancelled, rendering them invisible. Other colors reflect off the surface so that they are perfectly in phase with the light traveling through the film, and appear as an attractive swirl of color on the surface of the oil.

The phenomenon of light-wave interference with oily or filmy surfaces has the effect of filtering light, and, thus, has a number of applications in areas relating to optics: sunglasses, lenses for binoculars or cameras, and even visors for astronauts. In each case, unfiltered light could be harmful or, at least, inconvenient for the user, and the destructive interference eliminates certain colors and unwanted reflections.

Radio Waves

Visible light is only a small part of the electromagnetic spectrum, whose broad range of wave phenomena are, likewise, subject to constructive or destructive interference. After visible light, the area of the spectrum most people experience during an average day is the realm of relatively low-frequency, long-wave length radio waves and microwaves, the latter including television broadcast signals.

People who rely on an antenna for their TV reception are likely to experience interference at some point. However, an increasing number of Americans use either cable or satellite systems to pick up TV programs. These are much less susceptible to interference, due to the technology of coaxial cable, on the one hand, and digital compression, on the other. Thus, interference in television reception is a gradually diminishing problem.

Interference among radio signals continues to be a challenge, since most people still hear the radio via old-fashioned means rather than through new technology, such as the Internet. A number of interference problems are created by activity on the Sun, which has an enormously powerful electromagnetic field. Obviously, such interference is beyond the control of most radio listeners, but according to a Web page set up by WHKY Radio in Hickory, North Carolina, there are a number of things listeners can do to decrease interference in their own households.

Among the suggestions offered at the WHKY Web site is this: "Nine times out of ten, if your radio is near a computer, it will interfere with your radio. Computers send out all kinds of signals that your radio 'thinks' is a real radio signal. Try to locate your radio away from computers… especially the monitor." The Web site listed a number of other household appliances, as well as outside phenomena such as power lines or thunderstorms, that can contribute to radio interference.

Where to Learn More

Beiser, Arthur. Physics, 5th ed. Reading, MA: Addison-Wesley, 1991.

Bloomfield, Louis A. "How Things Work: Radio." How Things Work (Web site). <http://rabi.phys.virginia.edu/HTW//radio.html> (April 27, 2001).

Harrison, David. "Sound" (Web site). <http://www.newi.ac.uk/buckley/sound.html> (April 27, 2001).

Interference Handbook/Federal Communications Commission (Web site). <http://www.fcc.gov/cib/Publications/tvibook.html> (April 27, 2001).

Internet Resources for Sound and Light (Web site). <http://electro.sau.edu/SLResources.html> (April 25, 2001).

"Light—A-to-Z Science." DiscoverySchool.com (Web site). <http://school.discovery.com/homeworkhelp/worldbook/atozscience/l/323260.html> (April 27, 2001).

Oxlade, Chris. Light and Sound. Des Plaines, IL: Heinemann Library, 2000.

"Sound Wave—Constructive and Destructive Interference" (Web site). <http://csgrad.cs.vt.edu/~chin/interference.html> (April 27, 2001).

Topp, Patricia. This Strange Quantum World and You. Nevada City, CA: Blue Dolphin, 1999.

WHKY Radio and TV (Web site). <http://www.whky.com/antenna.html> (April 27, 2001).

Disturbance to the normal or expected operation of electrical or electronic devices, equipment, and systems. Electrical interference is sometimes called radio-frequency interference (RFI) or electromagnetic interference (EMI). Electrical noise is a broader term that includes those phenomena that are generally termed electrical interference, but also includes naturally occurring currents or voltages that are more or less continuous and cannot be completely eliminated.

Electrical interference originates from one or more of the following: transmitters such as those used for broadcast, communication, radar, and navigation; artificial incidental emission sources such as from sparking of motor brushes, automotive ignition, and fluorescent lamps; and natural phenomena such as lightning and electrostatic discharges. The interference emissions may be radiated through space or conducted along the paths of electrical wires in power lines and signal cables. See also Communications cable; Electromagnetic radiation; Transmission lines.

There are several means of mitigating electrical interference, including grounding, bonding, shielding, filtering, and transient control. There are two major approaches. One is to reduce radiation from boxes, cabinets, racks, and consoles by the design of multilayer printed circuit boards and backplanes, or to use metal or metallized plastic cases with EMI-protected apertures. The other involves reduction of radiation to or from the interconnecting cable by using filter pin connectors or foil-wrap shields terminated with complete coverage by the connector backshell at the respective box bulkhead. See also Electric filter; Electric transient; Electrical noise; Electrical shielding; Electromagnetic compatibility.

noun

The act or an instance of interfering or intruding: intervention, intrusion, meddling, obtrusion. See participate/abstain.

Definition: meddling, impedance
Antonyms: aid, assistance, help

1. An effect that occurs when training to improve two or more fitness components in the same microcycle (daily or weekly training sessions; see periodization) leads to a lower gain in any one component than would have been expected if it had been trained separately.

2. Conflict that occurs when two tasks are performed simultaneously, resulting in a lower quality of performance

3. Difficulty in learning or remembering a task or event due to confusion between the material that needs to be remembered and another experience occurring before or after the task or event in question. See also proactive inhibition; retroactive inhibition; capacity interference; structural interference.

In the law of patents, the presence of two pending applications, or an existing patent and a pending application that encompass an identical invention or discovery.

When interference exists, the Patent and Trademark Office conducts an investigation to ascertain the priority of invention between the conflicting applications, or the application and the patent. A patent is customarily granted to the earlier invention.

LearnThatWord.com is a free vocabulary and spelling program where you only pay for results!

The disturbance that results when two waves come together at a single point in space; the disturbance is the sum of the contribution of each wave. For example, if two crests of identical waves arrive together, the net disturbance will be twice as large as each incoming wave; if the crest of one wave arrives with the trough of another, there will be no disturbance at all.

In virology, the inhibition of viral replication by the presence of other viruses. Most instances of viral interference are mediated by interferon (inf).

• ultrasound i. lines — in ultrasonography, white lines across the image, usually caused by poor contact between the skin and transducer.

• Electricity and Magnetism - interference: combination of two waves or disturbances that arrive at same point at same time
• Data Transmission - interference: imperfect or distorted signal reception, esp. due to stray or unwanted signals
• Television Technology - interference: static or unwanted signals that distort image or audio
• Baseball - interference: illegal contact, whether intentional or unintentional, with the batter or baserunner by a fielder, catcher, or umpire, resulting in the batter or baserunner being awarded the next base
• Football
• Hockey

For interference in radio communications, see Interference (communication).

Two point interference in a ripple tank.

In physics, interference is a phenomenon in which two waves superimpose to form a resultant wave of greater or lower amplitude. Interference usually refers to the interaction of waves that are correlated or coherent with each other, either because they come from the same source or because they have the same or nearly the same frequency. Interference effects can be observed with all types of waves, for example, light, radio, acoustic, and surface water waves. It is actually a phenomena in which a light wave from two or more openings spaces strikes an opposite surface, the pattern observed is in form of dark and light patches due to the high or low amplitude of light respectively.

Contents 1 Mechanism 1.1 Between two plane waves 1.2 Between two spherical waves 1.3 Multiple beams 2 Optical interference 2.1 Light source requirements 2.2 Optical arrangements 2.3 Applications of optical interferometry 3 Radio interferometry 4 Acoustic interferometry 5 Quantum interference 6 See also 7 References 8 External links

Mechanism

Interference of waves from two point sources.

The principle of superposition of waves states that when two or more waves are incident on the same point, the total displacement at that point is equal to the vector sum of the displacements of the individual waves. If a crest of a wave meets a crest of another wave of the same frequency at the same point, then the magnitude of the displacement is the sum of the individual magnitudes – this is constructive interference. If a crest of one wave meets a trough of another wave then the magnitude of the displacements is equal to the difference in the individual magnitudes – this is known as destructive interference.

combined waveform
wave 1
wave 2
	Constructive interference	Destructive interference

Constructive interference occurs when the phase difference between the waves is a multiple of 2π, whereas destructive interference occurs when the difference is π, 3π, 5π, etc. If the difference between the phases is intermediate between these two extremes, then the magnitude of the displacement of the summed waves lies between the minimum and maximum values.

Consider, for example, what happens when two identical stones are dropped into a still pool of water at different locations. Each stone generates a circular wave propagating outwards from the point where the stone was dropped. When the two waves overlap, the net displacement at a particular point is the sum of the displacements of the individual waves. At some points, these will be in phase, and will produce a maximum displacement. In other places, the waves will be in anti-phase, and there will be no net displacement at these points. Thus, parts of the surface will be stationary—these are seen in the figure above and to the right as stationary blue-green lines radiating from the centre.

Between two plane waves

Geometrical arrangement for two plane wave interference

Interference fringes in overlapping plane waves

A simple form of interference pattern is obtained if two plane waves of the same frequency intersect at an angle.

One wave is travelling horizontally, and the other is travelling downwards at an angle θ to the first wave. Assuming that the two waves are in phase at the point B, then the relative phase changes along the x-axis. The phase difference at the point A is given by

It can be seen that the two waves are in phase when

,

and are half a cycle out of phase when

Constructive interference occurs when the waves are in phase, and destructive interference when they are half a cycle out of phase. Thus, an interference fringe pattern is produced, where the separation of the maxima is

and d_f is known as the fringe spacing. The fringe spacing increases with increase in wavelength, and with decreasing angle θ.

The fringes are observed wherever the two waves overlap and the fringe spacing is uniform throughout.

Between two spherical waves

Optical interference between two point sources for different wavelengths and source separations

A point source produces a spherical wave. If the light from two point sources overlaps, the interference pattern maps out the way in which the phase difference between the two waves varies in space. This depends on the wavelength and on the separation of the point sources. The figure to the right shows interference between two spherical waves. The wavelength increases from top to bottom, and the distance between the sources increases from left to right.

When the plane of observation is far enough away, the fringe pattern will be a series of almost straight lines, since the waves will then be almost planar.

Multiple beams

Interference occurs when several waves are added together provided that the phase differences between them remain constant over the observation time.

It is sometimes desirable for several waves of the same frequency and amplitude to sum to zero (that is, interfere destructively, cancel). This is the principle behind, for example, 3-phase power and the diffraction grating. In both of these cases, the result is achieved by uniform spacing of the phases.

It is easy to see that a set of waves will cancel if they have the same amplitude and their phases are spaced equally in angle. Using phasors each wave can be represented as for waves from to , where

.

To show that

one merely assumes the converse, then multiplies both sides by

The Fabry–Pérot interferometer uses interference between multiple reflections.

A diffraction grating can be considered to be a multiple-beam interferometer, since the peaks which it produces are generated by interference between the light transmitted by each of the elements in the grating. Feynman suggests that when there are only a few sources, say two, we call it "interference", as in Young's double slit experiment, but with a large number of sources, the process is labelled "diffraction".^[1]

Optical interference

Creation of interference fringes by an optical flat on a reflective surface. Light rays from a monochromatic source pass through the glass and reflect off both the bottom surface of the flat and the supporting surface. The tiny gap between the surfaces mean the two reflected rays have different path lengths and interfere when they combine. At locations (b) where the path difference is an even multiple of λ/2, the waves reinforce. At locations (a) where the path difference is an odd multiple of λ/2 the waves cancel. Since the gap between the surfaces varies slightly in width at different points, a series of alternating bright and dark bands are seen.

Because the frequency of light waves (~10¹⁴ Hz) is too high to be detected by currently available detectors, it is possible to observe only the intensity of an optical interference pattern. The intensity of the light at a given point is proportional to the square of the average amplitude of the wave. This can be expressed mathematically as follows. The displacement of the two waves at a point r is:

where A represents the magnitude of the displacement, φ represents the phase and ω represents the angular frequency.

The displacement of the summed waves is

The intensity of the light at r is given by

This can be expressed in terms of the intensities of the individual waves as

Thus, the interference pattern maps out the difference in phase between the two waves, with maxima occurring when the phase difference is a multiple of 2π. If the two beams are of equal intensity, the maxima are four times as bright as the individual beams, and the minima have zero intensity.

The two waves must have the same polarization to give rise to interference fringes since it is not possible for waves of different polarizations to cancel one another out or add together. Instead, when waves of different polarization are added together, they give rise to a wave of a different polarization state.

Light source requirements

The discussion above assumes that the waves which interfere with one another are monochromatic, i.e. have a single frequency—this requires that they are infinite in time. This is not, however, either practical or necessary. Two identical waves of finite duration whose frequency is fixed over that period will give rise to an interference pattern while they overlap. Two identical waves which consist of a narrow spectrum of frequency waves of finite duration, will give a series of fringe patterns of slightly differing spacings, and provided the spread of spacings is significantly less than the average fringe spacing, a fringe pattern will again be observed during the time when the two waves overlap.

Conventional light sources emit waves of differing frequencies and at different times from different points in the source. If the light is split into two waves and then re-combined, each individual light wave may generate an interference pattern with its other half, but the individual fringe patterns generated will have different phases and spacings, and normally no overall fringe pattern will be observable. However, single-element light sources, such as sodium- or mercury-vapor lamps have emission lines with quite narrow frequency spectra. When these are spatially and colour filtered, and then split into two waves, they can be superimposed to generate interference fringes.^[2] All interferometry prior to the invention of the laser was done using such sources and had a wide range of successful applications.

A laser beam generally approximates much more closely to a monochromatic source, and it is much more straightforward to generate interference fringes using a laser. The ease with which interference fringes can be observed with a laser beam can sometimes cause problems in that stray reflections may give spurious interference fringes which can result in errors.

Normally, a single laser beam is used in interferometry, though interference has been observed using two independent lasers whose frequencies were sufficiently matched to satisfy the phase requirements.^[3]

White light interference in a soap bubble

It is also possible to observe interference fringes using white light. A white light fringe pattern can be considered to be made up of a 'spectrum' of fringe patterns each of slightly different spacing. If all the fringe patterns are in phase in the centre, then the fringes will increase in size as the wavelength decreases and the summed intensity will show three to four fringes of varying colour. Young describes this very elegantly in his discussion of two slit interference. Some fine examples of white light fringes can be seen here. Since white light fringes are obtained only when the two waves have travelled equal distances from the light source, they can be very useful in interferometry, as they allow the zero path difference fringe to be identified.^[4]

Optical arrangements

To generate interference fringes, light from the source has to be divided into two waves which have then to be re-combined. Traditionally, interferometers have been classified as either amplitude-division or wavefront-division systems.

In an amplitude-division system, a beam splitter is used to divide the light into two beams travelling in different directions, which are then superimposed to produce the interference pattern. The Michelson interferometer and the Mach-Zender interferometer are examples of amplitude-division systems.

In wavefront-division systems, the wave is divided in space—examples are Young's double slit interferometer and Lloyd's mirror.

Interference can also be seen in everyday life. For example, the colours seen in a soap bubble arise from interference of light reflecting off the front and back surfaces of the thin soap film. Depending on the thickness of the film, different colours interfere constructively and destructively.

Applications of optical interferometry

Main article: Optical interferometry

Interferometry has played an important role in the advancement of physics, and also has a wide range of applications in physical and engineering measurement.

Thomas Young's double slit interferometer in 1803 demonstrated interference fringes when two small holes were illuminated by light from another small hole which was illuminated by sunlight. Young was able to estimate the wavelength of different colours in the spectrum from the spacing of the fringes. The experiment played a major role in the general acceptance of the wave theory of light.^[4] In quantum mechanics, this experiment is considered to demonstrate the inseparability of the wave and particle natures of light and other quantum particles (wave–particle duality). Richard Feynman was fond of saying that all of quantum mechanics can be gleaned from carefully thinking through the implications of this single experiment.^[5]

The results of the Michelson–Morley experiment, are generally considered to be the first strong evidence against the theory of a luminiferous aether and in favor of special relativity.

Interferometry has been used in defining and calibrating length standards. When the metre was defined as the distance between two marks on a platinum-iridium bar, Michelson and Benoît used interferometry to measure the wavelength of the red cadmium line in the new standard, and also showed that it could be used as a length standard. Sixty years later, in 1960, the metre in the new SI system was defined to be equal to 1,650,763.73 wavelengths of the orange-red emission line in the electromagnetic spectrum of the krypton-86 atom in a vacuum. This definition was replaced in 1983 by defining the metre as the distance travelled by light in vacuum during a specific time interval. Interferometry is still fundamental in establishing the calibration chain in length measurement.

Interferometry is used in the calibration of slip gauges (called gauge blocks in the US) and in coordinate-measuring machines. It is also used in the testing of optical components.^[6]

Radio interferometry

Main article: Astronomical interferometer

The Very Large Array, an interferometric array formed from many smaller telescopes, like many larger radio telescopes.

In 1946, a technique called astronomical interferometry was developed. Astronomical radio interferometers usually consist either of arrays of parabolic dishes or two-dimensional arrays of omni-directional antennas. All of the telescopes in the array are widely separated and are usually connected together using coaxial cable, waveguide, optical fiber, or other type of transmission line. Interferometry increases the total signal collected, but its primary purpose is to vastly increase the resolution through a process called Aperture synthesis. This technique works by superposing (interfering) the signal waves from the different telescopes on the principle that waves that coincide with the same phase will add to each other while two waves that have opposite phases will cancel each other out. This creates a combined telescope that is equivalent in resolution (though not in sensitivity) to a single antenna whose diameter is equal to the spacing of the antennas furthest apart in the array.

Acoustic interferometry

An acoustic interferometer is an instrument for measuring the physical characteristics of sound waves in a gas or liquid. It may be used to measure velocity, wavelength, absorption, or impedance. A vibrating crystal creates the ultrasonic waves that are radiated into the medium. The waves strike a reflector placed parallel to the crystal. The waves are then reflected back to the source and measured.

Quantum interference

See also: Quantum version of double-slit experiment

Quantum mechanics
Uncertainty principle
Introduction Glossary · History
Background Bra-ket notation · Classical mechanics Hamiltonian · Interference Old quantum theory
Fundamental concepts Complementarity · Decoherence Duality · Ehrenfest theorem Entanglement · Exclusion Measurement · Probability amplitude Nonlocality · Quantum state Superposition · Tunnelling Uncertainty · Wave function
Experiments Bell's inequality · Davisson–Germer Delayed choice quantum eraser Double-slit · Elitzur–Vaidman Popper · Quantum eraser Schrödinger's cat · Stern–Gerlach Wheeler's delayed choice
Formulations Formulations Heisenberg · Interaction Matrix mechanics · Schrödinger Sum over histories
Equations Dirac · Klein–Gordon Pauli · Rydberg Schrödinger
Interpretations Interpretations (overview) Consciousness-caused Consistent histories Copenhagen · de Broglie–Bohm Ensemble · Hidden variables Many-worlds · Objective collapse Pondicherry · Quantum logic Relational · Stochastic Transactional
Advanced topics Quantum chaos · Quantum field theory Quantum information science Scattering theory
Scientists Bell · Bohm · Bohr · Born · Bose de Broglie · Dirac · Ehrenfest Einstein · Everett · Feynman Heisenberg · Jordan · Kramers von Neumann · Pauli · Planck Schrödinger · Sommerfeld Wien · Wigner
v t e

If a system is in state its wavefunction is described in Dirac or bra-ket notation as:

where the s specify the different quantum "alternatives" available (technically, they form an eigenvector basis) and the are the probability amplitude coefficients, which are complex numbers.

The probability of observing the system making a transition or quantum leap from state to a new state is the square of the modulus of the scalar or inner product of the two states:

where (as defined above) and similarly are the coefficients of the final state of the system. * is the complex conjugate so that , etc.

Now let's consider the situation classically and imagine that the system transited from to via an intermediate state . Then we would classically expect the probability of the two-step transition to be the sum of all the possible intermediate steps. So we would have

,

The classical and quantum derivations for the transition probability differ by the presence, in the quantum case, of the extra terms ; these extra quantum terms represent interference between the different intermediate "alternatives". These are consequently known as the quantum interference terms, or cross terms. This is a purely quantum effect and is a consequence of the non-additivity of the probabilities of quantum alternatives.

The interference terms vanish, via the mechanism of quantum decoherence, if the intermediate state is measured or coupled with the environment.^[7][8]

See also

• Active noise control
• Beat (acoustics)
• Coherence (physics)
• Diffraction
• Double-slit experiment
• Young's Double Slit Interferometer
• Haidinger fringes
• Hong–Ou–Mandel effect
• Interference lithography
• Interferometer
• List of types of interferometers
• Lloyd's Mirror
• Moiré pattern
• Newton's rings
• Thin-film interference
• Optical feedback
• Retroreflector
• Upfade
• Multipath interference
• Inter-flow interference
• Intra-flow interference
• Bio-Layer Interferometry
• N-slit interferometric equation

References

1. ^ Richard Feynman, 1969, Lectures in Physics, Book 1, Addison Wesley, Reading, Mass.
2. ^ WH Steel, Interferometry, 1986, Cambridge University Press, Cambridge
3. ^ R. L. Pfleegor and L. Mandel, 1967, "Interference of independent photon beams", Phys. Rev., Volume 159, Issue 5. pp. 1084–1088.
4. ^ ^{a b} Max Born and Emil Wolf, 1999, Principles of Optics, Cambridge University Press, Cambridge.
5. ^ Greene, Brian (1999). The Elegant Universe: Superstrings, Hidden Dimensions, and the Quest for the Ultimate Theory. New York: W.W. Norton. pp. 97–109. ISBN 0-393-04688-5. 
6. ^ RS Longhurst, Geometrical and Physical Optics, 1968, Longmans, London.
7. ^ Wojciech H. Zurek, "Decoherence and the transition from quantum to classical", Physics Today, 44, pp 36–44 (1991)
8. ^ Wojciech H. Zurek, "Decoherence, einselection, and the quantum origins of the classical", Reviews of Modern Physics 2003, 75, 715.

External links

Wikimedia Commons has media related to: Interference

Look up interference in Wiktionary, the free dictionary.

• Expressions of position and fringe spacing
• Java demonstration of interference
• Java simulation of interference of water waves 1
• Java simulation of interference of water waves 2
• Flash animations demonstrating interference
• Lissajous Curves: Interactive simulation of graphical representations of musical intervals, beats, interference, vibrating strings
• Animations demonstrating optical interference by QED

This entry is from Wikipedia, the leading user-contributed encyclopedia. It may not have been reviewed by professional editors (see full disclaimer)

Common misspelling(s) of interference

• interferance

Dansk (Danish)
n. - interferens, indgriben, indblanding, forstyrrelse, mellemkomst

Nederlands (Dutch)
inmenging, bemoeienis, interferentie, hinder, radiostoring, obstructie

Français (French)
n. - ingérence, immixtion, interférence, brouillage, (Radio) parasites, (Ling) interférence

Deutsch (German)
n. - Einmischung, Störung, Notzucht

Ελληνική (Greek)
n. - επέμβαση, ανάμιξη, παρεμβολή, παράσιτα (ραδιοφώνου), παρέμβαση, ανάμειξη

Italiano (Italian)
interferenza

Português (Portuguese)
n. - interferência (f)

Русский (Russian)
вмешательство, интерференция

Español (Spanish)
n. - intervención, intromisión, obstrucción, estorbo, interferencia

Svenska (Swedish)
n. - ingripande, hinder, kollision, interferens (fys. el. gram.), störningar

中文（简体）(Chinese (Simplified))
冲突, 干涉

中文（繁體）(Chinese (Traditional))
n. - 衝突, 干涉

한국어 (Korean)
n. - 방해, 간섭, 혼신

日本語 (Japanese)
n. - 妨害, 邪魔, 障害, 干渉, 口出し, 妨害行為, 混信

العربيه (Arabic)
‏(الاسم) تدخل, تشوش, عقبه, عائق‏

עברית (Hebrew)
n. - ‮הפרעות אטמוספריות לשידורי רדיו, התערבות, חסימה, התערבלות גלים ליצירת גל חדש (פיסיקה)‬