# What are interference and diffraction

### Interference and diffraction

Interference and diffraction are typical wave phenomena, i.e. if you observe them you know that you are dealing with a wave.

Superposition
Superposition occurs when waves run over each other. In the undisturbed superposition, the waves do not influence each other, i.e. they run independently of each other through the overlay area. In the case of linear superposition, the instantaneous values ​​of the waves in the overlay area can be added. If the intensities are not too great, light and sound fulfill the linear superposition principle.

interference
If two waves overlap, the following extreme cases can occur: Figure: Constructive interference (gain). The waves (green and blue) are in phase, i.e. in the area under consideration the waves are in phase or in phase. are shifted against each other by at most an integral multiple of the wavelength. The sum (red) is much larger than the individual wave. Figure: Destructive interference (cancellation). The waves (green and blue) are out of phase or in push-pull or shifted half a wavelength against each other. The sum (red) disappears.

Of course there are also all intermediate stages (waves out of phase).

In order for interference to be clearly observed, the waves must have the same frequency. For complete cancellation, the waves involved must have the same amplitude.

Two synchronous point sources
If two sources send out waves synchronously (in phase), the following interference field is observed: Figure: The geometric locations of constructive interference of the waves from two synchronized sources are hyperbolic branches.

The condition of constructive interference is:
r1 - r2 = m?
where m is an integer, r1 is the distance from the first source to the place under consideration and r2 is the distance from the second source.
The condition of destructive interference is:
r1 - r2 = m λ + λ / 2
The geometric locations of all points that have the same distance difference from two given points (the sources) are hyperbolic branches.

Michelson interferometer
The Michelson interferometer is a precision measuring device that uses interference from waves. Figure: A wave, e.g. a laser beam, comes from the input side (E) and hits the beam splitter (ST), where it is split. The two partial beams run along the interferometer arms of lengths l1 and l2, meet a mirror (S) vertically and walk back the same way. At the beam splitter again, the partial beams are split up again. Those two partial beams that go in the direction of exit (A) can interfere there and be observed.

Assuming that the interferometer is adjusted so that there is destructive interference at the exit, then you only have to move a mirror outwards by λ / 4 so that constructive interference occurs at the exit. At 633 nm wavelength (red HeNe laser) that is only 158 nm!
There are interferometers in which a mirror can be moved many meters. It is then possible, through the interference, to measure its position precisely to a fraction of a wavelength.

Anti-reflective coating
Optical surfaces must be coated, otherwise reflections reduce the image quality. The basic principle can already be seen from a single layer (Fig.): Figure: A thin layer with refractive index n2 lie on a glass with refractive index n3 and border on air with refractive index n1. Light traverses the three media and is reflected to a small extent at each of the interfaces. As the waves expand laterally, the reflected lights overlap. The reflections disappear when the reflected waves interfere destructively.

The reflections interfere destructively if they have a λ / 2 path difference. In the case of perpendicular incidence of light, the layer must be λ / 4 thick because the layer is passed through twice.
Interference condition: d = λ2/ 4 = λvac/ 4n2 (for n1 2 3)

A single layer can only suppress reflections in the vicinity of a single wavelength. Several layers are necessary to reduce reflections in the entire visible area. An analogous principle can be used to produce mirror layers or interference filters. The colors of thin layers (soap bubbles, oil on water, etc.) are also based on this effect.

Huygens-Fresnel principle
Every point of a wave can be thought of as the starting point of an elementary wave, i.e. every wave can be broken down into elementary waves. Each wave can be represented as a superposition of elementary waves. Animation: A plane wave runs to the right. From the middle, straight wave fronts are no longer drawn, but elementary waves (here ring waves) that run from the center line. The envelope of the elementary waves forms a front that looks as if the original wave had simply continued to run. The elementary waves that are still visible behind the wave front would, according to Fresnel, be canceled out by destructive interference.

diffraction
You can hear someone speaking even though they're still behind the corner of the house. The sound is diffracted at the corner of the house. Diffraction can be made visible with light: Figure: If a light wave hits a slit, elementary waves can only emanate from that part of the wave that hits the slit. Since elementary waves are spherical waves in our picture, the wave can run in all directions after a narrow gap.

If the diffractive object has several gaps, many elementary waves can overlap and create a complicated diffraction pattern (interference pattern). The diffraction pattern shows sharp maxima if the diffraction pattern has a periodicity.

Diffraction at the periodic line grating
If light hits a periodic line grating perpendicularly, it is deflected perpendicularly to the "bars". The deflection angles are greater, the finer the grating. Diffraction can even be observed with the eye on a fine curtain. Figure: A periodic grating consists of alternating transparent and opaque strips. The most important variable is the lattice constant (spatial period length d, lattice bar spacing) Figure: At a greater distance from the grating, one only observes light in certain directions, the so-called diffraction orders.

The angles of the diffraction maxima satisfy the lattice diffraction equation:
d · sinαm = m · λ
with the diffraction order m (whole number) and lattice constant d. Order m = 0 is undeflected light. The grating equation says nothing about how much light goes into a certain diffraction order.

X-ray structure analysis
If one sends X-rays through a crystal, one observes sharp diffraction maxima (Max von Laue). This means that X-rays have the character of waves and that the atoms in a crystal are regularly arranged. The lattice period (atomic distances) can be calculated from the diffraction angles.