Today we will talk about the condition of maximum and minimum interference, we will reveal the reason for the appearance of bands when illuminating a narrow slit, and explain the nature of the wave properties of light quanta.
Quantum
The answer to this question exactly could give only research at the beginning of the twentieth century. Physics took a step forward when Max Planck discovered the concept of quantum. This value also applies to light. And before considering what are the conditions for maximum and minimum during interference, we must first thoroughly understand what light is.
So, a quantum is something one, indivisible. This is a minimal particle of some magnitude. Light is a quantum of the electromagnetic field.
When it moves through space, its properties cannot be changed. The energy, frequency, amplitude of one photon remains unchanged until the particle encounters any obstacle. In this case, the beam can be reflected, scattered, refracted, absorbed, interact with another quantum. In the latter case, light interference will occur. The maximum and minimum conditions will be described a bit later.
Particle
Since ancient times, people believed that light is something ephemeral, weightless. Fire, earth, water could be “touched”, the wind left sensations, but the radiation of the sun was something inherent in being, it simply existed, and that’s all.
But the curiosity of scientists moved science further and further until it became clear: light also has properties, it can be measured and registered. And finally, people realized: the light can be weighed! The first to make such experiments was the Russian scientist Lebedev. He proved that photons of light do indeed exert pressure on a thin silver plate. So, they have momentum and mass. The conclusion convinces scientists that light is a stream of particles. But how much does a photon weigh? The answer to this question will help us better explain the conditions for the maximum and minimum interference of light waves.
Traffic
First you need to clarify something. A photon exists while it is moving. He can stop moving in space only in a collision with an obstacle. If the path is clear, the photon can move forever, and in the literal sense of the word.
For example, the light of distant stars and galaxies has come to us for a very long time: thousands, millions, billions of years. Some of them are so far away that they may no longer exist, and we still see their radiation. And this demonstrates how tenacious and durable the particle is - the carrier of light, the photon.
But this is while he moves. If light falls on an object, for example, on a plastic scoop that children have forgotten in the yard, then it seems to dissolve in the volume of the substance, gives it its energy. In general, there are a lot of effects associated with the interaction of light and matter. These include the photoelectric effect, piezo and pyroeffects. But more often than not, the light simply heats up the object on which it falls. Surely everyone noticed: it is worth leaving a book in the sun, its lit side immediately heats up.
Returning to the topic of our conversation, we say: the photon has mass, only while it moves in space. When he encounters an obstacle, he ceases to exist. The rest mass of a particle of light is zero.
Field
Physical fields surround people: they penetrate the Earth, they are emitted by the Sun and some planets (for example, Jupiter and Saturn). But "touch", somehow you can not perceive them. You can measure and fix only the disturbance of the field, which is usually called the oscillation. Light is a quantum of the electromagnetic field. It is an oscillation of the electric and magnetic fields, correlated in mutually perpendicular planes.
In fact, electricity and magnetism have one source - a charged body. As Oersted proved by his experiments, they exist only together and are capable of influencing each other. But historically it happened that, as they were studied, researchers divided these fields.
From the conclusion that light is a field oscillation, another fact follows: it is also a wave. The last statement will help us formulate the conditions for the maximum and minimum interference a bit later.
Spectrum
As we said above, light is an oscillation of the electromagnetic field. A thoughtful reader will understand: fluctuations are different. When compared with the open sea, there are both light waves that gently lick the coastal sand, and tsunamis that can tear down mountains. To separate electromagnetic waves, there is a special scale. She shares different ranges and sources. In order of increasing energy that the photon carries, the electromagnetic scale is divided into:
- radio waves;
- infrared radiation;
- visible spectrum;
- ultraviolet waves;
- X-ray quanta
- gamma radiation.
And light is usually called only those photons that belong to visible radiation. Sometimes the areas of the infrared and ultraviolet spectra that are close to visible quanta are also called light. For example, the emission of ultraviolet lamps is sometimes called "black light." I must say that the visible spectrum is a very small piece of the entire scale.
In general, such a name is a deeply subjective term. There are creatures on our planet that are able to see infrared or ultraviolet rays, but man always focuses on himself.
Moreover, even those few electromagnetic field quanta that people are able to perceive, they see differently. The human eye has spectral sensitivity: green quanta are best perceived, and red and violet are already difficult. In other words, people do not feel all of the blue or yellow quanta that the surface objectively reflects. Thus, the world around is much brighter and more colorful than a person thinks.
Wave
Oscillations of the electromagnetic field are ordered. If a quantum has already appeared, then inside it there is a distribution law. This process is most clearly illustrated by the graph of cosine or sine in Cartesian coordinates.
Like any wave, light has the following characteristics:
- Wavelength. This is the distance between two identical phases of oscillation. For example, between adjacent highs or lows. In another way, the wavelength can be defined as the double distance over which the wave crosses the X axis. Usually, this value is denoted by the Greek letter λ (lambda).
- Frequency. This is the number of vibrations that fit in one second. It is indicated in the formulas by the Greek letter ν (nude) if the frequency is linear, ω (omega) if the frequency is cyclic, and by the Latin letter f if the frequency appears as a function.
- Amplitude. This is the height of the highs and lows. In essence, the amplitude is the perturbation force of an electromagnetic wave or the intensity of an electromagnetic field.
- Energy. The wavelength and photon frequency are related by the following relation: the shorter the wavelength, the higher the frequency and energy.
We need these characteristics of light to derive the conditions for maximum and minimum interference.
Interference
As we wrote above, waves of light are able to interact with matter and with each other. And what is the result of this meeting depends on the phase difference.
If two identical waves meet at the same point, and their “humps” and “hollows” coincide, then as a result the amplitude will double and maximum interference will be observed. If it happens that one wave arrives at the highest point and the other at the lowest point, then their intensities will cancel each other out, the amplitude will turn out to be zero, a dark band or dot will appear in the picture. These are the conditions for the formation of maxima and minima upon interference.
Some formulas
To express the above in the language of physical laws, we need to give several formulas.
The output will be a dark or light strip in the case of thin films, depending on the thickness of the coating. For the maximum, it is necessary that a half-integer number of waves develop: λ 2 = (λ 1 * n 1 ) / n 2 . In this formula, n are the refractive indices of the film and air medium.
In the case of interference of a parallel light beam on a narrow slit at the output, a series of dark and light bands with a step of I = 2 π / ( k 1 x - k 2 x ) will be obtained. In the formula, k are the wave vectors of two interacting light waves.