What is a wavefront in physics

Huygens principle

Huygens principle allows a visual and geometric explanation of phenomena such as reflection. You can find out how this works and what Huygens' principle is here.

Would you like to find out the most important things in the shortest possible time? Then just watch our animated video on the Huygens principle.

Huygens principle simply explained

In 1678 Christiaan Huygens developed a construction specification with which he wanted to describe the propagation of light. This rule is called Huygens principle (shorter too Huygens principle).

The construction according to Huygens principle is based on the following considerations: Everyone Point on the wavefront of a propagating wave is a center for spherical or circular elementary waves that propagate in the same medium with the same speed and frequency as the original wave. The wavefront, considered at a later point in time, is then than that Enveloping of all elementary waves.

The original formulation of Huygens' principle only considered the propagation of the elementary waves in the forward direction. It was not until 1991 that David A. B. Miller was able to resolve the problem of backward propagating elementary waves.

Huygens principle: propagation of a wave

Huygens' principle says that every point is on a spreading out Wavefront can be regarded as the starting point of elementary waves of the same frequency and wavelength, which also propagate with the same propagation speed. The wavefront at a later point in time is that Enveloping of all elementary waves.

But what does a wavefront actually mean and what exactly is meant by an envelope? You can find the answer to this in this section. We will consider electromagnetic waves for this, but the statements also apply to mechanical waves such as rope waves.

Wavefront and envelope

First of all, some terminology that you can find in connection with the Huygens principle. The wave from which all points send out further waves is also called Primary wave. The waves emitted from these points are known as Elementary- or Secondary waves.

Maybe you know how an electromagnetic wave is characterized. An electromagnetic wave is characterized by its spatial period (wavelength ), their time period (frequency ), the direction of propagation and the amplitude of the respective field component (these are two numbers for the electric and the magnetic field). A wave is generally a periodic phenomenon both in space and in time. Therefore you can assign a wave not only a temporal period but also a spatial period.

Wavefront

What exactly all these terms mean doesn't matter at first. It is only important that you know exactly what the wave is doing at a certain point in space at a certain point in time. Does it swing up or down, how high does it swing and so on. But that's just the information a single Point.

But what about if, for example, you leave the time the same, but move a little perpendicular to the direction of propagation of the wave. Again you would have to use all the parameters to determine how the wave would behave at this point. Of course, this also applies to all other points that you can reach by moving in space.

Here will help you Wavefront. What the wavefront does is connect all of the points at which the wave becomes one the exact same behavior at a certain point in time having. So if you move along the wave front, the behavior of the wave will not change. For example, if you are on a hill of the wave, then you will always be on a hill of exactly the same height along the corresponding wave front. This “exactly the same behavior at a certain point in time” is sometimes referred to by the name phase Find. The important thing here is that visual informationthat you get through the wavefronts. The wave fronts not only tell you how the wave is behaving, but also in which direction it is spreading. The direction of propagation of the wave is always there perpendicular to the wave fronts.

Enveloping

Now you know what a wavefront is. We want to use this knowledge directly. Let's look at a wave front that happens to be in the shape of a vertical line. Such a wave front is characteristic of a wave that plane wave called. According to Huygens' principle, every point along this line emits secondary waves. The wave fronts of these secondary waves are not lines but semicircles. Such waves are called circle- or. Spherical waves.

We are now waiting for a while and then we are interested in where the new wavefront of the propagating primary wave will be. The circular wavefronts of the secondary waves will have a radius of have, with is the speed of propagation of the wave. Since the wave front was a vertical line at the beginning, all semicircles along this line have the same orientation. If we now create a common tangent on each of these semicircles, we get a new vertical line. This new vertical line is just the wavefront of the primary wave at a later point in time. Instead of “common tangent to the semicircles” you will also find the shorter term Envelope of all elementary waves sometimes only Enveloping.

If the primary wave itself is not a plane wave but a circular wave, then the difference lies just in the orientation of the semicircles. The common tangent is then no longer a straight line, as you may be used to from tangents, but a curved line.

What you ultimately do when constructing the envelope is the following: You draw in a couple of semicircles whose centers lie on the wavefront of the primary wave and whose radius is proportional to the elapsed time. Then you look for a line, curved or not, that touches every circle but Not cuts. This line is then the envelope and thus the new wave front at a later point in time.

Huygens principle: reflection

If we want to use Huygens' principle for the description of the reflection (later also for the refraction), then we have to make a small change to the construction of the envelope. The centers of the elementary waves are located Not more on the wavefront of the primary wave, but rather on the interface between two media encountered by the primary wave.

Huygens' principle is first applied to the reflection used. The wave front hits with an angle of incidence of relative to the perpendicular at point F on the interface. As we mentioned in the section on the wavefront, the direction of propagation is perpendicular to the wavefront at any point in time. This is illustrated with the arrows. Without the presence of the interface AB, the wavefront CE would propagate to the wavefront JL. The point E passes through the points H and L. During the time interval in which the point E is propagating from H to L, the point D would move from G to K. The point D meets the interface at point I, which now forms the center for an elementary wave with the radius IK. Similarly, in the same time interval, point C would move to F and then to J, but meets the interface at point F. An elementary wave with point F as its center would therefore have the radius FJ at the point in time at which point E moved to L. The new wavefront LN can then be constructed as a tangent to the two circles and specifies the new direction of propagation (normal to the wavefront LN). The reflected wave then propagates with the angle of reflection relative to the perpendicular.

Huygens principle: refraction

The change in the refractive index leads to a change in the speed of propagation. Therefore, the radius of the elementary waves in the area also changes with the refractive index . Exactly this change leads to the observation of the refractionwhat we show you in this section, Huygens Principle: Refraction.

To do this, we arbitrarily assume that the refractive index is greater than the refractive index . A higher refractive index of a medium goes hand in hand with a lower propagation speed of the wave within this medium. Without the interface AB, the wave front CE would become the wave front JL when the point E has reached the point L. In the case of reflection, the wavelet around point F, after point E has moved to L, would become the radius have. Since we assumed is the radius the elementary wave in the second medium by the factor smaller than the radius of the same elementary wave in the first medium.

The construction of the new wavefront in the second medium is therefore similar to the construction in the case of reflection. The only difference is that the circles have a smaller radius. This again results in the new wave front LN of the wave in the second medium as a tangent to the two circles. You also get the new direction of propagation by drawing vertical lines on this wave front. The broken wave propagates in the second medium under the angle relative to the perpendicular at point F. You realize that this angle smaller is than the angle of reflection. The reason for this is precisely the lower speed of propagation due to the higher refractive index.

Huygens principle: diffraction

Finally, we will show you how Huygens' principle helps us diffraction of waves to explain geometrically.

To do this, we assume that we are looking at a plane wave that hits an opening. Only the part of the wavefront that is of interest is of interest within the opening is located. The wave front outside the opening is "blocked" and therefore does not matter.

Huygens' principle now instructs us to choose points along the wave front within the opening that act as centers for elementary waves. We arbitrarily choose a few points and draw the circular wavefronts for a number of different points in time.

Huygens' principle also states that the new wave front of the primary wave at a later point in time is precisely the envelope of the elementary waves. So at some point we stop drawing semicircles and then look for a line that touches but does not intersect all of the circles. This line is then the wave front we are looking for. If you now draw a few more lines perpendicular to the wave front, you will find the direction of propagation of the wave after the opening. What can you see The post-opening wave appears to propagate into areas that would not lie on the rectilinear motion of the plane wave. And it is precisely this deviation from the "straight line movement" that is called diffraction. You will also find the term "the wave spreads in the geometric shadow".

What all of this ultimately means is the following: If you were to expand the opening into a rectangle, then everything outside of this rectangle would be called "geometric shadow". If you now imagine horizontal lines, instead of the plane wave, that determine the direction of propagation, you would expect them to stay within the rectangle. But this is not the case and this observation is called diffraction. Huygens' principle allows a visual explanation of this observation.