The phenomenon of wave diffraction is one of the effects that reflects the wave nature of light. It was for light waves at the beginning of the 19th century that it was discovered. In this article, we consider what this phenomenon is, how it is described mathematically, and where it finds application.
Wave diffraction phenomenon
As you know, any wave, be it light, sound or disturbances on the surface of the water, in a homogeneous medium propagates along a direct path.
Imagine a wave front that has a flat surface and moves in a certain direction. What will happen if an obstacle arises in the way of this front? Anything can be an obstacle (a stone, a building, a narrow gap, and so on). It turns out that after passing the obstacle, the wavefront will no longer be flat, but will take a more complex shape. So, in the case of a small round hole, the wave front, passing through it, becomes spherical.
The phenomenon of a change in the direction of wave propagation, when it encounters an obstacle, is called diffraction (diffractus from Latin means "broken").
The result of this phenomenon is that the wave penetrates into the space behind the obstacle, where it would never have hit with its rectilinear motion.
An example of wave diffraction by the sea is shown in the figure below.
Diffraction Observation Conditions
The above-described effect of breaking a wave when passing an obstacle depends on two factors:
- wavelengths;
- geometric parameters of the obstacle.
Under what condition is wave diffraction observed? For a better understanding of the answer to this question, it should be noted that the phenomenon under consideration always occurs when a wave encounters an obstacle, however, it becomes noticeable only when the wavelength is on the order of the geometric parameters of the obstacle. Since the wavelengths of light and sound are small compared with the sizes of the objects surrounding us, diffraction itself manifests itself only in some special cases.
Why is wave diffraction? This can be understood by considering the Huygens-Fresnel principle.
Huygens principle
In the mid-17th century, the Dutch physicist Christian Huygens advanced a new theory of the propagation of light waves. He believed that, like sound, light moves in a special medium - the ether. A light wave is an oscillation of ether particles.
Considering the wave spherical front created by a point source of light, Huygens came to the following conclusion: in the process of movement, the front passes through a number of spatial points in the ether. As soon as he reaches them, he makes them hesitate. The oscillating dots, in turn, generate a new generation of waves, which Huygens called secondary. From each point, the secondary wave is spherical, but it alone does not determine the surface of a new front. The latter is the result of superposition of all spherical secondary waves.
The effect described above is called the Huygens principle. He does not explain the diffraction of waves (when the scientist formulated it, they still did not know about the diffraction of light), but he describes such effects as the reflection and refraction of light with success.
Since the corpuscular theory of light advanced by Newton triumphed in the 17th century, Huygens’s work was forgotten for 150 years.
Thomas Jung, Augustin Fresnel and the revival of the Huygens principle
The phenomenon of diffraction and interference of light was discovered in 1801 by Thomas Young. Carrying out experiments with two slits through which the monochromatic light front passed, the scientist received a picture from the alternating dark and light stripes on the screen. Jung fully explained the results of his experiments, referring to the wave nature of light, and thereby confirming Maxwell's theoretical calculations.
As soon as the corpuscular Newtonian theory of light was disproved by Jung's experiments, the French scientist Augustin Fresnel remembered Huygens's work and used its principle to explain the phenomenon of diffraction.
Fresnel believed that if an electromagnetic wave propagating in a straight line meets an obstacle, then part of its energy is lost. The rest is spent on the formation of secondary waves. The latter and lead to the emergence of a new wave front, the propagation direction of which differs from the original.
The described effect, which the ether does not take into account when generating secondary waves, is called the Huygens-Fresnel principle. He describes the diffraction of waves successfully. Moreover, at present, this principle is used to determine energy losses during the propagation of electromagnetic waves along which an obstacle is encountered.
Narrow gap diffraction
The theory of constructing diffraction patterns is quite complicated from a mathematical point of view, since it involves solving the Maxwell equations for electromagnetic waves. Nevertheless, the Huygens-Fresnel principle, as well as a number of other approximations, make it possible to obtain mathematical formulas suitable for their practical application.
If we consider diffraction on a thin slit, onto which a plane wave front falls parallel, then bright and dark stripes will appear on the screen located far from the slit. The minimums of the diffraction pattern in this case are described by the following formula:
y m = m * λ * L / a, where m = ± 1, 2, 3, ...
Here y m is the distance from the projection of the slit onto the screen to a minimum of the order of m, λ is the light wavelength, L is the distance to the screen, a is the width of the slit.
From the expression it follows that the central maximum will be more vague if we reduce the width of the gap and increase the length of the light wave. The figure below shows what the corresponding diffraction pattern will look like.
Diffraction grating
If you apply a set of slots from the example above on one plate, you get the so-called diffraction grating. Using the Huygens-Fresnel principle, one can obtain the formula for the maxima (bright bands) that are obtained when passing through a grating of light. The formula is as follows:
sin (θ) = m * λ / d, where m = 0, ± 1, 2, 3, ...
Here, the parameter d is the distance between the nearest slots on the grating. The smaller this distance, the greater the distance between the bright bands in the diffraction pattern.
Since the angle θ for the mth order maxima depends on the wavelength λ, multi-colored stripes appear on the screen when white light passes through the diffraction grating. This effect is used in the manufacture of spectroscopes capable of analyzing the characteristics of radiation or absorption of light by one or another source, for example, stars and galaxies.
The Importance of Diffraction for Optical Instruments
One of the main characteristics of devices such as a telescope or microscope is their resolution. By it is meant the minimum angle, when observed, under which individual objects are still distinguishable. This angle is determined from the analysis of wave diffraction according to the Rayleigh criterion according to the following formula:
sin (θ c ) = 1.22 * λ / D.
Where D is the diameter of the lens of the device.
If we apply this criterion to the Hubble telescope, we will see that the device at a distance of 1000 light-years is able to distinguish between two objects, the distance between which is similar to that between the Sun and Uranus.