Six important phenomena describe the behavior of a light wave if it encounters an obstacle in its path. These phenomena include reflection, refraction, polarization, dispersion, interference and diffraction of light. This article will focus on the last of them.
Disputes about the nature of light and experiments by Thomas Young
In the mid-17th century, two theories existed on an equal footing regarding the nature of light rays. The founder of one of them was Isaac Newton, who believed that light is a collection of rapidly moving particles of matter. The second theory was put forward by the Dutch scientist Christian Huygens. He believed that light is a special type of wave propagating in a medium similar to how sound moves in air. According to Huygens, the medium for light was ether.
Since no one found the ether, and Newton's authority was enormous at that time, Huygens's theory was rejected. However, in 1801, the Englishman Thomas Jung conducted the following experiment: he transmitted monochromatic light through two narrow slits located close to each other. He projected the passing light onto the wall.
What was the result of this experience? If the light were particles (corpuscles), as Newton believed, then the image on the wall would correspond to clear two bright stripes emanating from each of the cracks. However, Jung observed a completely different picture. A series of dark and light stripes appeared on the wall, and light lines appeared even beyond the boundaries of both slits. A schematic representation of the described light pattern is presented in the figure below.
This picture spoke of one thing: light is a wave.
Diffraction phenomenon
The light picture in Jung's experiments is associated with the phenomena of interference and diffraction of light. Both phenomena are difficult to separate from each other, since in a number of experiments their combined result can be observed.
Diffraction of light consists in a change in the wavefront when it encounters an obstacle in its path whose dimensions are comparable or less than the wavelength. From this definition it is clear that diffraction is characteristic not only of light, but also of any other waves, for example, sound waves or waves on the surface of the sea.
It is also understandable why this phenomenon cannot be observed in nature (the wavelength of the light is several hundred nanometers, therefore any macroscopic objects cast clear shadows).
Huygens-Fresnel principle
The phenomenon of light diffraction is explained by the above principle. Its essence is as follows: a propagating rectilinear plane wave front leads to the excitation of secondary waves. These waves are spherical, however, if the medium is homogeneous, then, superimposed on each other, they will lead to the initial plane front.
As soon as an obstacle arises (for example, two gaps in Jung's experiment), it becomes a source of secondary waves. Since the number of these sources is limited and determined by the geometric features of the obstacle (in the case of two thin slits of the secondary sources, there are only two), the resulting wave will no longer give the initial flat front. The latter will change its geometry (for example, it will acquire a spherical shape), moreover, there will appear maxima and minima of light intensity in its different parts.
The Huygens-Fresnel principle demonstrates that the phenomena of interference and diffraction of light are inseparable.
What conditions are necessary for diffraction to be observed?
One of them has already been announced above: this is the presence of small (of the order of the wavelength) obstacles. If the obstacle is relatively large in geometric dimensions, then the diffraction pattern will be observed only near its edges.
The second important condition for light diffraction is the coherence of waves from different sources. This means that they must have a constant phase difference. Only in this case, due to interference, can a stable picture be observed.
Coherence of sources is achieved in a simple way, it is enough to pass any light front from one source through one or more obstacles. Secondary sources from these obstacles will already act as coherent.
Note that to observe the interference and diffraction of light, it is absolutely not necessary that the primary source be monochromatic. This will be discussed below when considering the diffraction grating.
Fresnel and Fraunhofer diffraction
In simple terms, Fresnel diffraction consists in viewing the picture on a screen located close to the slit. Fraunhofer diffraction considers a picture that is obtained at a distance much wider than the width of the slit; moreover, it assumes that the wave front incident on the slit is flat.
These two types of diffraction are distinguished because the pictures in them are different. This is due to the complexity of the phenomenon under consideration. The fact is that in order to obtain an exact solution to the diffraction problem, it is necessary to use Maxwell's theory of electromagnetic waves. The Huygens-Fresnel principle, mentioned earlier, is a good approximation for obtaining practically suitable results.
The figure below shows how the image in the diffraction pattern changes when the screen is removed from the gap.
In the figure, the red arrow shows the direction of the screen approaching the slit, that is, the upper figure corresponds to the Fraunhofer diffraction and the lower one to Fresnel. As you can see, as the screen approaches the gap, the picture becomes more complex.
Further in the article we will consider only Fraunhofer diffraction.
Thin-gap diffraction (formulas)
As noted above, the diffraction pattern depends on the geometry of the obstacle. In the case of a thin slit having a width a, which is illuminated with monochromatic light with a wavelength λ, the position of the minima (shadow) can be observed for angles corresponding
sin (θ) = m × λ / a, where m = ± 1, 2, 3 ...
Theta angle is counted from the perpendicular connecting the center of the gap and the screen. Thanks to this formula, it is possible to calculate at what angles there will be a complete damping of the waves on the screen. Moreover, the diffraction order, i.e., the number m , can be calculated .
Since we are talking about Fraunhofer diffraction, then L >> a, where L is the distance from the gap to the screen. The last inequality allows us to replace the sine of the angle with a simple ratio of the y coordinate to the distance L, which leads to the following formula:
y m = m × λ × L / a.
Here y m is the coordinate of the minimum position of order m on the screen.
Fine Slit Diffraction (analysis)
The formulas given in the previous paragraph make it possible to analyze the changes in the diffraction pattern with a change in the wavelength λ or gap width a. So, an increase in a will lead to a decrease in the coordinate of the first-order minimum y 1 , that is, the light will concentrate at a narrow central maximum. Reducing the width of the gap will lead to a stretching of the central maximum, that is, it becomes vague. This situation is illustrated in the figure below.
Changing the wavelength is the opposite. Large values of λ lead to blurring of the picture. This means that long waves are better diffracted than short ones. The latter is of fundamental importance in determining the resolution of optical devices.
Diffraction and resolution of optical instruments
Observation of light diffraction is a limiter of the resolution of any optical devices, such as a telescope, microscope, and even the human eye. When it comes to these devices, they consider diffraction not on the slit, but on a round hole. Nevertheless, all the conclusions made earlier remain true.
For example, we will consider two luminous stars, which are at a great distance from our planet. The hole through which light enters our eye is called the pupil. From two stars on the retina, two diffraction patterns are formed, each of which has a central maximum. If the light from the stars falls into the pupil at a certain critical angle, then both maxima will merge into one. In this case, a person will see a single star.
The resolution criterion was established by Lord J.W. Rayleigh, so he currently bears his last name. The corresponding mathematical formula looks like this:
sin (θ c ) = 1.22 × λ / D.
Here D is the diameter of the round hole (lens, pupil, and so on).
Thus, the resolution can be increased (decrease θ c ) if you increase the diameter of the lens or reduce the wavelength. The first option is implemented in telescopes, allowing several times to reduce θ c compared with the human eye. The second option, that is, a decrease in λ, is used in electron microscopes, which have 100 thousand times better resolution than similar light devices.
Diffraction grating
It is a collection of thin slots located at a distance d from each other. If the wave front is flat and falls parallel to this lattice, then the position of the maxima on the screen is described by the expression
sin (θ) = m × λ / d, where m = 0, ± 1, 2, 3 ...
The formula shows that a maximum of zero order occurs in the center, the rest are located at some angles θ.
Since the formula contains the dependence of θ on the wavelength λ, this means that the diffraction grating can decompose light into colors like a prism. This fact is used in spectroscopy to analyze the spectra of various luminous objects.
Perhaps the most famous example of light diffraction is the observation of color shades on a DVD. The grooves on it are a diffraction grating, which, reflecting the light, decomposes it into a number of colors.