Diffraction is one of the important effects characteristic of a wave of any nature. People take this phenomenon into account when manufacturing optical and sound devices (microscopes, telescopes, loudspeakers). This article will focus on diffraction by a slit of light.
What is diffraction?
Before talking about diffraction by a gap, one should get acquainted with the concept of this phenomenon. Any wave (sound, light) that a certain source generated will propagate in parallel and rectilinearly if the parameters of the space in which it moves are kept unchanged. For example, for light, such parameters will be the density of the medium and the characteristics of the gravitational field.
Diffraction is a deviation from the straight-line propagation of a wave when it encounters an opaque obstacle in its path. As a result of such a curvature of the trajectory, the wave propagates in some regions of space behind the obstacle.
There are two types of diffraction:
- Envelope obstacle wave. This happens if the size of the opaque object is smaller than the wavelength. Since the macroscopic bodies surrounding us are much larger than the wavelength of light, this type of diffraction is not observed in everyday life for light, but it often happens for sound.
- The passage of the wavefront through a narrow hole. If the wavelength is comparable with the width of the hole, then the phenomenon appears clearly. Diffraction on a slit of light belongs to this type.
What is the cause of this phenomenon?
To answer the question, it is necessary to recall the Huygens-Fresnel principle, which was proposed by Christian Huygens in the middle of the XVII century, and then refined for electromagnetic representations of light by Auguste Fresnel in the first half of the XIX century.
The noted principle states that each point of the wave front, in turn, is also a source of secondary waves. When light moves in a homogeneous medium, the result of the addition of the amplitudes of the secondary waves leads to the expansion and propagation of the wave front. When light encounters an opaque obstacle, many sources of secondary waves are blocked, and the resulting wave of the few remaining sources has a different path from the original, that is, diffraction occurs.
The complexity of solving the diffraction problem
The noted phenomenon is easy to explain in words, however, to obtain the trajectories of diffracted waves from different obstacles, one should use the Maxwell equations for electromagnetic waves. This mathematical problem is rather laborious and for the general case it has no solution.
In practice, they often use not the Maxwellian theory, but the aforementioned Huygens-Fresnel principle. But even its application involves the introduction of a number of approximations in obtaining the mathematical laws of diffraction.
Below, when considering diffraction by a slit, we assume that the wave front is flat and horizontally falls on the hole. In addition, we will analyze the picture obtained far from the gap. The combination of these conditions is characteristic of the so-called Fraunhofer diffraction.
Narrow Gap Diffraction and Interference
Suppose that a plane front of a light wave of length λ is incident on a slit of width b. After passing through the slit, the following light (diffraction) picture appears on the remote screen: there is a bright maximum opposite the slit, it accounts for most of the wave intensity (up to 90% of the original). To the left and to the right of it there will appear other less bright maxima, which are separated by dark stripes (minima). The figure below shows the corresponding graph and formula for the intensity of I bands in the diffraction pattern.
In the formula, β is the angle of observation.
The graph shows that the maximum conditions for diffraction by a gap can be written as follows:
sin (β) = λ * (2 * m + 1) / (2 * b) if m = 1, 2, 3, ...
sin (β) = λ * (2 * m - 1) / (2 * b) if m = -1, -2, -3, ...
sin (β) = 0 is the central maximum.
With an increase in the observation angle, the intensity of the maxima decreases.
It is important to understand that the described diffraction pattern is the result of not only the diffraction phenomenon, but also interference, that is, the superposition of waves of different phases on top of each other. The interference phenomenon imposes certain conditions under which a diffraction pattern can be observed. The main one is the coherence of the diffracted waves, that is, the constancy of the difference in their phases in time.
Change Slit Width
What will happen with diffraction on the gap, if you increase or decrease the width of the latter. In the expressions given in the previous paragraph for the maxima, the gap width b is in the denominator. This means that as its value increases, the angle of observation of the maxima will decrease, that is, they will narrow. The central peak will become narrower and more intense. This conclusion is consistent with the fact that the larger the width of the gap, the weaker diffraction appears on it.
The figure above shows the noted conclusion.
Note that for a constant slit width b, peaks can be narrowed (weaken the diffraction) if the light wavelength (λ) is reduced.