What is the difference between diffraction and dispersion? A simple way to calculate the maximum order of a spectrum

School course physics seems not at all complicated, understandable and quite interesting. It’s not so difficult to explain to the teacher in class how it differs diffraction spectrum from dispersion, and get good mark. But when it comes to physics in higher educational institutions, everything becomes dramatically more complicated. Some problems can force you to spend more than one sleepless night trying to solve them.

Different ways to decompose light into a spectrum

AND diffraction And dispersion represent decomposition light beam into components, but there are always some nuances:

Many people have seen experience with dispersion in physics lessons. To do this, it was enough to direct the beam at a prism, next to which there was a simple landscape sheet. And ordinary sunlight or a directed beam from a flashlight was decomposed into all the colors of the rainbow.

But at the same time, red color took up very little space on the sheet, the width of the remaining colors increased towards purple. It was he who occupied significant part the entire spectrum.

The highest order of the spectrum of a diffraction grating

Optics is exact science which requires logical thinking and correct calculations. Physicists once developed a formula that we can use to this day:

In this complex, but only at first glance, equality, the desired quantity is k- spectrum order:

• λ - wavelength of light incident on the grating.
• φ - diffraction angle.
• ά - angle of incidence of the light wave on the grating.
• đ - lattice period.

From this equality we can deduce the formula we are interested in, for determining maximum order spectrum Enough for this right side equalities divided by the light wavelength, while the sine of the diffraction angle can be replaced by unity for ease of calculation.

Some of the quantities needed for the calculation are constant, so no problems should arise. The main thing is not to get confused in the calculations.

Unfortunately, sometimes science is moving too far from practice and the meaning of most of these calculations remains a mystery for students and schoolchildren; they solve it as an abstract problem, in no way connected with real life.

A simple way to calculate the maximum order of a spectrum

Physicists also have a simpler way to determine maximum order. You can use the values ​​from the previous equation for the formula. Only this time there will be much less initial data, and the calculations themselves can be presented as:

It is easy to understand the desired value directly depends on the grating period and wavelength. We safely discarded the sines and expressed the maximum order in the form m.

It's hard to spend more than a minute dividing two numbers, so any optics problem that just requires determining the order value won't take that long. But more often than not, this calculation is only the first step towards finding an answer to a more complex question.

If you understand the issue and understand the essence of the concept, the formula seems extremely logical. The easiest way to solve the problem is with white light, because in this case the wavelength is the same for everything luminous flux.

Now imagine that there are several shades in the stream, which, of course, have different lengths. The task becomes somewhat more complicated; the calculations will take more time. And so it happened, in real life that waves of exclusively white light are extremely rare.

Diffraction spectrum width

In the experiment with a prism, you could observe the heterogeneity and width of the spectrum. This option has great value in optics, especially when it comes to the diffraction spectrum. The fact is that, unlike the dispersive one, it is not compressed in any direction, all shades are presented evenly and the width depends only on the indicators of the grating itself, with the help of which the beam is decomposed into a spectrum. While the width of the dispersion spectrum depends on the wavelength. In a diffraction grating:

1. There are transparent strokes.
2. There are opaque gaps.
3. The sum of their lengths is the lattice period.
4. This value can be obtained by dividing one by the number of lines per unit length of the grating.

The spectrum width we are interested in is in inverse relationship from the lattice period, which already appeared in previous formulas. Only now the shorter this period, the greater the width.

If we return to the definition of maximum order, we can see that with increasing lattice period values order also increased. From this, purely logically, it is easy to draw another conclusion - the width of the diffraction spectrum and its maximum order are in an inverse relationship.

The smaller one value, the more other, and vice versa. Of course, this knowledge will not help to obtain exact values. But checking your calculations in such a simple way is quite possible.

Difference between spectra

To highlight the differences between the dispersion and diffraction spectra, it is necessary to understand what each of them is.
Dispersive:

• Appears as a result of the decomposition of a light beam into its components after passing through a prism.
• Spreads from red to purple.
• The spectrum is compressed in the same direction, the red range has the smallest width, the violet range has the largest.
• There can only be one color picture.

Diffraction:

• It results from light hitting a diffraction grating.
• Goes in reverse order, from purple to red.
• The spectrum is uniform throughout its entire length.
• There may be several color pictures.

Here are the main four differences that allow us to understand what both spectrums are. Although the names are somewhat similar, they are based on completely different principles, so you should not confuse these concepts.

With knowledge of how the diffraction spectrum differs from the dispersion spectrum, you can begin the study of optics. The prospects of this discipline are underestimated, so researchers can expect guaranteed employment in the future, and perhaps serious discoveries.

Video: differences between diffraction and dispersion spectrum

In this video, physicist Denis Logachev will give a lesson in which he will talk about the difference between the diffraction spectrum and the dispersion spectrum, we will learn what a diffraction grating is:

To the question: How does the diffraction spectrum differ from the dispersion spectrum? given by the author European the best answer is The dispersive spectrum is obtained when light is refracted by a prism (rainbow).
The diffraction spectrum is obtained by diffraction on a grating.
They differ in the order of colors. In the dispersive mode they go (counting from the initial ray) - red, orange, yellow, green, blue, indigo, violet; in diffraction (counting from the main maximum) - violet, blue, cyan, green, yellow, orange, red.

Answer from 22 answers[guru]

Hello! Here is a selection of topics with answers to your question: How does the diffraction spectrum differ from the dispersive spectrum?

Answer from Yoasha Bodchenko[newbie]
diffraction is wave phenomenon- light scattering (well, electromagnetic wave V general case) on an obstacle. Particularly on the cracks.
A diffraction grating is spectral device, consisting of large quantity slits (parallel). Diffraction of light occurs at each slit. When the viewing angle changes (relative to the grating), a path difference arises between the light passing in a certain direction from the slits (between rays from different slits). For radiation with a certain wavelength, maxima appear at certain angles. The angles depend on the wavelength and the grating pitch.
In this way, it is possible to observe the spectrum of light that falls on the grating (since there is a dependence of the direction to the spectral maximum on the wavelength).
Long wavelength signals are more strongly deflected.
The main maxima are of several orders of magnitude. The number of effectively observable (non-overlapping) ones depends on the width of the spectrum of the observed radiation and the quality of the grating (number of lines per mm).
Dispersion is the dependence of the refractive index of a medium on the wavelength of electromagnetic radiation.
Since the ratio of the angles of incidence and refraction depends on the refractive index, a prism can be used to separate light into its spectral components.
Here, each component goes only in one direction.
Which light is more strongly deflected depends on the ratio of the refractive indices of the medium and the material from which the prism is made.
Differences.
After the prism, each spectral component is deflected in only one direction. After the diffraction grating - each component goes in all directions, but unevenly - has its own main and secondary maxima.
Visually this appears like this:
After the prism a solid strip or line spectrum- from blue to red.
After the diffraction grating, an achromatic maximum (in the middle) and several maxima on the right and left are visible - already stratified into components. If an object is considered - in maxima of the first order - its components different colors may overlap. Further they are better separated, but adjacent maxima may begin to overlap.
The nature of the phenomena is different.
Frequencies deviate in different ways.
In short, diffraction is “penetration”, dispersion is bending

Answer from Yebastian Rachowski[guru]
Hmm, strange, we were asked the same question today. In short, it seems like they’ve gone through all the answers that are here, but she still doesn’t like it.

Answer from scatter[guru]
My brain is melting!! AAA!

Answer from compound[guru]
One sec.
A spectrum is a set of values. For example, wavelengths. White light is a collection of light rays of different wavelengths ( various colors) ; if you direct a beam onto the surface of a trihedral prism parallel rays light, then upon exiting the prism the beam will no longer be parallel, but each ray will go in its own direction, and a spectrum of waves of different lengths will appear on the screen. That is, a “rainbow”, the stripes of which (they are of different colors) are spaced at different distances. The set of these stripes is the dispersion spectrum. That is, the dispersive spectrum is the spectrum of waves (meaning their lengths), obtained as a result varying degrees refraction of waves of different lengths (different colors). In short: disp. spectrum is the spectrum resulting from dispersion. What is the concept of diffraction spectrum associated with? Of course, with diffraction - the bending of waves of various obstacles, the sizes of which are commensurate with the sizes of the waves under consideration. For example, when it rains, small water droplets are formed in the atmosphere, which leads to diffraction. However, different wavelengths diffract differently - they are different lengths. They diffract differently, which means they deviate at different distances. That's why we can see a rainbow when it rains. So, the diffraction spectrum is the spectrum of waves obtained as a result of differences in the bending around obstacles of waves of different lengths. In short: dif. spectrum is the spectrum obtained by diffraction. Generalization: the words “dispersive” or “diffraction” spectrum complement what we're talking about- about the dispersion process, or the diffraction process. In general, we can talk about a wave of the same length. Then the spectrum will consist of one strip. Although in the case of diffraction, then it is also possible to redistribute the intensity of the wave on the screen - this is called the diffraction pattern.

DEFINITION

Diffraction spectrum is the intensity distribution on the screen that results from diffraction.

In this case, the main part of the light energy is concentrated in the central maximum.

If we take a diffraction grating as the device under consideration, with the help of which diffraction is carried out, then from the formula:

(where d is the grating constant; is the diffraction angle; is the wavelength of light; . is an integer), it follows that the angle at which the main maxima appear is related to the wavelength of the light incident on the grating (light falls normally on the grating). This means that the intensity maxima produced by light of different wavelengths occur in different places in the observation space, which makes it possible to use a diffraction grating as a spectral device.

If a diffraction grating falls White light, then all maxima with the exception of the central maximum are decomposed into a spectrum. From formula (1) it follows that the position of the th order maximum can be determined as:

From expression (2) it follows that with increasing wavelength, the distance from the central maximum to the maximum with number m increases. It turns out that the violet part of each main maximum will face the center of the diffraction pattern, and the red part will face outward. It should be remembered that when spectral decomposition In white light, violet rays are deflected more than red ones.

A diffraction grating is used as a simple spectral device with which the wavelength can be determined. If the grating period is known, then finding the wavelength of light will be reduced to measuring the angle that corresponds to the direction to the selected line of the order of the spectrum. Typically, first- or second-order spectra are used.

It should be noted that high-order diffraction spectra overlap each other. Thus, when white light is decomposed, the spectra of the second and third orders already partially overlap.

Diffraction and disperse decomposition into spectrum

Using diffraction, like dispersion, a beam of light can be broken down into its components. However there is fundamental differences in these physical phenomena. Thus, the diffraction spectrum is the result of light bending around obstacles, for example, dark areas near a diffraction grating. Such a spectrum spreads evenly in all directions. The violet part of the spectrum faces the center. A dispersive spectrum can be obtained by passing light through a prism. The spectrum is stretched in the violet direction and compressed in the red. The violet part of the spectrum occupies a larger width than the red part. During spectral decomposition, red rays deviate less than violet rays, which means that the red part of the spectrum is closer to the center.

Maximum spectral order during diffraction

Using formula (2) and taking into account the fact that it cannot be greater than one, we obtain that:

Examples of problem solving

EXAMPLE 1

EXAMPLE 2

In optics, a distinction is made between diffraction and dispersive light spectra. What are their features?

What is the diffraction spectrum?

This spectrum is formed when light passes through many small holes or slits. So, you can see it if you squint and look at the sun or a lamp. If you pay attention to the moon in the cold winter, it is easy to see multi-colored circles around it: they are also diffraction spectra. In this case, they are formed due to the passage of light through frozen water particles in the atmosphere. In order to carry out scientific experiments a kind of standard diffraction spectra are created using special diffraction gratings.

Diffraction spectrum

The type of spectrum under consideration is characterized by the deviation of the rays, which is proportional to the wavelength. Therefore, ultraviolet, as well as violet rays of the spectrum, which have short waves, deviate to the least extent. In turn, long-wave red and infrared are the opposite. It can be noted that the spectrum under consideration in to the greatest extent stretched towards long-wave rays.

What is a dispersive spectrum?

This spectrum is formed as a result of the refraction of light - for example, when it passes through a prism. Thus, it looks like a collection of light strips of different colors. Dispersion of light is the decomposition of its flux, which has White color, into monochromatic rays that form the light spectrum.

A remarkable fact is known in the history of physics: before it was discovered dispersive spectrum, it was a common view that white light was colored when passing through a prism. It turned out that this was not the case.

In the dispersion spectrum, the greatest deviation during refraction is characteristic of violet rays. The spectrum under consideration is stretched more evenly than the diffraction spectrum - across all types of rays, but to the greatest extent - towards short-wavelength ones.

Comparison

The main difference between the diffraction spectrum and the dispersive spectrum is that the first spectrum is formed as a result of the passage of light through narrow holes (and other areas that do not interfere with the passage of rays between some closely located objects), and the second - as a result of its refraction (for example, due to passing through a prism ).

There may also be differences between the spectra under consideration in terms of:

• deviations of red and violet rays;
• degree of spectrum stretching;
• the degree of spectrum stretching relative to red and violet rays.

To more clearly display what the difference between the diffraction and dispersion spectrum is in terms of the noted parameters, a small table will help us.