What does a diffraction grating look like? Diffraction grating

Diffraction grating– an optical device that is a collection large number parallel, usually equally spaced slits. A diffraction grating can be obtained by applying opaque scratches (striations) to a glass plate. Unscratched places - cracks - will let light through, while strokes will scatter and not let light through (Fig. 3).

Rice. 3. Cross section of a diffraction grating (a) and its graphical representation (b)

To derive the formula, consider a diffraction grating under the condition of perpendicular incidence of light (Fig. 4). Let us choose two parallel rays that pass through two slits and are directed at an angle φ to the normal.

With the help of a collecting lens (eye), these two rays will fall into one point of the focal plane P and the result of their interference will depend on the phase difference or on their path difference. If the lens is perpendicular to the rays, then the path difference will be determined by the segment BC, where AC is perpendicular to rays A and B. In the triangle ABC we have: AB = a + b = d - the period of the grating, BAC = φ, as angles with mutually perpendicular parties.

From formulas (8) and (9) we obtain diffraction grating formula:

Rice. 4. Diffraction of light by a diffraction grating

Those. the position of the light line in the diffraction spectrum does not depend on the grating material, but is determined by the grating period, which is equal to the sum of the slit width and the gap between the slits.

Resolution of the diffraction grating.

If the light incident on the diffraction grating is polychromatic, i.e. consists of several wavelengths, then in the spectrum the maxima of individual  will be at different angles. The resolution can be characterized angular dispersion:

Consequently, the greater the spectral order k, the greater the angular dispersion.

II. Students' work during a practical lesson.

Exercise 1.

Get permission to take classes. To do this you need:

- have notes in workbook, containing the title of the work, the basic theoretical concepts of the topic being studied, the objectives of the experiment, a table based on the sample for entering experimental results;

– successfully pass control according to the experimental methodology;

– obtain permission from the teacher to perform the experimental part of the work.

Task 2.

Carrying out laboratory work, discussing the results obtained, writing notes.

Devices and accessories

Rice. 5 Installation diagram

1. Diffraction grating.

2. Light source.

4. Ruler.

In this laboratory work It is proposed to determine the wavelengths for red and green colors, which are obtained when light passes through a diffraction grating. In this case, a diffraction spectrum is observed on the screen. A diffraction grating consists of a large number of parallel slits, very small compared to the wavelength. The slits allow light to pass through, while the space between the slits is opaque. Total slits – N, with a distance between their centers – d. Diffraction grating formula:

where d is the grating period; sin φ – sine of the angle of deviation from the rectilinear propagation of light; k – maximum order; λ – wavelength of light.

The experimental setup consists of a diffraction grating, a light source and a movable screen with a ruler. The diffraction spectrum is observed on the screen (Fig. 5).

The distance L from the diffraction grating to the screen can be changed by moving the screen. Distance from the central ray of light to a separate line of the spectrum l. At small angles φ.

Diffraction grating

Very large reflective diffraction grating.

Diffraction grating - an optical device operating on the principle of light diffraction, is a collection of a large number of regularly spaced strokes (slots, protrusions) applied to a certain surface. The first description of the phenomenon was made by James Gregory, who used bird feathers as a lattice.

Types of gratings

Reflective: Strokes are applied to a mirror (metal) surface, and observation is carried out in reflected light
Transparent: Strokes are applied to a transparent surface (or cut out in the form of slits on an opaque screen), observation is carried out in transmitted light.

Description of the phenomenon

This is what the light from an incandescent flashlight looks like when it passes through a transparent diffraction grating. Zero maximum ( m=0) corresponds to light passing through the grating without deviation. Due to lattice dispersion in the first ( m=±1) at the maximum, one can observe the decomposition of light into a spectrum. The deflection angle increases with increasing wavelength (from purple to red)

The front of the light wave is divided by the grating bars into separate beams of coherent light. These beams undergo diffraction by the streaks and interfere with each other. Since each wavelength has its own diffraction angle, white light is decomposed into a spectrum.

Formulas

The distance through which the lines on the grating are repeated is called the period of the diffraction grating. Designated by letter d.

If the number of strokes is known ( N), per 1 mm of grating, then the grating period is found using the formula: 0.001 / N

Diffraction grating formula:

d- grating period, α - maximum angle of a given color, k- order of maximum, λ - wavelength.

Characteristics

One of the characteristics of a diffraction grating is angular dispersion. Let us assume that a maximum of some order is observed at an angle φ for wavelength λ and at an angle φ+Δφ for wavelength λ+Δλ. The angular dispersion of the grating is called the ratio D=Δφ/Δλ. The expression for D can be obtained by differentiating the diffraction grating formula

Thus, angular dispersion increases with decreasing grating period d and increasing spectrum order k.

Manufacturing

Good gratings require very high manufacturing precision. If at least one of the many slots is placed with an error, the grating will be defective. The machine for making gratings is firmly and deeply built into a special foundation. Before starting the actual production of gratings, the machine runs for 5-20 hours Idling to stabilize all its nodes. Cutting the grating lasts up to 7 days, although the stroke time is 2-3 seconds.

Application

Diffraction gratings are used in spectral instruments, also as optical sensors of linear and angular displacements (measuring diffraction gratings), polarizers and filters infrared radiation, beam splitters in interferometers and so-called “anti-glare” glasses.

Literature

Sivukhin D.V. General physics course. - 3rd edition, stereotypical. - M.: Fizmatlit, MIPT, 2002. - T. IV. Optics. - 792 p. - ISBN 5-9221-0228-1
Tarasov K.I., Spectral devices, 1968

Types of gratings

Reflective: Strokes are applied to a mirror (metal) surface, and observation is carried out in reflected light
Transparent: Strokes are applied to a transparent surface (or cut out in the form of slits on an opaque screen), observation is carried out in transmitted light.

Description of the phenomenon

The front of the light wave is divided by the grating bars into separate beams of coherent light. These beams undergo diffraction by the streaks and interfere with each other. Since for different lengths Since the interference waves are at different angles (determined by the difference in the path of the interfering rays), the white light is decomposed into a spectrum.

Formulas

The distance through which the lines on the grating are repeated is called the period of the diffraction grating. Designated by letter d.

If the number of lines () per 1 mm of the grating is known, then the period of the grating is found using the formula: mm.

The conditions for the interference maxima of the diffraction grating, observed at certain angles, have the form:

- grating period, - angle of maximum of a given color, - order of maximum, that is serial number maximum, measured from the center of the picture, is the wavelength.

If the light hits the grating at an angle, then:

Characteristics

Thus, angular dispersion increases with decreasing grating period d and increasing spectrum order k.

Manufacturing

Good gratings require very high manufacturing precision. If at least one of the many slots is placed with an error, the grating will be defective. The machine for making gratings is firmly and deeply built into a special foundation. Before starting the actual production of gratings, the machine runs for 5-20 hours at idle speed to stabilize all its components. Cutting the grating lasts up to 7 days, although the stroke time is 2-3 seconds.

Application

Diffraction gratings are used in spectral instruments, also as optical sensors of linear and angular displacements (measuring diffraction gratings), polarizers and filters of infrared radiation, beam splitters in interferometers and so-called “anti-glare” glasses.

Examples

Rainbow on CD

One of the simplest and most common examples of reflective diffraction gratings in everyday life is a CD or DVD. On the surface of the CD there is a track in the form of a spiral with a pitch of 1.6 microns between turns. Approximately a third of the width (0.5 µm) of this track is occupied by a recess (this is the recorded data), which scatters the light incident on it, and approximately two-thirds (1.1 µm) is an untouched substrate that reflects the light. Thus, a CD is a reflective diffraction grating with a period of 1.6 microns.

Literature

Sivukhin D.V. General physics course. - M.. - T. IV. Optics.
Tarasov K.I., Spectral devices, 1968

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See what a “Diffraction grating” is in other dictionaries:

Diffraction grating- Diffraction grating. Scheme for the formation of spectra using a transparent diffraction grating consisting of slits: d grating period; a is the angle of incidence of the rays on the grating; b the angle between the normal to the grating and the direction of propagation of the diffracted... ... Illustrated Encyclopedic Dictionary

DIFFRACTION GRATING- optical a device that is a periodic a structure of a large number of regularly arranged elements on which light diffraction occurs (for example, parallel and equally spaced lines applied to a flat or concave optical surface) ... Physical encyclopedia

DIFFRACTION GRATING- DIFFRACTION GRATING, an optical device that is a periodic structure of a large number (300-1200 per 1 mm for the ultraviolet and visible region) of regularly spaced elements (slits in an opaque or streaks in a reflective... ... Modern encyclopedia

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diffraction grating- difrakcinė gardelė statusas T sritis fizika atitikmenys: engl. diffraction grating vok. Beugungsgitter, n; Diffraktionsgitter, n rus. diffraction grating, f pranc. réseau de diffraction, m … Fizikos terminų žodynas

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DEFINITION

Diffraction grating called a spectral device, which is a system of a number of slits separated by opaque spaces.

Very often in practice, a one-dimensional diffraction grating is used, consisting of parallel slits of the same width, located in the same plane, which are separated by opaque intervals of equal width. Such a grating is made using a special dividing machine, which applies parallel strokes to a glass plate. The number of such strokes can be more than a thousand per millimeter.

Reflective diffraction gratings are considered the best. This is a collection of areas that reflect light with areas that reflect light. Such gratings are a polished metal plate on which light-scattering strokes are applied with a cutter.

The diffraction pattern on the grating is the result of mutual interference of waves that come from all the slits. Consequently, with the help of a diffraction grating, multi-beam interference of coherent beams of light that have undergone diffraction and coming from all slits is realized.

Let us assume that the width of the slit on the diffraction grating is a, the width of the opaque section is b, then the value is:

is called the period of the (constant) diffraction grating.

Diffraction pattern on a one-dimensional diffraction grating

Let us imagine that a monochromatic wave is incident normally to the plane of the diffraction grating. Due to the fact that the slits are located at equal distances from each other, the path differences of the rays () that come from a pair of adjacent slits for the chosen direction will be the same for the entire given diffraction grating:

The main intensity minima are observed in the directions determined by the condition:

In addition to the main minima, as a result of the mutual interference of the light rays sent by a pair of slits, in some directions they cancel each other, which means that additional minima appear. They arise in directions where the difference in the path of the rays is an odd number of half-waves. The condition for additional minima is written as:

where N is the number of slits of the diffraction grating; k’ accepts any integer values except 0, . If the lattice has N slits, then between the two main maxima there are an additional minimum that separates the secondary maxima.

The condition for the main maxima for a diffraction grating is the expression:

Since the sine value cannot be greater than one, the number of main maxima is:

If white light is passed through the grating, then all maxima (except for the central m = 0) will be decomposed into a spectrum. In this case, the violet region of this spectrum will face the center of the diffraction pattern. This property Diffraction gratings are used to study the composition of the light spectrum. If the grating period is known, then calculating the wavelength of light can be reduced to finding the angle , which corresponds to the direction to the maximum.

Examples of problem solving

EXAMPLE 1

Exercise

What is the maximum spectral order that can be obtained using a diffraction grating with constant m if a monochromatic beam of light with wavelength m is incident on it perpendicular to the surface?

Solution

As a basis for solving the problem, we use the formula, which is the condition for observing the main maxima for the diffraction pattern obtained when light passes through a diffraction grating:

The maximum value is one, so:

From (1.2) we express , we get:

Let's carry out the calculations:

Answer

EXAMPLE 2

Exercise

Monochromatic light of wavelength . is passed through a diffraction grating. A screen is placed at a distance L from the grating. Using a lens located near the grating, a projection of the diffraction pattern is created onto it. In this case, the first diffraction maximum is located at a distance l from the central one. What is the number of lines per unit length of the diffraction grating (N) if light falls on it normally?

Solution

Let's make a drawing.

It is no secret that, along with tangible matter, we are also surrounded by wave fields with their own processes and laws. These can be electromagnetic, sound, and light vibrations, which are inextricably linked with the visible world, interact with it and influence it. Such processes and influences have long been studied by various scientists, who have derived basic laws that are still relevant today. One of the widely used forms of interaction between matter and waves is diffraction, the study of which led to the emergence of such a device as a diffraction grating, which is widely used both in instruments for further research of wave radiation and in everyday life.

Concept of diffraction

Diffraction is the process of light, sound and other waves bending around any obstacle encountered along their path. More generally, this term can be used to describe any deviation of wave propagation from the laws of geometric optics that occurs near obstacles. Due to the phenomenon of diffraction, waves fall into the region of a geometric shadow, go around obstacles, penetrate through small holes in screens, etc. For example, you can clearly hear a sound when you are around the corner of a house, as a result of the sound wave going around it. Diffraction of light rays manifests itself in the fact that the shadow area does not correspond to the passage opening or existing obstacle. The operating principle of a diffraction grating is based on this phenomenon. Therefore, the study of these concepts is inseparable from each other.

Concept of a diffraction grating

A diffraction grating is an optical product that is a periodic structure consisting of a large number of very narrow slits separated by opaque spaces.

Another version of this device is a set of parallel microscopic lines of the same shape, applied to a concave or flat optical surface with the same specified pitch. When light waves fall on the grating, a process of redistribution of the wave front in space occurs, which is due to the phenomenon of diffraction. That is, white light is decomposed into individual waves of different lengths, which depends on the spectral characteristics of the diffraction grating. Most often, to work with the visible range of the spectrum (with a wavelength of 390-780 nm), devices with from 300 to 1600 lines per millimeter are used. In practice, the grille looks like a flat glass or metal surface with rough grooves (strokes) applied at a certain interval that do not transmit light. With the help of glass gratings, observations are carried out in both transmitted and reflected light, with the help of metal gratings - only in reflected light.

Types of gratings

As already mentioned, according to the material used in manufacturing and the features of use, diffraction gratings are divided into reflective and transparent. The first include devices that are made of metal mirror surface with applied strokes, which are used for observations in reflected light. In transparent gratings, strokes are applied to a special optical surface that transmits rays (flat or concave), or narrow slits are cut in an opaque material. Studies when using such devices are carried out in transmitted light. An example of a coarse diffraction grating in nature is eyelashes. Looking through squinted eyelids, you can at some point see spectral lines.

Operating principle

The operation of a diffraction grating is based on the phenomenon of diffraction of a light wave, which, passing through a system of transparent and opaque regions, is broken into separate beams of coherent light. They undergo diffraction by the lines. And at the same time they interfere with each other. Each wavelength has its own diffraction angle, so white light is decomposed into a spectrum.

Diffraction grating resolution

Being an optical device used in spectral instruments, it has a number of characteristics that determine its use. One of these properties is resolution, which consists in the possibility of separately observing two spectral lines with close wavelengths. An increase in this characteristic is achieved by increasing the total number of lines present in the diffraction grating.

IN good device the number of lines per millimeter reaches 500, that is, with a total grating length of 100 millimeters, the total number of lines will be 50,000. This figure will help achieve narrower interference maxima, which will allow identifying close spectral lines.

Application of diffraction gratings

Using this optical device, you can accurately determine the wavelength, so it is used as a dispersing element in spectral devices for various purposes. A diffraction grating is used to separate monochromatic light (in monochromators, spectrophotometers and others), as an optical sensor of linear or angular displacements (the so-called measuring grating), in polarizers and optical filters, as a beam splitter in an interferometer, and also in anti-glare glasses .

In everyday life, you can often come across examples of diffraction gratings. The simplest of reflective devices can be considered the cutting of compact discs, since a track is applied to their surface in a spiral with a pitch of 1.6 microns between turns. A third of the width (0.5 microns) of such a track falls on the recess (where the recorded information is contained), which scatters the incident light, and about two thirds (1.1 microns) is occupied by an untouched substrate capable of reflecting the rays. Therefore, a CD is a reflective diffraction grating with a period of 1.6 µm. Another example of such a device is holograms various types and directions of application.

Manufacturing

To obtain a high-quality diffraction grating, it is necessary to maintain very high manufacturing accuracy. An error when applying even one stroke or gap leads to immediate rejection of the product. For the manufacturing process, a special dividing machine with diamond cutters is used, attached to a special massive foundation. Before starting the grating cutting process, this equipment must run for 5 to 20 hours in idle mode to stabilize all components. Manufacturing one diffraction grating takes almost 7 days. Despite the fact that each stroke takes only 3 seconds to apply. When manufactured in this way, the gratings have parallel strokes equally spaced from each other, the cross-sectional shape of which depends on the profile of the diamond cutter.

Modern diffraction gratings for spectral instruments

Currently widespread new technology their production by creating an interference pattern obtained from laser radiation on special light-sensitive materials called photoresists. As a result, products with a holographic effect are produced. You can apply strokes in this way on a flat surface, obtaining a flat diffraction grating or a concave spherical one, which will give a concave device that has a focusing effect. Both are used in the design of modern spectral instruments.

Thus, the phenomenon of diffraction is common in Everyday life everywhere. This leads to the widespread use of a device based on this process, such as a diffraction grating. It can either become part of scientific research equipment or be found in everyday life, for example, as the basis for holographic products.

What does a diffraction grating look like? Diffraction grating

Resolution of the diffraction grating.

II. Students' work during a practical lesson.

Devices and accessories

Types of gratings

Description of the phenomenon

Formulas

Characteristics

Manufacturing

Application

Literature

see also

See what “Diffraction grating” is in other dictionaries:

Types of gratings

Description of the phenomenon

Formulas

Characteristics

Manufacturing

Application

Examples

see also

Literature

See what a “Diffraction grating” is in other dictionaries:

Diffraction pattern on a one-dimensional diffraction grating

Examples of problem solving

Concept of diffraction

Concept of a diffraction grating

Types of gratings

Operating principle

Diffraction grating resolution

Application of diffraction gratings

Manufacturing

Modern diffraction gratings for spectral instruments