Formula for the light wavelength of a diffraction grating. Work order

MINISTRY OF EDUCATION AND SCIENCE OF RUSSIA

Yegoryevsk Technological Institute (branch)

federal state budgetary educational institution

higher professional education

"Moscow State Technological University "STANKIN"

(ETI FSBEI VPO MSTU "STANKIN")

Faculty of Technology and Production Management

Department of Natural Sciences

Determining the wavelength of light using a diffraction grating

Guidelines for performing laboratory work

ETI. F.LR.05.

Yegoryevsk 2014

Compiled by: _____________ V.Yu. Nikiforov, Art. UNM teacher

The guidelines give the basic definitions of geometric optics, discuss the basic laws of geometric optics, as well as diffraction of light, the Huygens-Fresnel principle, diffraction by slits in parallel rays of light, spectral instruments and diffraction gratings, experimental determination of the wavelength of light using a diffraction grating.

The guidelines are intended for 1st year students studying in the areas of bachelor's training: 151900 Design and technological support of automated engineering production, 220700 Automation of technological processes and production, 280700 Technosphere safety for laboratory work in the discipline "Physics".

Methodological guidelines were discussed and approved at a meeting of the educational and methodological group (UMG) of the UNM department

(protocol No. ___________ dated __________)

Chairman of the UMG _____________ G.G Shabaeva

Determining the wavelength of light using a diffraction grating

1 Purpose of the work: study of light diffraction by a grating and determination

light wavelength, using a diffraction grating with a known period d.

2 Equipment and materials: Device for determining the wavelength of light (optical bench), stand for the device, diffraction grating, illuminator, light filters.

3.1 Study theoretical material.

3.2 Perform experiments.

3.3 Enter the obtained measurements into the table.

3.4 Enter the results of measurements and calculations into the Report Table.

3.5 Draw a conclusion.

3.6 Create a report.

4 Theoretical information about the work

4.1 Geometric optics. Basic laws of geometric optics

Optics – a branch of physics that studies the properties and physical nature of light, as well as its interaction with matter. The doctrine of light is usually divided into three parts:

geometric or beam optics , which is based on the idea of light rays;

wave optics , which studies phenomena in which the wave properties of light are manifested;

quantum optics , which studies the interaction of light with matter, in which the corpuscular properties of light appear.

The basic laws of geometric optics were known long before the physical nature of light was established.

Law of rectilinear propagation of light : In an optically homogeneous medium, light travels in a straight line. An experimental proof of this law can be the sharp shadows cast by opaque bodies when illuminated by light from a source of sufficiently small size (“point source”). Another proof is the well-known experiment of passing light from a distant source through a small hole, resulting in the formation of a narrow beam of light. This experience leads to the idea of a light ray as a geometric line along which light propagates. It should be noted that the law of rectilinear propagation of light is violated and the concept of a light beam loses its meaning if the light passes through small holes whose dimensions are comparable to the wavelength. Thus, geometric optics, based on the idea of light rays, is the limiting case of wave optics at λ → 0. The limits of applicability of geometric optics will be discussed in the section on light diffraction.

At the interface between two transparent media, light can be partially reflected so that part of the light energy will propagate in a new direction after reflection, and part will pass through the boundary and continue to propagate in the second medium.

Law of Light Reflection : the incident and reflected rays, as well as the perpendicular to the interface between the two media, reconstructed at the point of incidence of the ray, lie in the same plane ( plane of incidence ). The angle of reflection γ is equal to the angle of incidence α.

Law of light refraction : the incident and refracted rays, as well as the perpendicular to the interface between the two media, reconstructed at the point of incidence of the ray, lie in the same plane. The ratio of the sine of the angle of incidence α to the sine of the angle of refraction β is a constant value for two given media:

The law of refraction was experimentally established by the Dutch scientist W. Snellius in 1621.

Constant value n called relative refractive index the second environment relative to the first. The refractive index of a medium relative to vacuum is called absolute refractive index .

The relative refractive index of two media is equal to the ratio of their absolute refractive indices:

n = n 2 / n 1 . (2)

The laws of reflection and refraction are explained in wave physics. According to wave concepts, refraction is a consequence of changes in the speed of propagation of waves when passing from one medium to another. The physical meaning of the refractive index is the ratio of the speed of propagation of waves in the first medium υ 1 to the speed of their propagation in the second medium υ 2:

The absolute refractive index is equal to the ratio of the speed of light c in vacuum to the speed of light υ in the medium:

Figure 1 illustrates the laws of reflection and refraction of light.

A medium with a lower absolute refractive index is called optically less dense.

When light passes from an optically denser medium to an optically less dense one n 2 < n 1 (for example, from glass to air) the phenomenon can be observed total reflection , that is, the disappearance of the refracted ray. This phenomenon is observed at angles of incidence exceeding a certain critical angle α pr, which is called limiting angle of total internal reflection (see Figure 2).

For the angle of incidence α = α pr sin β = 1; value sin α pr = n 2 / n 1 < 1.

If the second medium is air ( n 2 ≈ 1), then it is convenient to rewrite the formula in the form

sin α pr = 1 / n, (5)

Where n = n 1 > 1 – absolute refractive index of the first medium.

For the glass–air interface ( n= 1.5) the critical angle is α pr = 42°, for the water-air interface ( n= 1.33) α pr = 48.7°.

The phenomenon of total internal reflection is used in many optical devices. The most interesting and practically important application is the creation fiber light guides , which are thin (from several micrometers to millimeters) arbitrarily curved threads made of optically transparent material (glass, quartz). Light incident on the end of the light guide can travel along it over long distances due to total internal reflection from the side surfaces (Figure 3). The scientific and technical direction involved in the development and application of optical fibers is called fiber optics .

LABORATORY WORK

DETERMINING THE WAVELENGTH OF LIGHTBY USING

DIFFRACTION GRATING

GOAL OF THE WORK: Determine the wavelength of red and violet light.

EQUIPMENT: 1. A device for determining the wavelength of light,

2. light source, 3. diffraction grating.

THEORY: A parallel beam of light, passing through a diffraction grating, due to diffraction behind the grating, propagates in all possible directions and interferes. An interference pattern can be observed on a screen placed in the path of interfering light. Light maxima are observed at points on the screen for which the following condition is met:  =n, where D is the wave path difference,n– maximum number,l- light wavelength. The central maximum is called zero; for it  = 0. To the left and right of it are maxima of higher orders.

Diffraction Screen

lattice

The condition for the occurrence of a maximum can be written differently:

n = dsin

Whered– period of the diffraction grating,j– the angle at which the light maximum is visible (diffraction angle).

Since diffraction angles are, as a rule, small, for them we can take

sin  = tan ,Atan  = a/b

Therefore n×l = d×a/b

White light is complex in composition. The zero maximum for it is a white stripe, and the maximum of higher orders is a set of seven colored stripes, the totality of which is called the spectrum, respectively 1 th , 2 th , ... order, and the longer the wavelength, the further the maximum is from zero.

The diffraction spectrum can be obtained using a device to determine the wavelength of light.

ORDER OF WORK:

Place the lamp on the demonstration table and turn it on.

Looking through the diffraction grating, point the device at the lamp so that the lamp filament is visible through the window of the device screen.

Install the instrument screen at a distance of 400 mm from the diffraction grating and obtain a clear image of the spectra on it 1 th and 2 th orders of magnitude.

Determine the distance from the zero division “0” of the screen scale to the middle of the purple stripe, as to the left side “a” l ", and to the right "a P ", for first order spectra and calculate the average value "a sr.f »

A sr.f1 = (a l + a P ) / 2

cr. f. f. cr.

diffraction grating

screen

Repeat the experiment with a second order spectrum. Determine a for him sr.f2

Perform the same measurements for the red bands of the diffraction spectrum.

Calculate the wavelength of violet light, the wavelength of red light (for 1 th and 2 th orders) according to the formula:

= ,

Whered = 10 -5 m – constant (period) lattice,

n – spectrum order,

b– distance from the diffraction grating to the screen, mm

8. Determine the average values:

λ f = ; λ cr =

9. Determine measurement errors:

absolute –Δ λ f = |λ sr.f. - λ tab.f. | ; Whereλ tab.f = 0.4 µm

– Δ λ cr = |λ Wed cr. - λ tab.cr. | ; Whereλ tab.cr = 0.76 µm

relative –δ λ f = %; δ λ cr = %

10. Prepare a report. Enter the results of measurements and calculations into the table.

Order

spectrum

spectrum edge

violet. colors

spectrum edge

red colors

light wavelength

op.

« A l »,

« A P »,

« A Wed »

« A l »,

« A P »,

« A Wed »

f ,

cr ,

11. Draw a conclusion.

CONTROL QUESTIONS:

What is light diffraction?
What is a diffraction grating?
At what points on the screen are the 1st, 2nd, 3rd maximums obtained? How do they look?
Determine the diffraction grating constant if, when illuminated with light with a wavelength of 600 nm, the second-order maximum is visible at an angle of 7
Determine the wavelength if the first-order maximum is 36 mm from the zero maximum, and a diffraction grating with a constant of 0.01 mm is located at a distance of 500 mm from the screen.
Determine the wavelength incident on a diffraction grating with 400 lines on each millimeter. The diffraction grating c is located at a distance of 25 cm from the screen, the third-order maximum is 27.4 cm away from the zero maximum.

Determining the wavelength of light using a diffraction grating

Goal of the work: Determination using a diffraction grating of the wavelengths of light in different parts of the visible spectrum.

Devices and accessories: diffraction grating; flat scale with a slot and an incandescent lamp with a matte screen, mounted on an optical bench; millimeter ruler.

1. THEORY OF THE METHOD

Wave diffraction is the bending of waves around obstacles. Obstacles are understood as various inhomogeneities that waves, in particular light waves, can bend around, deviating from rectilinear propagation and entering the region of a geometric shadow. Diffraction is also observed when waves pass through holes, bending around their edges. Diffraction is noticeably pronounced if the sizes of obstacles or holes are of the order of the wavelength, as well as at large distances from them compared to their sizes.

Diffraction of light has practical applications in diffraction gratings. A diffraction grating is any periodic structure that affects the propagation of waves of one nature or another. The simplest optical diffraction grating is a series of identical parallel very narrow slits separated by identical opaque stripes. In addition to such transparent gratings, there are also reflective diffraction gratings, in which light is reflected from parallel irregularities. Transparent diffraction gratings are usually a glass plate on which stripes (strokes) are drawn with a diamond using a special dividing machine. These streaks are almost completely opaque spaces between the intact parts of the glass plate - the slits. The number of strokes per unit length is indicated on the grid. Period of the (constant) lattice d is the total width of one opaque line plus the width of one transparent slit, as shown in Fig. 1, where it is assumed that the strokes and stripes are located perpendicular to the plane of the drawing.

Let a parallel beam of light fall on the grating (GR) perpendicular to its plane, Fig. 1. Since the slits are very narrow, the phenomenon of diffraction will be strongly pronounced, and the light waves from each slit will go in different directions. In what follows, we will identify rectilinearly propagating waves with the concept of rays. From the entire set of rays propagating from each slit, we select a beam of parallel rays traveling at a certain angle  (diffraction angle) to the normal drawn to the grating plane. Of these rays, consider two rays, 1 and 2, which come from two corresponding points A And C adjacent slots, as shown in Fig. 1. Let’s draw a common perpendicular to these rays AB. At points A And C the phases of oscillations are the same, but on the segment CB a path difference  arises between the rays, equal to

 = d sin. (1)

After direct AB the path difference  between beams 1 and 2 remains unchanged. As can be seen from Fig. 1, the same path difference will exist between rays coming at the same angle  from the corresponding points of all adjacent slits.

Rice. 1. Passage of light through a diffraction grating DR: L – collecting lens, E – screen for observing the diffraction pattern, M – point of convergence of parallel rays

If now all these rays, i.e. waves, are brought together at one point, then they will either strengthen or weaken each other due to the phenomenon of interference. The maximum amplification, when the amplitudes of the waves are added, occurs if the path difference between them is equal to an integer number of wavelengths:  = k, where k– integer or zero,  – wavelength. Therefore, in directions satisfying the condition

d sin = k , (2)

maxima of light intensity with wavelength  will be observed.

To reduce rays coming at the same angle  to one point ( M) a collecting lens L is used, which has the property of collecting a parallel beam of rays at one of the points of its focal plane, where the screen E is placed. The focal plane passes through the focus of the lens and is parallel to the plane of the lens; distance f between these planes is equal to the focal length of the lens, Fig. 1. It is important that the lens does not change the difference in the path of the rays , and formula (2) remains valid. The role of the lens in this laboratory work is played by the lens of the observer's eye.

In directions for which the diffraction angle  does not satisfy relation (2), partial or complete attenuation of light will occur. In particular, light waves arriving at the meeting point in opposite phases will completely cancel each other out, and minimum illumination will be observed at the corresponding points on the screen. In addition, each slit, due to diffraction, sends rays of different intensities in different directions. As a result, the picture that appears on the screen will have a rather complex appearance: between the main maxima, determined by condition (2), there are additional or side maxima, separated by very dark areas - diffraction minima. However, in practice only the main maxima will be visible on the screen, since the light intensity in the secondary maxima, not to mention the minima, is very low.

If the light incident on the grating contains waves of different lengths  1,  2,  3, ..., then using formula (2) it is possible to calculate for each combination k and  their diffraction angle values , for which the main maxima of light intensity will be observed.

At k= 0 for any value of  it turns out  = 0, i.e., in the direction strictly perpendicular to the grating plane, waves of all lengths are amplified. This is the so-called zero-order spectrum. In general, the number k can take values k= 0, 1, 2, etc. Two signs, , for all values k 0 correspond to two systems of diffraction spectra located symmetrically with respect to the zero-order spectrum, to the left and to the right of it. At k= 1 spectrum is called the first order spectrum, when k= 2 a second-order spectrum is obtained, etc.

Since always |sin|  1, then from relation (2) it follows that for given d and  value k cannot be arbitrarily large. Maximum possible k, i.e. the limiting number of spectra k max , for a specific diffraction grating can be obtained from the condition that follows from (2) taking into account the fact that |sin|  1:

That's why k max is equal to the maximum integer not exceeding the ratio d/. As mentioned above, each slit sends rays of different intensity in different directions, and it turns out that at large values of the diffraction angle  the intensity of the sent rays is weak. Therefore, spectra with large values of | k|, which should be observed at large angles , will practically not be visible.

The picture that appears on the screen in the case of monochromatic light, i.e. light characterized by one specific wavelength , is shown in Fig. 2a. On a dark background you can see a system of individual bright lines of the same color, each of which corresponds to its own meaning k.

Rice. 2. Type of picture obtained using a diffraction grating: a) the case of monochromatic light, b) the case of white light

If non-monochromatic light containing a set of waves of different lengths (for example, white light) falls on the grating, then for a given k 0 waves with different lengths  will be amplified at different angles , and the light will be decomposed into a spectrum when each value k corresponds to the entire set of spectral lines, Fig. 2b. The ability of a diffraction grating to decompose light into a spectrum is used in practice to obtain and study spectra.

The main characteristics of a diffraction grating are its resolution R and variance D. If there are two waves with close lengths  1 and  2 in the light beam, then two closely spaced diffraction maxima will appear. With a small difference in wavelengths  =  1   2 these maxima will merge into one and will not be visible separately. According to the Rayleigh condition, two monochromatic spectral lines are still visible separately in the case when the maximum for the line with wavelength  1 falls in the place of the nearest minimum for the line with wavelength  2 and vice versa, as shown in Fig. 3.

Rice. 3. Diagram explaining the Rayleigh condition: I– light intensity in relative units

Usually, to characterize a diffraction grating (and other spectral devices), not the minimum value of  is used, when the lines are visible separately, but a dimensionless value

called resolution. In the case of a diffraction grating, using the Rayleigh condition, one can prove the formula

R = kN, (5)

Where N– the total number of grating lines, which can be found knowing the width of the grating L and period d:

Angular dispersion D is determined by the angular distance  between two spectral lines, related to the difference in their wavelengths :

It shows the rate of change in the diffraction angle  of rays depending on the change in wavelength .

The ratio / included in (7) can be found by replacing it with its derivative d/d, which can be calculated using relation (2), which gives

. (8)

For the case of small angles , when cos  1, from (8) we obtain

Along with angular dispersion D linear dispersion is also used D l, which is determined by the linear distance  l between spectral lines on the screen, related to the difference in their wavelengths :

Where D– angular dispersion, f– focal length of the lens (see Fig. 1). The second formula (10) is valid for small angles  and is obtained if we take into account that for such angles  l  f .

The higher the resolution R and variance D, the better the quality of any spectral device containing, in particular, a diffraction grating. Formulas (5) and (9) show that a good diffraction grating should contain a large number of lines N and have a short period d. In addition, it is desirable to use spectra of large orders (with large values k). However, as noted above, such spectra are difficult to see.

The purpose of this laboratory work is to determine the wavelength of light in various regions of the spectrum using a diffraction grating. The installation diagram is shown in Fig. 4. The role of the light source is played by a rectangular hole (slit) A in Shk scale, illuminated by an incandescent lamp with a matte screen S. The eye of the observer G, located behind the diffraction grating DR, observes the virtual image of the slit in those directions in which light waves coming from different slits of the grating are mutually amplified, i.e., in the directions of the main maxima.

Rice. 4. Laboratory setup diagram

Spectra of no higher than third order are studied, for which, in the case of the diffraction grating used, the diffraction angles  are small, and therefore their sines can be replaced by tangents. In turn, the tangent of the angle , as can be seen from Fig. 4, equal to the ratio y/x, Where y– distance from hole A to the virtual image of the spectral line on the scale, and x– distance from the scale to the grating. Thus,

. (11)

Then instead of formula (2) we will have , whence

2. PROCEDURE FOR PERFORMANCE OF THE WORK

1. Install as shown in Fig. 4, scale with hole A at one end of the optical bench close to the incandescent lamp S, and the diffraction grating - at its other end. Turn on the lamp in front of which there is a matte screen.

2. Moving the grating along the bench, ensure that the red border of the right spectrum of the first order ( k= 1) coincided with any whole division on the Shk scale; write down its value y in table 1.

3. Using a ruler, measure the distance x for this case and also enter its value in the table. 1.

4. Perform the same operations for the violet border of the right spectrum of the first order and for the middle of the green section located in the middle part of the spectrum (hereinafter this middle will be called the green line for brevity); values x And y for these cases also enter into the table. 1.

5. Make similar measurements for the left spectrum of the first order ( k= 1), entering the measurement results in the table. 1.

Please note that for left-handed spectra of any order k y.

6. Perform the same operations for the red and violet boundaries and for the green line of the second-order spectra; Enter the measurement data in the same table.

7. Enter in the table. 3 diffraction grating width L and the value of the grating period d, which are indicated on it.

Table 1

Lamp spectrum incandescent	x, cm	y, cm	 i, nm	 i =  i, nm




Purple

3. PROCESSING OF EXPERIMENTAL DATA

Using formula (12), calculate the wavelengths  i for all measurements taken

(d = 0.01 cm). Enter their values in the table. 1.

2. Find the average wavelengths separately for the red and violet boundaries of the continuous spectrum and the green line under study, as well as the average arithmetic errors in determination  using the formulas

Where n= 4 – number of measurements for each part of the spectrum. Enter the values in the table. 1.

3. Present the measurement results in the form of a table. 2, where write down the boundaries of the visible spectrum and the wavelength of the observed green line, expressed in nanometers and angstroms, taking as  the average values of the obtained wavelengths from the table. 1.

table 2

4. Using formula (6), determine the total number of grating lines N, and then using formulas (5) and (9) calculate the resolution R and angular dispersion of the grating D for the second order spectrum ( k = 2).

5. Using formula (3) and its explanation, determine the maximum number of spectra k max, which can be obtained using a given diffraction grating, using the average wavelength of the observed green line as .

6. Calculate the frequency  of the observed green line using the formula  = c/, where With– the speed of light, taking as  also the quantity .

All calculated in paragraphs. Enter 4–6 values in the table. 3.

Table 3

4. CHECK QUESTIONS

1. What is the phenomenon of diffraction and when is diffraction most noticeable?

Wave diffraction is the bending of waves around obstacles. Diffraction of light is a set of phenomena observed when light propagates through small holes, near the boundaries of opaque bodies, etc. and caused by the wave nature of light. The phenomenon of diffraction, common to all wave processes, has specific features for light, namely here, as a rule, the wavelength λ is much smaller than the dimensions d of barriers (or holes). Therefore, diffraction can only be observed at sufficiently large distances. l from the barrier ( l> d2/λ).

2. What is a diffraction grating and what are similar gratings used for?

A diffraction grating is any periodic structure that affects the propagation of waves of one nature or another. A diffraction grating produces multi-beam interference of coherent diffracted beams of light coming from all slits.

3. What is a typical transparent diffraction grating?

Transparent diffraction gratings are usually a glass plate on which stripes (strokes) are drawn with a diamond using a special dividing machine. These streaks are almost completely opaque spaces between the intact parts of the glass plate - the slits.

4. What is the purpose of the lens used in conjunction with the diffraction grating? What is the lens in this work?

To bring rays coming at the same angle φ to one point, a collecting lens is used, which has the property of collecting a parallel beam of rays at one of the points of its focal plane where the screen is placed. The role of the lens in this work is played by the lens of the observer's eye.

5. Why does a white stripe appear in the central part of the diffraction pattern when illuminated with white light?

White light is non-monochromatic light containing a set of wavelengths of different wavelengths. In the central part of the diffraction image k = 0, a central maximum of zero order is formed, therefore, a white stripe appears.

6. Define the resolution and angular dispersion of a diffraction grating.

The main characteristics of a diffraction grating are its resolution R and dispersion D.

Typically, to characterize a diffraction grating, it is not the minimum value of Δλ, when the lines are visible separately, that is used, but a dimensionless value

Angular dispersion D is determined by the angular distance δφ between two spectral lines, related to the difference in their wavelengths δλ:

It shows the speed of change in the diffraction angle φ of rays depending on the change in wavelength λ.

With the help Manual >> Physics

Calculation formula for calculation lengths light waves at help diffraction gratings. Measurement length waves comes down to definition ray deflection angle...

Goal of the work: Determination of wavelengths of red, green and violet rays for clearly visible spectra of the 1st and 2nd orders.

Devices and accessories: Diffraction grating, screen, backlight lamp.

Theoretical introduction

If a beam of parallel rays of light encounters an opaque circular body in its path, or is passed through a sufficiently small circular aperture, a light or dark spot will be seen on the screen in the center of alternating dark and light rings.

This phenomenon of light propagation into the region of a geometric shadow, indicating a deviation from the law of rectilinearity of light propagation, is called light diffraction.

To obtain bright diffraction spectra, they are used diffraction sieves ki. A diffraction grating is a flat glass plate on which a number of parallel lines are applied using a dividing machine (in good gratings - up to 1000 lines per millimeter). The strokes are practically opaque to light, because due to their roughness, they mainly scatter light. The spaces between the strokes allow light to pass through freely and are called slits.

The combination of the stroke width and the transparent gap is called period or lattice constant. If we denote the stroke width by b, and the width of the slit A, then the lattice period

Let light rays fall on the grating perpendicular to the plane. Light passing through each slit experiences diffraction, i.e. deviates from the straight direction. If a lens is placed in the path of the rays propagating from the slits of the grating, and a screen is placed in the focal plane of the lens, then all parallel rays coming at the same angle to the normal will gather at one point on the screen (Figure 1). Rays coming from a different angle will converge at a different point. The illumination of each point of the screen will depend both on the intensity of light given by each slit separately, and on the result of the interference of rays passing through different slits. As can be seen from Figure 1, the difference in the path of the rays for two adjacent slits

where d is the grating period, φ is the angle of deflection of the rays.

Picture 1

If this difference is equal to an even number of half-waves, maximum illumination will be observed in the direction of the angle φ:

d sinφ = 2kλ/2 = kλ, (1)

and on condition

d sinφ = (2k+1)λ/2 (2)

a minimum is observed.

It is easy to see that with a path difference ∆=kλ, all other gaps in the direction of the angle φ will also give a maximum, because in all cases the path differences will be multiples. These maxima are called major.

So, with normal incidence of rays on the grating, for the main maxima obtained on the screen from the diffraction grating, we have the following relation:

d sinφ = kλ, (3)

where k - 1,2,3,...integer number, called by spectrum row. The concept of spectrum order is associated with the fact that a number of maxima are observed on the screen, symmetrically located relative to the white stripe (zero-order spectrum), formed by light passing through the grating without deflection.

From formula (3) it is clear that the longer the wavelength, the larger the diffraction angle the position of the maximum corresponds to (Figure 2). When monochromatic light falls on the grating, single-color stripes appear on the screen. Formula (3) allows us to determine the light wavelength:

λ =d sinφ/k. (4)

Determining the wavelength comes down to measuring the angle φ. A special device, a goniometer, is used to measure angles (Figure 3). Where K is a callimator with a slit (to obtain a narrow beam of parallel rays); T - telescope; OK – eyepiece with a thread for pointing the telescope to a specific line of the spectrum; C - circular scale with vernier;

Figure 2

Dr - diffraction grating.