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Measuring the wavelength of light wave with transmission grating

Physics Yang Guihong.

Yunnan Honghe University Physics Department Yunnan Mengzi 66 1 100

This paper introduces how to measure the wavelength of light wave with transmission grating, as well as the details of measurement and the experimental preparation before measurement.

Key words: grating, principal maximum, secondary maximum, spectrometer, monochromatic light, polychromatic light.

Introduction:

We can't live without sunshine. Generally, we think that sunlight is monochromatic light [1] (light with a single wavelength). In fact, the light around us is polychromatic light (light composed of two or more monochromatic lights), which is composed of monochromatic lights with different wavelengths.

Broadly speaking, diffraction screens with periodic spatial structure or optical properties (such as transmittance and refractive index) are collectively called gratings. There are many kinds of gratings, such as transmission grating and reflection grating, plane grating and concave grating, black-and-white grating and sine grating, one-dimensional grating, two-dimensional grating and three-dimensional grating, etc. The grating used in this experiment is a holographic transmission grating shot by holographic technology. If the grating surface is not easy to clean after being polluted, special attention should be paid when using it [2].

Spectrometer is an optical instrument that can accurately measure angles. It is often used to measure the refractive index, dispersion rate, wavelength of light wave and spectral observation of materials. Because the equipment is precise and has many complicated control parts, it must be adjusted in strict accordance with certain rules and procedures in order to measure accurate results.

The spectrometer is mainly composed of five parts: triangular base, collimator, telescope, calibration disk and stage. See table 1 for the name and function of the regulating device in the figure.

Schematic diagram of basic structure of spectrometer

Table 1 Name and function of spectrometer adjusting device

Code function

1 slit width adjustment screw adjusts the slit width to change the incident light width.

2 slit device

3 When loosening the locking screw of the slit device, pull the slit device back and forth to adjust the parallel light. After adjustment, lock it to fix the slit device.

Collimator produces parallel light.

5. The optical element is placed on the stage. Three fine-tooth screws 7 are installed under the table top for adjusting the inclination of the table top. Loosen screw 8 to lift and rotate the stage.

6. Clamp the reed of the object to be measured and clamp the optical element on the stage.

Seven stage adjustment screws (3) are used to adjust the level of the stage.

8 Loosen the locking screw of the stage, and the stage can rotate and lift independently; After locking, the stage can rotate synchronously with the reading cursor disk.

9 telescope to observe the light after the action of optical elements.

When the locking screw of 10 eyepiece device is loosened, the eyepiece device can be extended and rotated (telescope focusing); After locking, fix the eyepiece device.

1 1 abbe autocollimator eyepiece device can be telescopic and rotated (telescope focusing).

12 eyepiece focusing handwheel adjusts the eyepiece focal length, so that the crosshairs and forks are clear.

13 telescope optical axis elevation adjustment screw adjusts the elevation of the telescope.

14 telescope optical axis horizontal adjustment screw Adjust this screw to make the telescope rotate in the horizontal plane.

15 telescope bracket

The two cursors are symmetrically arranged on the 16 cursor disk.

17 The cursor is divided into 30 cells, and each cell corresponds to an angle 1'.

18 telescope fine-tuning screw This screw is located on the reverse side of figure 14- 1. After locking the brake screw 2 1 of the telescopic bracket, adjust the screw 18 to slightly rotate the telescopic bracket.

19 dial is divided into 360 degrees, and the minimum scale is half a degree (30'). If it is less than half a degree, read it with the cursor.

20 Eyepiece Lighting Power Turn on the power 20, and a green dot and a black cross can be seen from the eyepiece.

2 1 telescopic bracket brake screw This screw is located on the reverse side of Figure 14- 1. After locking, the telescope bracket can only rotate slightly with the telescope fine-tuning screw 18.

After the telescope bracket is locked with the dial locking screw, the telescope rotates synchronously with the dial.

23 spectrometer power socket

The triangular base of the spectrometer is the base of the whole spectrometer. The center of the base is provided with a rotating shaft sleeve along the vertical direction, and the whole telescope assembly, dial and vernier disk can rotate independently around the central axis. The collimator is fixed on one foot of the triangular base.

25 collimator bracket

26 Vernier caliper adjusting screw After locking vernier caliper braking screw 27, adjusting screw 26 can make vernier caliper rotate slightly.

27 After locking the screw of the disc brake, the disc brake can only rotate slightly with the fine adjustment screw of the disc 26.

28 collimator optical axis horizontal adjustment screw, so that the collimator rotates in the horizontal plane.

Adjust the elevation angle of the optical axis of the collimator by adjusting the screw.

Experimental principle:

In figure 1, several curves of interference factors between coal seams with different numbers are given. For comparison, the ordinate is reduced, and they have the following characteristics:

(1) Size, location and number of main strong peaks

When (),,, but their ratio, these places are the main maxima of the interference factor between slits (there are some new intensity maxima and minima in the multi-slit diffraction pattern, in which the stronger bright lines are called the main maxima and the weaker bright lines are called the sub-maxima). This means that the diffraction angle satisfies the following conditions:

( 1)

Equation (1) shows that whenever there is a main maximum in the direction where the diffraction angle satisfies equation (1), the intensity of the main maximum is twice that of a single slit in that direction. The position of the main strength point has nothing to do with the number of joints.

(2) The position of the zero point, the width of the major half angle and the number of minor half angles.

When Nβ is equal to an integer multiple of π, but β is not an integer multiple of π, sinNβ=0, sinβ≠0, where is the zero point of the interference factor between cracks. The zero point is in the following position:

Sinθ=(k+m/N)λ/d (2) where k = 0, 1, 2, …; m= 1，…，N- 1。

So there are N- 1 dark lines (zeros) between the strong points, and there is a sub-strong point between adjacent dark lines, so * * * has N-2 sub-strong points.

The formula of half-angle width is △θ=λ/Nd? cosθk .(3)

The width △ θ of the half angle of the principal extreme value is inversely proportional to nd, and the greater the Nd, the smaller the △ θ, which means the greater the sharpness of the principal extreme value. Reflected on the screen, that is, the thinner the main strong bright line.

Above, we only analyzed the characteristics of the interference factor between slits, and the actual light intensity distribution has to be multiplied by the single slit diffraction factor. Multiply the interference factor between slits shown in figure 1 with the single slit diffraction factor shown in figure 1 to obtain the light intensity distribution shown in figure 2[(a), (b) and (c)]. It can be seen that the actual light intensity distribution obtained by multiplying the single slit diffraction factor is at all levels.

Given the interval d of the slit, the position of the main pole is determined. At this time, the single slit diffraction factor does not change the position and half-angle width of the main pole, but only changes the intensity of the main poles at all levels. In other words, the single slit diffraction factor affects the intensity distribution between the principal poles at all levels.

As shown in fig. 3, let s be a slender slit light source located on the focal plane of the lens L 1 and g be a grating. The distance d between two corresponding adjacent slits on the grating is called grating constant, and the parallel light emitted from L 1 irradiates the grating G vertically ... The lens L2 converges the diffracted light at an angle θ with the normal of the grating at the point Pθ on its image focal plane, which is obtained by the grating splitting principle of (1).

(3)

The above formula is called grating equation, where θ is diffraction angle, λ is wavelength of light wave, and k is spectral series (k=0, 1, 2 …). Diffraction bright stripe is actually a diffraction image of light source with slit, which is a sharp and thin bright line. When k=0, in the direction of θ=0, bright lines of various wavelengths overlap together to form a bright zero-order image. For other values of k, bright lines with different wavelengths appear in different directions to form spectra. At this time, bright lines with different wavelengths are called spectral lines. The two groups of spectra corresponding to the positive and negative values of k are symmetrically distributed on both sides of the zero-order image. Therefore, if the grating constant d is known. When the diffraction angle θ and spectral order K of a spectral line are determined, the wavelength λ of the spectral line can be obtained by formula (1); On the other hand, if the wavelength λ is known. The grating constant d can be found.

Experimental steps:

1. Adjust the spectrometer during the experiment,

(1) coarse tune.

A, rotate the eyepiece handwheel to make the crosshairs and green crosses as clear as possible.

B, adjust the stage, so that the protruding parts of the following three screws are equal in height, and the plane of the stage is roughly perpendicular to the spindle (visual inspection).

C, adjust the telescope optical axis pitch adjustment screw, make the telescope optical axis as horizontal as possible (visual inspection).

Coarse adjustment requirements: put a prism on the stage. When an optical surface of the prism is almost perpendicular to the optical axis of the telescope, you should be able to see the reflected cross image, which generally does not coincide with the intersection point of the cross line, so that the coarse adjustment is completed.

(2) fine-tuning.

A, make the spectrometer telescope adapt to parallel light (focusing on infinity), the main axes of the telescope and collimator are perpendicular to the main axis of the instrument, and the collimator emits parallel light.

B, aim the telescope at the collimator, observe the image of the slit of the irradiated collimator from the telescope to make it coincide with the vertical line of the reticle, and fix the telescope. Refer to Figure 3, place the grating, light up the crosshead illumination of the eyepiece (remove or turn off the slit illumination), turn the stage left and right, and see the reflected "green cross". Adjust b2 or b3 so that the "green cross" coincides with the adjustment crosshead in the eyepiece. At this time, the grating surface is perpendicular to the incident light.

Illuminate the slit of the collimator with a mercury lamp and rotate the telescope to observe the spectrum. If the spectral lines on the left and right sides are not equal to the horizontal line of the crossed wires in the eyepiece (as shown in Figure 3), it means that the diffraction surface of the grating is inconsistent with the observation surface. At this point, adjust the screws b 1 on the platform to make them consistent. Finally, the diffraction plane of the grating surface should be adjusted to be consistent with the dial plane of the observation surface.

2. Measurement of grating constant d: As long as the diffraction angle of the spectral line with known wavelength λ in the k-th spectrum is measured, the value of d can be obtained according to formula (3).

(1). Adjust the spectrometer according to (1).

(2). Adjust the grating position

(3) Irradiate the collimator with a mercury lamp, rotate the telescope to one side of the grating, align the vertical line of the reticle with the center of the kth spectral line with known wavelength, and record two vernier values.

(4) Turn the telescope to the other side of the grating so that the vertical line of the reticle is aligned with the center of the kth spectral line with known wavelength, and record two vernier values.

(5) Repeat steps 4 and 5 twice to obtain three sets of data.

3. The spectral order k is up to us. Because the grating constant d has been measured, as long as the diffraction angle of the k-th spectral line of the wavelength is unknown, its wavelength value can be obtained.

To know the wavelength, you can use the green line (nm) in the spectrum of mercury lamp or one of the two yellow lines in the spectrum of sodium lamp.

Measuring unknown wavelength

(1). Irradiate the collimator with a mercury lamp, rotate the telescope to one side of the grating, align the vertical line of the reticle with the center of the kth spectral line of known wavelength, and record two vernier values.

(2) Turn the telescope to one side of the grating, align the vertical lines of the intersecting lines, know the center of the kth spectral line of the wavelength, and record two vernier values; Turn the telescope to the other side of the grating and measure as described above. The difference between two readings of the same cursor is twice the diffraction angle.

(3) Repeat steps 1 and 2 twice to obtain three sets of data.

Experimental data: See the experimental data record table.

Experimental data record table

Table 2 experimental data of grating constant d

Measurement sequence ()

1

2

three

Table 3 Experimental data of measuring unknown wavelength

Measurement sequence ()

1

2

three

Experimental results:

1. measure grating constant

According to the average value obtained from Table 2.

= ( 1)

Based on the grating principle,

So there is

And because in this experiment, the wave line nm of green light is the average value of diffraction angle, the average value of d is obtained.

(Nano) (2)

2. Measure the wavelength of blue-violet light

According to the average value obtained from Table 3.

= (3)

Due to, get

Because in this experiment, the grating constant nm is the average value of diffraction angles, so the average value is taken.

(Nano) (4)

References:

[1], Zhao Kaihua. New concept physics course-optics. Higher Education Press, 2004.

[2] Jin Qing, editor in chief. Basic physics experiment. Zhejiang University Press, 2006

[3] Yang, editor-in-chief, editor-in-chief of Wang Dingxing. General physics experiment (optical part). Higher Education Press, 1993.