Novel light velocity measuring device based on table type rotating gear method
By designing a tabletop rotating gear method for measuring the speed of light, the problem of dependence on outdoor space and atmospheric conditions for measuring the speed of light was solved. It achieved simplified optical path adjustment and low-cost measurement of the speed of light on the experimental platform, and provided an intuitive physical picture, making it suitable for teaching applications.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Utility models(China)
- Current Assignee / Owner
- SHANGHAI UNIV
- Filing Date
- 2025-04-11
- Publication Date
- 2026-04-17
AI Technical Summary
Existing light speed measurement devices require an outdoor space spanning 8 kilometers, are greatly affected by weather, experimental time, and atmospheric visibility, have complex optical path adjustments, and are expensive and unable to display clear and intuitive physical images.
A light speed measurement device based on the benchtop rotating gear method was designed, including a rotating gear, a DC motor, a tachometer, an infrared laser, an optical fiber, an automatic scoping optical power meter, a pigtail fiber collimator, and an XY axis displacement platform. By simplifying the optical path structure and instrument design, the light speed measurement can be performed on the experimental bench. The combination of the rotating gear and the fiber collimator simplifies the optical path adjustment and reduces costs.
It enables the measurement of the speed of light on an experimental platform, provides intuitive images of objects, allows for controllable experimental processes, features a simple and reliable operating principle, low cost, accurate measurement results, and is easy for students to understand, making it suitable for physics experimental teaching.
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Figure CN224137826U_ABST
Abstract
Description
Technical Field
[0001] This utility model relates to the field of light speed measurement, and in particular to a novel light speed measurement device based on the benchtop rotating gear method. Background Technology
[0002] The determination of the speed of light is of great significance in optical research. It is one of the earliest physical constants measured. Advances in methods for measuring the speed of light have not only improved the accuracy of the value but also reflected the development of modern physics and experimental methods. The measurement of the speed of light provided criterion for the debate on the nature of light, supported the wave theory, and played a crucial role in establishing the electromagnetic theory of light. The principle of the invariance of the speed of light is the foundation of special relativity, stating that the speed of light in a vacuum is a constant, unaffected by the relative motion between the observer and the light source. The significance of the speed of light is also reflected in the definition of the physical unit "meter." In 1983, the General Conference on Weights and Measures redefined the meter, defining it as the distance light travels in a vacuum in 1 / 299,792,458 of a second, thus making the speed of light a fixed constant and improving the measurement accuracy of other fundamental physical constants.
[0003] The speed of light is the ultimate speed limit for all matter, making its measurement extremely difficult. From astronomical observations to successful ground-based experiments, and finally to precise laboratory measurements, the process has taken nearly 400 years. For this reason, measuring the speed of light has become a very typical physics experiment project in higher education institutions.
[0004] In 1849, French physicist A.H. Fizeau successfully measured the speed of light directly on Earth for the first time using the method of rotating gears. Because gears have backlash and teeth, when light passes through a gap, the observer can see the returning light; when the light happens to hit a tooth, it is blocked. The time from the start to the first disappearance of the returning light is the time it takes for the light to make one round trip, which is also the time it takes for the gear to rotate exactly through one tooth. This time is not difficult to calculate based on the gear's rotation speed. Fizeau measured the speed of light as c = 3.153 × 10⁻⁶. 8 m / s.
[0005] This method is simple in principle and provides an intuitive physical picture, marking a significant milestone in light speed measurement. However, it also has several drawbacks. For example, the device requires an outdoor space spanning 8 kilometers to reflect visible light rays, which will inevitably be affected by weather, experimental time, and atmospheric visibility.
[0006] Currently, most physics experiments on measuring the speed of light in universities employ indirect measurement using the optical beat frequency method. This method involves generating beat frequency interference between two beams of light with similar frequencies, and then indirectly calculating the speed of light using the relationship between the frequency difference and the wavelength of the light wave. However, this method suffers from several drawbacks: complex optical path adjustments can make the experiment difficult for students; furthermore, the instrumentation required for measuring the speed of light using the optical beat frequency method is sophisticated, complex, and costly. Additionally, because it uses an indirect measurement method, it cannot effectively present a clear and intuitive physical picture during the teaching process. Summary of the Invention
[0007] In view of the aforementioned shortcomings of the prior art, the technical problem to be solved by this utility model is that existing light speed measurement devices require an outdoor space spanning 8 kilometers, and are greatly affected by weather, experimental time, and atmospheric visibility. Furthermore, existing indirect measurement methods using optical imaging techniques involve complex optical path adjustments, difficult experiments, and require high-performance, complex, and costly experimental instruments that cannot display clear and intuitive physical images. This utility model provides a novel light speed measurement device based on the benchtop rotating gear method, which is simple in principle, low in cost, and provides intuitive physical images.
[0008] To achieve the above objectives, this utility model provides a novel optical speed measurement device based on the benchtop rotating gear method, comprising a rotating gear mounted on an optical platform, a DC motor, a tachometer, an infrared laser, an optical fiber, an automatic scoping optical power meter, a breadboard support, a DC regulated power supply, a pigtail fiber collimator, and an XY axis displacement platform.
[0009] The system consists of several components: a pigtail-type fiber optic collimator fixed on an XY-axis displacement platform, with each platform mounted on an optical platform; a fiber optic cable connected to the pigtail-type collimator; a rotating gear connected to a DC motor mounted on a breadboard support, with the motor aligned with the center of the gear; a DC regulated power supply connected to the motor's input to control its speed; an automatic range optical power meter positioned above the optical platform, also mounted on the breadboard support; a tachometer positioned on the breadboard support, with its transmitter vertically aligned with the rotating gear disk; and an infrared laser connected to the fiber optic cable.
[0010] Furthermore, the pigtail-type fiber collimator includes a concave aluminum alloy bracket, one end of which is provided with an output end and the other end is provided with a receiving end. The output end and the receiving end correspond to each other and are at the same height.
[0011] Furthermore, the pigtail-type fiber collimator includes a first pigtail fiber collimator and a second pigtail fiber collimator; the XY-axis displacement platform includes a first XY-axis displacement platform and a second XY-axis displacement platform; wherein, the first pigtail fiber collimator is fixed to the first XY-axis displacement platform, and the second pigtail fiber collimator is fixed to the second XY-axis displacement platform.
[0012] Furthermore, one end of the optical fiber is connected to the receiving end of the first pigtail fiber collimator, and the other end is connected to the emitting end of the second pigtail fiber collimator.
[0013] Furthermore, the infrared laser, as a light source, is connected to the output end of the first pigtail fiber collimator. The light source exits from the output end, passes through the tooth gap of the rotating gear, and then enters the corresponding receiving end. Then, it exits from the output end of the second pigtail fiber collimator through the optical fiber, passes through another tooth gap of the rotating gear, and then enters the corresponding receiving end.
[0014] Furthermore, the receiving end of the second pigtail fiber collimator is connected to an automatic ranging optical power meter.
[0015] Furthermore, the rotating gear is designed with a hollowed-out flying disc shape, with each tooth and the gap between teeth having the same central angle.
[0016] Furthermore, the rotating gear is connected to the DC motor via a metal flange and a motor connecting rod.
[0017] Furthermore, the DC motor is fixedly connected to the breadboard bracket via a motor bracket.
[0018] Furthermore, when the rotating gear is stationary, the incident light and the outgoing light pass through the tooth gap at equidistant positions, such that the positions where the incident light and the outgoing light pass through the tooth gap satisfy the condition that they are in the same state.
[0019] Technical effect
[0020] This invention provides a novel light speed measuring device based on the benchtop rotating gear method. For the first time, the Fizeau light speed measurement experiment has been moved from the ground, which spans several kilometers, to an ordinary experimental table. The object image is intuitive, the experimental process is controllable, the instrument's operating principle is simple and reliable, the cost is low, the measurement results are relatively accurate, and it is easy for students to understand. It is suitable for widespread application in physics experiment teaching.
[0021] The following will further explain the concept, specific structure and technical effects of this utility model in conjunction with the accompanying drawings, so as to fully understand the purpose, features and effects of this utility model. Attached Figure Description
[0022] Figure 1 This is a schematic diagram of the structure of a novel light speed measuring device based on the benchtop rotating gear method, which is a preferred embodiment of this utility model.
[0023] Figure 2 This is a novel optical path diagram based on the benchtop rotating gear method, which is a preferred embodiment of this utility model.
[0024] Figure 3 This is a schematic diagram of a novel gear structure based on the benchtop rotary gear method, which is a preferred embodiment of this utility model.
[0025] Figure 4 This is a schematic diagram of a novel fiber-optic collimator structure based on a tabletop rotating gear method, which is a preferred embodiment of this utility model.
[0026] Among them, 1-optical platform; 2-XY axis displacement platform; 3-fiber collimator; 3a-emitting end; 3b-receiving end; 3c-"concave" shaped aluminum alloy bracket; 4-infrared laser; 5-alloy gear; 6-metal flange; 7-motor connecting rod; 8-motor bracket; 9-DC motor; 10-DC regulated power supply; 11-tachometer; 12-breadboard bracket; 13-optical fiber; 14-automatic range optical power meter. Detailed Implementation
[0027] To make the technical problem to be solved, the technical solution, and the beneficial effects of this utility model clearer, the present utility model will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the present utility model and are not intended to limit the present utility model.
[0028] In the following description, specific details, such as particular internal procedures and techniques, are set forth for illustrative purposes and not for limitation, in order to provide a thorough understanding of the embodiments of the present invention. However, those skilled in the art will understand that the present invention may be implemented in other embodiments without these specific details. In other instances, detailed descriptions of well-known systems, apparatuses, circuits, and methods have been omitted so as not to obscure the description of the present invention with unnecessary detail.
[0029] like Figure 1-4 As shown, this utility model provides a novel optical speed measuring device based on the benchtop rotating gear method, including a rotating gear 5, a DC motor 9, a tachometer 11, an infrared laser 4, an optical fiber 13, an automatic range optical power meter 14, a breadboard bracket 12, a DC regulated power supply 10, a pigtail fiber collimator 3, and an XY axis displacement platform 2, all mounted on an optical platform 1.
[0030] The fiber optic collimators 3 are fixed on XY-axis displacement platforms 2, each of which is fixed on an optical platform 1. An optical fiber 13 is connected to the fiber optic collimator 3. A rotating gear 5 is connected to a DC motor 9, which is fixed on a breadboard bracket 12, connecting the center of the DC motor 9 to the rotating gear 5. A DC regulated power supply 10 is connected to the input of the DC motor 9 to control its speed. An automatic range optical power meter 14 is placed horizontally above the optical platform 1, and the breadboard bracket 12 is fixed above the optical platform 1. A tachometer 11 is placed horizontally on the breadboard bracket 12, with its transmitter vertically aligned with the disk surface of the rotating gear 5. Each fiber optic collimator pair is fixed to the XY-axis displacement platform with screws, and the same state point is adjusted by adjusting the platform along a direction parallel to the gear plane. An infrared laser is connected to the optical fiber.
[0031] The pigtail-type fiber collimator 3 includes a concave aluminum alloy bracket 3c. One end of the concave aluminum alloy bracket 3c is provided with an output end 3a, and the other end is provided with a receiving end 3b. The output end 3a and the receiving end 3b correspond to each other and are at the same height.
[0032] The pigtail fiber collimator 3 includes a first pigtail fiber collimator and a second pigtail fiber collimator; the XY axis displacement platform 2 includes a first XY axis displacement platform and a second XY axis displacement platform; wherein, the first pigtail fiber collimator is fixed to the first XY axis displacement platform, and the second pigtail fiber collimator is fixed to the second XY axis displacement platform.
[0033] One end of optical fiber 13 is connected to the receiving end of the first pigtail fiber collimator, and the other end is connected to the emitting end of the second pigtail fiber collimator. The optical fiber is connected to the pigtail fiber collimator via an FC / APC patch cord interface.
[0034] Infrared laser 4 serves as a light source and is connected to the output end of the first pigtail fiber collimator. The light source exits from the output end, passes through the tooth gap of the rotating gear, and then enters the corresponding receiving end. It then exits from the output end of the second pigtail fiber collimator through the optical fiber, passes through the other tooth gap of the rotating gear again, and then enters the corresponding receiving end. The receiving end of the second pigtail fiber collimator is connected to the automatic ranging optical power meter 14.
[0035] In this embodiment, the rotating gear 5 is designed as a hollowed-out flying disc, with each tooth and the corresponding central angle being the same. The rotating gear 5 is connected to the DC motor 9 via a metal flange 6 and a motor connecting rod 7. The DC motor 9 is fixedly connected to the breadboard bracket 12 via a motor bracket 8.
[0036] The plane of the rotating gear is perpendicular to the line connecting the transmitter and receiver of each pigtail fiber collimator.
[0037] The rotational speed of the rotating gear is precisely adjusted by the constant current mode of the DC regulated power supply.
[0038] When the rotating gear is stationary, the incident and outgoing light pass through the tooth gap at equidistant positions, ensuring that their positions are at the same state point. This is equivalent to achieving the experimental condition in Fizeau's classic experiment where the emitted and reflected light coincide on a straight line. When the rotating gear is stationary and the light source passes through the tooth gap, the optical power meter receives the maximum light intensity. When the rotating gear rotates but at a slow speed, the outgoing light may be blocked by a tooth at some point, resulting in a flash and a decrease in average light intensity. Gradually increasing the rotational speed of the gear to a certain speed v (unit: rev / s) allows the outgoing light to be blocked by an adjacent tooth of another gear, preventing outgoing light from entering the optical power meter and minimizing the average light intensity. The time it takes for the gear to rotate exactly half a tooth corresponds to the time required for light to travel from the tooth gap of the first gear to the distance of the adjacent tooth of the other gear (approximately equivalent to the total length of the optical fiber).
[0039] A point of common state represents a point on the same gear. Depending on the direction of gear rotation, if two points need to reach the edge of their respective teeth or tooth gaps, the gears must rotate at the same angle and in the same direction, and these two points must not be on the same tooth or tooth gap. Since teeth and tooth gaps are periodically arranged, points of common state at different positions are in the same state at any given time, whether they are blocked or not. Therefore, the introduction of points of common state removes the spatial constraint that emitted and reflected light must coincide in classical experiments. Two beams of light, provided they pass exactly through a point of common state on the gear, can have spatially independent paths, but the effect remains the same as in classical experiments where emitted and reflected light coincide.
[0040] The following specific examples illustrate a novel method for measuring the speed of light using a tabletop rotating gear method.
[0041] according to Figure 1 Fix each experimental device in a suitable position on the optical platform, ensuring that the gear plane fixed to the motor passes parallel to the two symmetrical collimator grooves on the left and right. Figure 2 Connect the optical path. Connect the infrared laser 4, the pigtail fiber collimator 3, the optical fiber 13, the pigtail fiber collimator 3, and the automatic ranging optical power meter 14 through the FC / APC interface fiber optic patch cord.
[0042] First, perform the actual operation of adjusting the same state point.
[0043] Align the center of the first pigtail fiber collimator with the backlash of the gear. Connect the outer emitter of the first pigtail fiber collimator to the infrared laser source, and the inner receiver to an auto-range optical power meter. Fine-tune the first XY axis displacement platform in one direction. When the auto-range optical power meter reading is exactly 0 nW, the initial position adjustment of the first pigtail fiber collimator is complete. Next, adjust the second pigtail fiber collimator in the same way, being careful not to touch the gear during adjustment to avoid rotating it. After adjustment, ensure the incident and emitted light are at the same position after passing through the gear. Then, restore the optical path to its initial connection method.
[0044] After adjustment, turn on the DC regulated power supply and connect the positive and negative terminals of the output to the positive and negative terminals of the motor, respectively. Set the voltage to 16V. Place a tachometer on the breadboard support, adjusting its angle so that the red light emitted hits the spokes of the gear precisely and is reflected back to the receiving point. Divide the reading by four to get the gear's rotational speed. Turn on the tachometer and simultaneously start the DC regulated power supply.
[0045] Turn on the DC regulated power supply to begin the experiment. Control the motor speed by adjusting the current. After the speed stabilizes, record the speed and the minimum light intensity. Then, slowly increase the current. When the minimum light intensity at a certain speed is the lowest within the speed range, the speed at that point is the desired speed. Continue to slowly increase the current; you will see the minimum value increase as the motor speed increases. Record the speed at the corresponding current symmetrically to further determine the target speed. Record multiple sets of data and perform data analysis. Monitor the motor temperature during the experiment to prevent overheating. After completion, turn off the regulated power supply. After the motor cools to room temperature, repeat the experimental steps, recording multiple sets of data and performing data analysis. During the experiment, avoid standing in the radial direction of the gears. Final test results: stable data and accurate results.
[0046] To further understand the content, features, and effects of this utility model, the following embodiments are described:
[0047] Example 1:
[0048] The rotating gear used is made of aluminum alloy, with a diameter of 56cm, a thickness of 4mm, and a total of 360 teeth.
[0049] The DC motor used operates at 24V, has a power of 80W, and a no-load speed of 10000r / min.
[0050] It uses G652D international standard optical fiber, with a length of 25304.00m and a refractive index of 1.466.
[0051] The non-contact tachometer used measures speeds ranging from 3 to 99,999 r / min, with the normal operating speed of the gears not exceeding 3,000 r / min. The instrument has a measurement accuracy of 0.1 r / min, a sampling time of 0.8 s, and an instrument error of 0.04%.
[0052] An infrared laser with a wavelength of 1480nm is used, with a maximum optical power of 0.3mW and a minimum optical power of 4.5nW when the light is transmitted.
[0053] When the automatic range optical power meter reading is at its minimum, the output current of the DC regulated current source is 3.621A. The tachometer measures the rotational speed of the alloy gear's four spokes, which is 2684 r / min. Dividing this by 4 gives the actual rotational speed of the gear as 671 r / min, or 11.167 r / s. This rotational speed is the target rotational speed.
[0054] Using the formula c = 2nLNν, where L is the fiber length (m), N is the number of gear teeth, v is the target rotational speed (r / s), n is the refractive index, and c is the speed of light (m / s), the measured value of the speed of light is c = 2.986 × 10⁻⁶. 8 m / s, the experimental measurement results are as follows:
[0055] c = (2.986 ± 0.029) × 10 8 m / s
[0056] This embodiment shows that the experimental measurement results of the obtained speed of light are consistent with the internationally recognized value (2.99792458 × 10⁻⁶). 8 The m / s value is close to the value, with a relative deviation of only 0.4%, and the expanded uncertainty is less than 0.03 × 10⁻⁶. 8 The speed of light is measured in m / s with a relative uncertainty of less than 1%. Compared with traditional light speed measurement teaching experiments—rotating mirror method or optical beat method—the experimental results are superior, while the principle is simple and intuitive, the experimental adjustment is convenient, and it avoids the cumbersome requirements of optical path adjustment. It is easier for students to operate and is suitable for university physics experimental teaching and promotion.
[0057] Example 2:
[0058] The rotating gear used is made of aluminum alloy, with a diameter of 56cm, a thickness of 4mm, and a total of 360 teeth.
[0059] The DC motor used operates at 24V, has a power of 80W, and a no-load speed of 10000r / min.
[0060] It uses G652D international standard optical fiber, with a length of 25304.00m and a refractive index of 1.466.
[0061] The non-contact tachometer used measures speeds ranging from 3 to 99,999 r / min, with the normal operating speed of the gears not exceeding 3,000 r / min. The instrument has a measurement accuracy of 0.1 r / min, a sampling time of 0.8 s, and an instrument error of 0.04%.
[0062] An infrared laser with a wavelength of 1310nm is used, with a maximum optical power of 0.4mW and a minimum optical power of 3.2nW when the light is transmitted.
[0063] When the automatic range optical power meter reading is at its minimum, the output current of the DC regulated current source is 3.607A. The tachometer measures the rotational speed of the four spokes of the alloy gear, which is 2680 r / min. Dividing this by 4 gives the actual rotational speed of the gear as 667.75 r / min, or 11.129 r / s. This rotational speed is the target rotational speed.
[0064] Using the formula c = 2nLNν, where L is the fiber length (m), N is the number of gear teeth, v is the target rotational speed (r / s), n is the refractive index, and c is the speed of light (m / s), the measured value of the speed of light is c = 2.982 × 10⁻⁶. 8 m / s, the experimental measurement results are as follows:
[0065] c = (2.982 ± 0.029) × 10 8 m / s
[0066] This embodiment shows that the experimental measurement results of the obtained speed of light are consistent with the internationally recognized value (2.99792458 × 10⁻⁶). 8 The relative deviation is only 0.5% (m / s), and the expanded uncertainty is less than 0.03 × 10⁻⁶. 8 The speed of light is measured in m / s with a relative uncertainty of less than 1%. Compared with traditional light speed measurement teaching experiments—rotating mirror method or optical beat method—the experimental results are superior, the repeatability is better, the range of laser light source wavelengths that can be selected is wider, the principle is simple and intuitive, the experimental adjustment is convenient, and it avoids the cumbersome requirements of optical path adjustment. It is easier for students to operate and is suitable for university physics experimental teaching and promotion.
[0067] The preferred embodiments of this utility model have been described in detail above. It should be understood that those skilled in the art can make numerous modifications and variations based on the concept of this utility model without creative effort. Therefore, all technical solutions that can be obtained by those skilled in the art based on the concept of this utility model through logical analysis, reasoning, or limited experimentation on the basis of existing technology should be within the scope of protection defined by the claims.
Claims
1. A novel light speed measuring device based on the desktop rotary gear method, characterized in that, It includes a rotating gear, DC motor, tachometer, infrared laser, optical fiber, automatic range optical power meter, breadboard bracket, DC regulated power supply, pigtail fiber collimator, and XY axis displacement platform, all mounted on the optical platform. The fiber optic collimators are fixed to an XY-axis displacement platform, and each XY-axis displacement platform is fixed to an optical platform. The optical fiber is connected to the fiber optic collimator. The rotating gear is connected to the DC motor, which is fixed to the breadboard support, such that the DC motor is connected to the center of the rotating gear. The output of the DC regulated power supply is connected to the input of the DC motor to control its speed. The automatic range optical power meter is placed flat above the optical platform, and the breadboard support is fixed above the optical platform. The tachometer is placed flat on the breadboard support, and its emitting end is vertically aligned with the rotating gear disk. The infrared laser is connected to the optical fiber.
2. A novel light speed measuring device based on the desktop rotating gear method according to claim 1, characterized in that, The pigtail-type fiber collimator includes a concave aluminum alloy bracket. One end of the concave aluminum alloy bracket is provided with an output end, and the other end is provided with a receiving end. The output end and the receiving end correspond to each other and are at the same height.
3. A novel device for measuring the speed of light based on the desktop rotating gear method as claimed in claim 2, characterized in that, The pigtail fiber collimator includes a first pigtail fiber collimator and a second pigtail fiber collimator; the XY-axis displacement platform includes a first XY-axis displacement platform and a second XY-axis displacement platform; wherein, the first pigtail fiber collimator is fixed on the first XY-axis displacement platform, and the second pigtail fiber collimator is fixed on the second XY-axis displacement platform.
4. A novel device for measuring the speed of light based on the desktop rotating gear method as claimed in claim 3, characterized in that, One end of the optical fiber is connected to the receiving end of the first pigtail fiber collimator, and the other end is connected to the emitting end of the second pigtail fiber collimator.
5. A novel device for measuring the speed of light based on the desktop rotating gear method as claimed in claim 4, characterized in that, The infrared laser serves as a light source and is connected to the output end of the first pigtail fiber collimator. The light source exits from the output end, passes through the tooth gap of the rotating gear, and then enters the corresponding receiving end. Then, the light is emitted from the output end of the second pigtail fiber collimator through the optical fiber, passes through another tooth gap of the rotating gear, and then enters the corresponding receiving end.
6. A novel device for measuring the speed of light based on the desktop rotating gear method as claimed in claim 5, characterized in that, The receiving end of the second pigtail fiber collimator is connected to the automatic ranging optical power meter.
7. A novel device for measuring the speed of light based on the desktop rotating gear method as claimed in claim 1, wherein, The rotating gear is designed in the shape of a hollowed-out flying disc, with each tooth and the gap between teeth having the same central angle.
8. A novel device for measuring the speed of light based on the desktop rotating gear method as claimed in claim 1, characterized in that, The rotating gear is connected to the DC motor via a metal flange and a motor connecting rod.
9. A novel device for measuring the speed of light based on the desktop rotating gear method as claimed in claim 8, characterized in that, The DC motor is fixedly connected to the breadboard bracket via a motor bracket.
10. A novel device for measuring the speed of light based on the desktop rotating gear method as claimed in claim 5, wherein, When the rotating gear is stationary, the incident light and the outgoing light pass through the tooth gap at equidistant positions, such that the positions where the incident light and the outgoing light pass through the tooth gap satisfy the condition that they are in the same state.