# Double slit experiment using Arduino and Light sensors 1. Aim and Motivation

#### a. Motivation

What is light? Many scientists from the past have questioned this. What I learned about light through science classes and literature research is that light has two different characteristics. In summary, light exhibits wave-particle duality. Scientific observation of the nature of light is a complicated problem. Einstein\’s photoelectric experiment proved the particle nature of light, while Young\’s double-slit experiment proved the wave nature of light. The physicists Max Plank, Albert Einstein, Louis de Broglie, Arthur Compton, Niels Bohr, etc., furthermore, said that all particles other than light are like light: they have both the property of light and wave.

#### b. Aim

This experiment is a diffraction and interference experiment of light to prove the two properties of light. Therefore, assuming that light has a wave property, the distance of the diffraction pattern\’s interference fringes is theoretically calculated, and the value is experimentally verified. Calculating the wavelength of the laser light source was an enjoyable and useful experiment.
In this experiment, I used fusion 360 and Arduino. These tools were used for quantitative analysis, not just observing the interference fringes. The experimental tools\’ accuracy was also tested by comparing the experimental results with the values derived through simulation using Java coding.

## 2. Contents

### a. Abstract

In this experiment, based on the double-slit experiment of physicist Thomas Young, the interference of light was quantitatively observed using electronic tools such as MCU (Micro Controlling Unit) and the wave nature of light was confirmed. The distance between the first and second floors of the interference fringe depends on the distance between the double slit, the distance between the double slit and the light sensor, and the wavelength of light. Therefore, it is possible to calculate the wavelength of the laser light source, which is difficult to observe directly with the eye. The optical tools necessary for the experiment were purchased and used, and all frames were designed and manufactured using fusion360 and Arduino. In the process, the range of experimental errors such as twisting of the double slit, tilting of the laser, and resolution of the optical sensor was predicted.

### b. Theoretical Background

##### 1. Duality of Light

Light has both properties of particles and waves. Physicists said that all matter, not just light, has universal duality. Atoms, heavier than photons, and even complex molecules have wave properties. However, the wave nature of these macroscopic particles are difficult to observe because their wavelength is extremely short when interpreted as waves.
In the early 11th century, Arab scientist Alhazen explained the reflection and refraction of light under the assumption that light consists of photons. In 1630, Rene Descartes revealed in his book that the properties of light are explained by assuming light as a wave. In 1670, Isaac Newton insisted that light can only go straight through particles. Contemporaries Robert Hooke, Christiaan Huygens, and Jean Fresnel mathematically supported the wave motion of light and accurately predicted light\’s refraction. With the help of Huygens and Fresnel\’s research, Thomas Young in 1803 proved the wave nature of light through a double-slit experiment.

##### 2) Double-Slit Experiment

The double-slit experiment is an experiment to show that a substance can be described as a wave and a particle. Furthermore, it is also an experiment that allows you to observe quantum mechanics\’ basic assumptions, which can see nature as probabilistic. Davisson and Germer did the modern double-slit experiment in 1927. Fig. 1 Schematic of a double-slit experiment using an electron beam. In addition to electrons, any particles, such as photons, neutrons, protons, and molecules, also causes the above interference phenomenon.

A simpler double-slit experiment was conducted by Thomas Young in 1803 before quantum mechanics was fully understood. His experiment can be seen as the origin of the 1927 double-slit experiment in that light is divided into two branches and combined to form an interference pattern.
In the double-slit experiment, light interferes like a wave after passing through two slits, creating an interference pattern on the screen. However, if you check which slit the light passes through by attaching a sensor to monitor photons in both slits, the light moves like particles, and no interference pattern occurs on the screen. Therefore, both particle and wave properties of light can be seen through the double-slit experiment. This phenomenon can be observed with atomic beams rather than light, and the double-slit experiment has been successfully conducted with molecules composed of 810 atoms so far. In theory, monochromatic light with a single wavelength of incident light is considered, but in reality, white light and sunlight with many wavelengths can also produce interference fringes. Fig. 2 Interference pattern of the double-slit experiment using sunlight. It can be seen that the central part is observed as white, and a rainbow pattern appears as the spectroscopy occurs toward the periphery.

When calculating light as a wave in the double-slit experiment, the intensity of light at a certain point passing through the double-slit can be calculated by adding the phase and amplitude of the two waves passing through the double slit. This method is called the Huygens-Fresnel principle. When the amplitude of the wave is obtained, the intensity of light is proportional to the square of the amplitude.
When light enters the double slit in the form of a wave, the wave diffracts through a narrow gate. For a wave to diffract, the size of the slit should be less than the wave\’s wavelength. In the case of visible light, the wavelength ranges from 300 to 800 nm. In terms of millimeters, it is 0.0003mm to 0.0008mm. The diffracted light passing through the narrow slit cancels out or constructively interferes between the double slit and the screen. Whether cancelled or reinforced depends on how different the two waves are. It is reinforced when the wave trough and the trough meet but is cancelled when the wave trough and the crest meet. On the other hand, at which point on the screen, the two waves will be cancelled or reinforced can be predicted by knowing the distance the two waves have passed when they reach that point. Fig. 3 Schematic of the double-slit experiment. The intensity of light reaching an arbitrary point P can be calculated by knowing the angle .

As shown in Fig. 3, when a specific position of the screen forms an angle with the center of the double slit, the difference between the paths the two waves travel to reach the position is ( is the gap between the two slits). If it is much less than 1 radian, it can be approximated to: .
Path difference: ###### Equation. 1 The path difference between the two waves calculated by approximating the angle to be small

If the path difference obtained in Equation 1 is an integer multiple of the wavelength of light, constructive interference occurs because the two lights are the same phase. Conversely, if the difference is as much as half the wavelength of light, destructive interference occurs. Therefore, the conditions in which constructive interference occurs are as follows. ###### Equation. 2 Conditions for constructive interference to occur. There is an assumption that is small.

Equation. 2 is a condition in which constructive interference occurs. Therefore, the angular difference between the center crest of the screen and the first crest can be calculated as . The distance between the crest and the crest can be approximated by the length of an arc whose radius is the distance between the double slit and the screen. If you know the angle and radius, you can get the length of the arc through the arc diagram method, so it is as follows. ##### 3.Thomas Young\’s Double Slit Experiment

Young\’s double-slit experiment, which is also called Young\’s interference experiment, is the beginning of the modern double-slit experiment that was discussed earlier. This experiment played an important role in verifying the wave nature of light. This was judged as his best achievement.
In the 1790s, studying medicine in Göttingen, Young published the physical and mathematical journal in sound. In 1800 he published a paper in the Royal Society journal claiming the pulsation of light. Fig. 4 Young\’s double-slit experiment sketch inspired by the water wave.

“My experiments can be done with sunlight without any other device.”
Thomas Young attended the Royal Society of London on November 24, 1803, and spoke about his experiment as above. Isaac Newton, who attended the same conference at the time, believed that light was made up of small bullet-like particles, and so did others. Thomas Young\’s experiment was shocking to people at the time.
Thomas Young\’s double-slit experiment at the time did not actually use a double-slit but was carried out by dividing the light into two pieces using paper as shown in Fig. 5. In fact, it is said that even with 1 or 2 sheets of paper of 0.02cm, the interference pattern can be observed by splitting the laser light source. This width is very large compared to the wavelength of light. In this case, it is said that Fraunhofer diffraction occurs. Fig. 5 Thomas Young\’s diagram of the double-slit experiment at the time. Thomas Young split the light in two
with a piece of paper.

### C. Preparation of the optical device

1. ##### Double-Slit

Two methods of making double slits were investigated. The first was to make the transparent plate opaque and then use a sharp tool such as a razor to leave a gap in two. The research of the National Science Exhibition describes how to produce double slits with this method most accurately. However, making double slits in this way is very difficult. This is because the gap between the two slits should be approximately the same size as the wavelength of the light source used, and the gap between the slits should be very narrow.
Thomas Young in the 1800s also did not make the double-slit using the above method. He succeeded in forming the interference pattern by dividing the light into two using paper. In this experiment, as shown in Fig. 6, the interference pattern could be successfully observed when the laser was passed through the paper double-slit. Fig. 6 Diffraction pattern using green and red lasers.
However, in actual experiments, commercially available double slits were purchased and used for more accurate results.

#### 2. Light Sensor

TEMT6000 light sensor is a light sensor manufactured and sold by YWRobot that can be easily connected to Arduino and boasts high accuracy. Also, unlike cadmium sulfide, the size of the sensor unit was small, so it was judged to be an appropriate sensor for measuring a diffraction pattern formed by a laser light source. Fig. 7 Light Sensor TEMT6000.

### d. Design and manufacture of experimental frame

1. Arduino

The Arduino board, the hardware of the Arduino project, is a kind of MCU board, and the most popular Arduino board, the Arduino Uno board, has an MCU chip called Atmega328. In order to upload the desired coding to this board, you need to download and install the software through the Arduino official webpage. Arduino programming language used in this software has the characteristics of C and C++ languages at the same time. The programming language is very simple and easy to understand because Casey Rias of the MIT Media Lab, who developed the language, developed a programming language for ordinary artists, not professional programmers.
The Arduino programming language consists of two basic functions: a Setup function that is executed only once when the Arduino is turned on and a Loop function that repeats continuously after the Arduino is turned on. If you want, you can add other functions. Meanwhile, the code that starts with #include is the header which calls the complex functions more simply than creating new functions. Although it is one line in the code, it basically fetches the entire library called by the header, which is an object-oriented nature of C++. In this experiment, a motor driver shield was used to control the stepper motor, and the header required to drive the shield was used, and AFMotor is the library name. By calling this header, you can easily command the motor\’s speed and drive with commands such as run and set speed.

#### 2. Fusion 360

Fusion 360 is a CAD program that allows you to create 3D shapes you want to create with a computer in advance. It is a program developed by Autodesk and can be used for free. Although it is possible to design all three-dimensional complex curved surfaces and unusual shapes, since the acrylic plate was cut and used to make this experimental frame, the design was designed to be as simple as drilling a hole in a rectangular parallelepiped. After designing each part, you can pre-assemble the parts in a virtual space, and you can make the assembled image into an image as if the real thing was taken through a process called rendering.

#### 3. Stepper Motors

A stepper motor refers to a motor that can rotate as much as the desired angle in the desired direction. It is driven by using several pairs of coils, and it can be divided into two-phase and five-phase stepper motors depending on the number of coil pairs. In this experiment, one two-phase stepper motor was used. A separate motor driver is required to drive the stepper motor. The motor driver was purchased and used in the form of a shield that can be immediately connected to the Arduino, and this driver receives a large current that the Arduino cannot handle and delivers it to the motor. Fig. 8 Arduino motor driver shield. It can control two stepper motors.

#### 4.Frame design and fabrication Fig. 9 (Left) Design rendering image of a laser mounting part (Right) Design rendering image of optical sensor mounting part

The frame was designed using acrylic and wood. Designed parts were fixed with bolts, nuts and pieces, and the rotational friction of the step motor was reduced by using a timing pulley and a timing belt while using bearings. The timing belt has a total length of 400mm, allowing the optical sensor to move about 160mm reciprocating. This is a value determined by the judgment that the width can be measured at the level of approximately 160mm when the observed interference pattern is observed through a simple experiment. Fig. 10 (Left) Laser mount and double-slit fabrication completed (Right) Optical sensor scanner

### e. Results

1. #### Interference pattern spacing change according to the distance between the double slit and illuminance sensor Fig. 11 Double slit diffraction pattern test results. One step on the horizontal axis corresponds to 0.4mm. The distance between the slit and the optical sensor was measured under three distance conditions: 1.2, 1.5 and 1.8m. Inset shows the correlation between.

Fig. 11 shows the observation result of the light diffraction pattern in the double slit experiment. If the distance between the slit and the light sensor is 1.2m apart, there is an average difference of 6.5 steps (2.6mm) between the first and second floors. If it is 1.5m away, there is an average difference of 9.25 steps (3.7mm). If the distance is 1.8m apart, there is a difference of 13 steps (5.2mm). Therefore, as the slit-optical sensor distance increased, the interference fringe spacing also increased.

#### 2. Wavelength prediction of used laser light source

The Inset graph in Fig. 11 shows the correlation between the slit-light sensor distance and the interference fringe spacing, and the proportional relationship can be seen. The slope was 0.0043. Substituting this value into Equation 3, the wavelength of the inverted laser light source can be calculated. ###### Equation. 4 Calculation of wavelength of laser light source

As shown in Equation 4 above, the wavelength of the laser light source can be calculated. If the gap of the double slit is 0.1mm, the wavelength is about 430nm. However, this wavelength is close to blue (the green wavelength is about 500nm.) It is thought that the gap between the purchased double slits is not exactly being 0.1mm caused this error. In fact, if it is 0.12mm, a green visible wavelength of about 500nm is calculated.

#### 3. Simulation using Java

##### i. Coherent Case

When the incident rays are coherent, the double-slit pattern is affected by two phenomena. One is the Fraunhofer diffraction that occurs in Single-Slit (Ref.14 page15), and the other is the Interference that occurs in Double-Slit (Ref.15 page15). It is implemented as a function, and this document will call it like this for convenience.

##### a. Variables

The variables in the simulation are:
-λ : Wavelength
-Init_intensity : Initial light intensity
-d : Distance of two slits
-l : The distance from the slit to the screen
-a : Gap of each slits

##### b. Diffraction

Diffraction is defined as .
where public static double distance(double h1, double h2, double width) { return Math.sqrt(Math.pow((h1-h2), 2)+Math.pow(width, 2)); } public static double diffraction(double slit, double point, double width) { double dist= distance(slit, point, width); double sin_seta = (Math.abs(slit-point))/dist; double beta = (2*Math.PI*a*sin_seta)/wavelength; double beta_sin = Math.pow((Math.sin(beta/2)/(beta/2)), 2); double intensity = beta_sin; if(slit==point) intensity=1; return intensity; }

The code above implements this as a function. If you apply this function and draw a graph, you can see the following pattern. Fig. 12 Diffraction Pattern Graph

#### c. Interference

Interference is defined as: where public static double interference(double slit1,double slit2, double point, double width) { double dist1= distance(slit1, point, width); double dist2= distance(slit2, point, width); double seta = 2*Math.PI*((Math.abs(dist1-dist2)%wavelength)/wavelength); double result = Math.pow(Math.cos(seta/2),2); return result; }

The code above implements this as a function. If you apply this function and draw a graph, you can see the following pattern. Fig. 13 Interference Pattern Graph

#### d. Coherent Pattern

The pattern of combining these two elements can be obtained by simply multiplying the result of the two functions and dividing it by Init_intensity. res_arr[i]=math.init_intensity*math.diffraction(slit1, res_arr[i]*grid, math.l); res_arr[i]=math.init_intensity*math.interference(slit1,slit2, res_arr[i]*grid, math.l); double i_max = res_arr[i]*res_arr[i]/math.init_intensity;

The code above implements this as a function. If you apply this function and draw a graph, you can see the following pattern. Fig. 14 Coherent Pattern Graph

##### ii. Incoherent Case

The fact that the incident ray is incoherent means that the phase of the ray is different when it enters the slit. However, until now, the direction of development was not a mechanism to separate particles and think about them, but to follow a formula calculated by collecting them all. Therefore, it was not possible to implement the difference in phase as it is, and as an alternative method, the concept of fringe covered in [Ref.14].
It introduces several new concepts. First of all, the intensity oscillation of interference occurs due to the incoherent nature of the light beam. This is called fringe. Also, in this oscillation, the waveform at the maximum intensity is , and the waveform at the minimum is . Therefore, init_intensity can also be divided into two types: maximum and minimum, which are defined in the code as init_intensity and minimum_intensity, respectively. Finally, the concept of visibility can be created from these two concepts, which is defined as .

##### a. Variables

The variables in the simulation are:
-λ : Wavelength
-Init_intensity : Initial light intensity
-minimum_intensity : minimum initial light intensity
-d : Distance of two slits
-l : The distance from the slit to the screen
-a : Gap of each slits

1. Diffraction

The diffraction pattern can be viewed as two cases in which the intensity is max and min. The graph below is for . Fig. 15 Diffraction Pattern Graph

##### c. Incoherent Pattern

When conceiving the Incoherent Pattern, the graph was drawn using the concept of weight as an alternative method: after defining two waveforms in the case of and the waveform in the case of , the weights of the two functions are vibrated according to the frequency of the Interference waveform. For example, if the waveform is applied by 30%, the waveform of is applied by 70%.
The waveform of was applied in the same way as the waveform in the case of coherent. Fig. 16 Intensity MAX Pattern Graph

In the case of the waveform of , if the phase of is the same, only constructive interference occurs, so it is made in the same way as but the phase of the interference is reversed to cause destructive interference. Fig. 17 Intensity MIN Pattern Graph

Finally, the method of weighting them is to match the frequency of the interference pattern. Fig. 18 Incoherent Pattern Graph

As a result, the intensity oscillation of the incoherent pattern could be roughly visualized. At this time, it can be said that . Below is the code to implement this.

 res_arr[i]=math.init_intensity*math.diffraction(slit1, res_arr[i]*grid, math.l); res_arr[i]=math.minimum_intensity*math.diffraction(slit1, res_arr[i]*grid, math.l); res_arr[i]=math.init_intensity*math.interference(slit1,slit2, res_arr[i]*grid, math.l); double minimumInterference = res_arr[i]*math.minimum_intensity/math.init_intensity; double i_max = res_arr[i]*res_arr[i]/math.init_intensity; double i_min_reverse=res_arr[i]*(math.minimum_intensity+minimumInterference*(-1))/math.minimum_intensity; res_arr[i] = i_max*(res_arr[i]/math.init_intensity)+i_min_reverse*(1-res_arr[i]/math.init_intensity);

In this method, we could not find an appropriate function or method that can be substituted, so we approached it with an alternative method. A more accurate simulation will be possible if an exact equation that can be substituted for or is determined.

## f. Error Analysis

1. ##### Errors in alignment of laser light source, slit, and screen Fig. 19 Schematic diagram showing misalignment of laser light source, slit, and screen.

Theoretically, the laser light source, the slit and the screen should be aligned perfectly vertically. However, it cannot be sorted that way in practice, and an error occurs here. In reality, a misalignment error occurs as shown in Fig. 19. From the experimental results in Fig. 11, it can be seen that the second floor, located to the left and right of the first floor, is not symmetrical with respect to the center. In other words, the distance between the first floor and the second floor on the left is greater or less than the distance between the second floor on the right. This error can be interpreted as a phenomenon that occurs because the alignment of the light source, the slit, and the screen is not perfect.

##### 2. Error in twisting between double slit and laser light source

In the process of fixing the double slit to the laser light source, there may be a case where the double slit deviates from the center of the laser light source. In this case, the intensity of the measured light may be weakened or the diffraction pattern may be shifted in parallel to the left or right. Fig. 20 Twisting between double slit and laser light source
Also, tape was used in the process of fixing the double slit. Therefore, distortion may occur as shown in Figure 13 above at the bottom. In this case, the interference fringes formed on the screen are not horizontal. If the interference fringe is out of the horizontal, the optical sensor will deviate from the interference fringe and the measured value will be distorted when the measurement is made in the measuring instrument.

##### 3. Horizontal distortion between interference fringe and measuring instrument

The double slit generating the interference fringe and the optical sensor meter were placed on the same floor. It is difficult to say that the floor of a general home is perfectly horizontal at a distance of up to 2m. As a result, the optical sensor cannot accurately scan the diffraction pattern and scans at an angle. This factor will also contribute to making the left and right second floors asymmetric with respect to the first floor. However, this result is a cause that the intensity of the second floor on the left and the right is different, and the location of the peak cannot be changed.
g. Conclusions
First, using the apparatus made using arduinos, light sensors, and various electronic parts, I have successfully observed the interference pattern of light and proved the wave nature of light. Moreover, I was able to measure the coherence of light. Second, I’ve successfully calculated the wavelength of the laser source as 430nm using equation 4. However, due to error sources 1) Alignment of laser light source, slit, and screen(Fig 19) 2) Twisting between double slit and laser light source (Fig 20) the empirical value of the laser was not exactly the same with the theoretical value. Lastly, I’ve proved that if the slit-optical sensor distance increased, the interference fringe spacing also increased.
In order to eliminate these error factors, I’ve coded a simulation program using Java to find out the coherent and incoherent patterns and found out the intensity Max and Min patterns. In the future, I want to use the gap between slits as the variable and design an apparatus that automatically changes the gap between the slits.
Reference
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Figure Reference
Fig 1. Schematic of a double-slit experiment using an electron beam. In addition to electrons, any particles, such as photons, neutrons, protons, and molecules, also causes the above interference phenomenon. (Source: https://en.wikipedia.org/wiki/Double-slit_experiment)
Fig 2. Interference pattern of the double-slit experiment using sunlight. It can be seen that the central part is observed as white, and a rainbow pattern appears as the spectroscopy occurs toward the periphery. (Source: https://physics.stackexchange.com/questions/445754/intensity-of-fringes-in-a-double-slit-experiment)
Fig 3. Schematic of the double-slit experiment. The intensity of light reaching an arbitrary point P can be calculated by knowing the angle θ. (Source: https://www.pngwing.com/es/free-png-ijuxp)
Fig 4. Young\’s double-slit experiment sketch inspired by the water wave. (Source: https://skullsinthestars.com/2009/03/28/optics-basics-youngs-double-slit-experiment/)
Fig 5. Thomas Young\’s diagram of the double-slit experiment at the time. Thomas Young split the light in two with a piece of paper (Source: https://www.cavendishscience.org/phys/tyoung/tyoung.htm)
Fig 6. Diffraction pattern using green and red lasers. (Source: Taken by Writer)
Fig 7. YWROBOT Light Sensor TEMP6000. (Source: https://www.compuzone.co.kr/product/product_detail.htm?ProductNo=462211&BigDivNo=99&MediumDivNo=1291&DivNo=)
Fig 8. Arduino motor driver shield L293D. It can control two stepper motors. (Source: https://www.lelong.com.my/arduino-l293d-motor-driver-shield-teagreen-F2555765-2007-01-Sale-I.htm)
Fig. 9 (Left) Design rendering image of a laser mounting part (Right) Design rendering image of optical sensor mounting part (Source: Fusion 360, Designed and Rendered by Writer)
Fig. 10 (Left) Laser mount and double-slit fabrication completed (Right) Optical sensor scanner (Source: Taken by Writer)
Fig. 11 Double slit diffraction pattern test results. One step on the horizontal axis corresponds to 0.4mm. The distance between the slit and the optical sensor was measured under three distance conditions: 1.2, 1.5 and 1.8m. Inset shows the correlation between. (Source: Graph drawn by Writer)
Fig. 12 Diffraction Pattern Graph (Source: Graph drawn by Writer Using Excel)
Fig. 13 Interference Pattern Graph (Source: Graph drawn by Writer Using Excel)
Fig. 14 Coherent Pattern Graph (Source: Graph drawn by Writer Using Excel)
Fig. 15 Diffraction Pattern Graph (Source: Graph drawn by Writer Using Excel)
Fig. 16 Intensity MAX pattern Graph (Source: Graph drawn by Writer Using Excel)
Fig. 17 Intensity MIN pattern Graph (Source: Graph drawn by Writer Using Excel)
Fig. 18 Incoherent pattern Graph (Source: Graph drawn by Writer Using Excel)
Fig. 19 Schematic diagram showing misalignment of laser light source, slit, and screen. (Source: Diagram drawn by Writer Using PowerPoint)
Fig. 20 Fig. 20 Twisting between double slit and light source (Source: Diagram drawn by Writer Using PowerPoint)
Acknowledgements
Thanks to my parents for the economical and psychological support.
Thanks to Mr.Gillings (Head of Physics in NLCS JEJU) and YSJ for the comments. I am a student who is very interested in science and technology. I am always full of curiosity and try to use my abilities to solve them. Also, makers\’ activity is my main strength. I enjoy to make my dream come true using boards like Arduino, design tools like fusion 360, and coding languages such as Java and Python.
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