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# Universal phenomena of single slit, double slit, cross double slit, triple slit, disc ring, 1D grating and 2D grating wave experiments —Non-interference patterns evolving to orthogonal interference patterns

Hui Peng

► To cite this version:

Hui Peng. Universal phenomena of single slit, double slit, cross double slit, triple slit, disc ring, 1D grating and 2D grating wave experiments —Non-interference patterns evolving to orthogonal interference patterns. 2023. hal-03932202

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Preprint submitted on 10 Jan 2023

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# Universal phenomena of single slit, double slit, cross double slit, triple slit, disc ring, 1D grating and 2D grating wave experiments
## --- Non-interference patterns evolving to orthogonal interference patterns

Hui Peng, davidpeng1749@gmail.com

## Abstract

Young's double slit (and Arago spot) experiments revived the wave theory of light. The standard interpretation is that the light behaves as waves *before and after* passing through the double slit. Feynman called the double slit experiment the only mystery in quantum mechanics. In this article, we postulate and experimentally confirm the precise rules of convex lenses. Based on those Postulates, we study the evolution of the patterns of single slit, double slit, triple slit, cross-double slit, disc ring, 1D-grating and 2D-grating experiments.

<figure><img src="image_3.png" /></figure>
The experiments show, for the first time, the novel universal phenomena: (1) Within a certain macroscopic distance from the diaphragm (Zone-1), light behaves as photons and produces a non-interference pattern, while near the screen (the far field, Zone-3), the photons produce an interference pattern, while between Zone-1 and Zone-3 (Zone-2), the photons produce an non-interference pattern; namely the nature and characteristics of the pattern are distance dependent; (2) The non-interference pattern evolves to the orthogonal interference pattern gradually in the same experiment; (3) The convex lens stops the evolution of the patterns at where it is placed; (4) The experiments violate the existing wave theories that describe the wave experiments, and violate Bohr's complementarity principle/wave particle duality. The experiments provide profound phenomena/data for further theoretical development of optics and for understanding the nature of light. We suggest that a complete theory should be able to interpret the non-interference pattern in Zone-1, the non-interference pattern in Zone-2, and the interference pattern in Zone-3; and the evolution from one pattern to another.

**Keywords:** double slit, grating, interference pattern, diffraction pattern, non-interference pattern, non-interference pattern evolving to interference pattern, single slit, triple slit, cross double slit, disc ring, 1D-grating, 2D-grating, wave nature of light, particle nature of light, wave particle duality, Bohr's complementarity principle, wave interpretations of double slit/grating experiments

# 1. Introduction

Historically, the study of the nature of light reached basically two concepts: wave and particle.

In 1690, Christiaan Huygens established the wave theory of light [1].

In 1704, Newton established particle theory [2], which states that light is made up of small discrete particles that travel in a straight line with a finite velocity.

In 1801, Young's double slit experiment [3] and the Arago-spot experiment [4] revived Huygens' wave theory.

In 1905, Einstein's photon theory [5] revived, in some sense, particle theory.

In 1927, Bohr proposed the complementarity principle [6] that stating that either (1) the wave and particle phenomena cannot be observed simultaneously in the same experiment or (2) if these two phenomena can be observed simultaneously in the same experiment, then the interpretations of the phenomena given by the wave theories are not complete. The wave-particle duality emerged.

In 1950s, wave-particle duality still puzzled physicists. Einstein (1951) [7] wrote to M. Besso: "All these 50 years of conscious brooding have brought me no nearer to the answer to the question: What are light quanta?". Feynman (1956) [8] called the interference pattern of the double slit experiment "a phenomenon which is impossible [...] to explain in any classical way, and which has in it the heart of quantum mechanics. In reality, it contains the only mystery [of quantum mechanics]."

The different versions of the double slit experiments with lens have been proposed for different purposes. Next let us briefly discuss three examples.

(1) Firstly, in 2003, Afshar [9,10] proposed/conducted the experiment of double slit with convex lens, and screen $σ_2$ (Figure 1). In Afshar's experimental setup, the light passes through two pinholes. A lens L directs the light so that the image of each pinhole falls on screen (Fig. 1), providing complete path knowledge. A series of thin wires are then placed at previously measured positions corresponding to the dark fringes of the interference pattern upstream of the lens.
<figure><img src="image_4.png" /><figcaption>Fig.1 Afshar's Experiment: (a) The configuration testing the effect of the wires in the wire grid; (b) Data representing the images of pinholes 1 and 2.</figcaption></figure>

With both pinholes open, Afshar claims that pinhole 1 remains correlated to photon Detector 1', as well as pinhole 2 to photon Detector 2'. The lens collects the light and obtains the images of the two pin-holes, respectively. Two detectors collect the photons for these two images respectively. Afshar claims that, when both pinholes are open, the light exhibits wave-like behavior when going past the wires, since the light goes through the spaces between the wires but avoids the wires themselves, but also exhibits particle-like behavior after going through the lens, with photons going to a correlated screen. This behavior violates the complementarity principle, since it shows both wave and particle characteristics in the same experiment for the same photons (Wikipedia). We show, in this article, the different phenomena.

There are arguments, for example, [11,12], on Afshar's conclusion.

(2) Secondly, in 2016, a double slit experiment with the lenses OL/TL has been reported for studying the effect of the slit width on the claimed resolution (Figure 2) [13].

<figure><img src="image_5.png" /><figcaption>Figure 2. System setup: P, polarizer; S, double-slit sample; OL, objective lens; F, Fourier spectrum plane; TL, tube lens; CCD, charge-coupled device camera.</figcaption></figure>

(3) Thirdly, the model of the double slit experiments with the lenses are utilized in the textbook.

<figure><img src="image_6.png" /><figcaption>Figure 3. Schematics of wave experiments with convex lenses</figcaption></figure>

For examples, the textbook [14,15], for establishing the math formulas to calculate the pattern (Figure 3). In the model, the convex lens is used to bring parallel light rays to a focal point P on the screen. However, the textbook did not show experimental data to support this model.

We show in this article that this model is inappropriate.

Let us summarize the previous experimental/theoretical works (Table 1):
<table><caption>Table 1: Comparing Afshar experiment, You-Kuan-Zhang experiment and Textbooks</caption><thead><tr><th></th><th>Afshar [9,10]</th><th>S. You, C.Kuan, B.Zhang [13]</th><th>Textbook [14,15]</th></tr></thead><tbody><tr><td>Experiment</td><td>yes</td><td>yes</td><td>none</td></tr><tr><td>purpose</td><td>Testing Bohr's complementary principle</td><td>Test how the slit width affects the resolution</td><td>Establishing the math formulas to calculate the pattern</td></tr><tr><td>Experimental setup</td><td>Two pinholes, lens, vertical wires, two detectors</td><td>Double slit, objective lens, tube lens, one CCD detector</td><td>Double slit, multi slits, lens, screen</td></tr><tr><td>Role of lens</td><td>Lens obtains images of two pinholes respectively. The detectors show two images.</td><td>The objective lens and the tube lens form a 4f system, and the Fourier spectrum plane is at the common focal plane of the two lenses.</td><td>bring parallel light rays to a focal point P on the screen</td></tr><tr><td>procedure</td><td>Close pinhole-1; close pinhole-2; open both pinholes</td><td>acquire the far-field image by vectorial Fourier optics</td><td>none</td></tr><tr><td>Observation</td><td>Bohr's complementary principle is violated.</td><td>the slit width has minimal influence when the illuminating light is polarized parallel to the slits.</td><td>none</td></tr><tr><td>Location of lens</td><td>fixed</td><td>fixed</td><td>fixed</td></tr></tbody></table>

In 2021, we conducted double slit experiments with shields and blockers, which show, for the first time, that, even in double slit experiments, light behaves as a particle and distribute as wave [16-18].

In the middle of 2022, the photon chamber was proposed and applied for the first time to the standard wave experiments, such as double slit, 1D grating and 2D grating experiments [19-22]. The photon chamber has been used to study the photon behavior near the detecting screen. Both the particle nature and the wave-like distribution of light are observed simultaneously in the same experiment. The photons propagate along the straight-line trajectories and the trajectories are distributed as waves.

In the latter of 2022, we proposed and utilized three methods to study the photon behavior near the double slit/cross double slit [23-25]. Experiments showed that within a certain macroscopic distance from the double slit/cross double slit, the patterns of the double slit experiments having two equal maximum intensities near the double slit (Figure 3a), i.e., the pattern is non-interference. Namely, by the definition, the photons behave as particles near the double slit. Furthermore, we show that when the distance increases, the non-interference gradually evolves to the orthogonal interference pattern for the first time [26]. The non-interference and the orthogonal interference patterns coexist in the same “wave” experiment.

In this article, we show that the following phenomena are universal phenomena in the single slit, double slit, cross double slit, disc ring, 1D grating and 2D grating experiments: (1) in Zone-1, the patterns are non-interference; in Zone-2, the patterns are non-interference; and in Zone-3, the patterns are interference; (2) the non-interference patterns in Zone-1 evolve to the orthogonal interference patterns in Zone-3 in the same experiment; (3) The convex lens stops the evolution of the patterns at where it is placed; (4) Bohr's complementarity principle/wave particle duality are experimentally violated.

## 2. Non-interference pattern of double slit experiments

### 2.1. Interference pattern: standard description

First, let us briefly review the standard description of the double slit experiments. The standard interpretation is that *before and after* passing through the double slit the light propagates as waves and interferes after passing through the double slit. The interference pattern is formed on the detecting screen (Figure 4).
<figure><img src="image_7.png" /><figcaption>Figure 4. Schematics of wave description of double slit experiment</figcaption></figure>

To describe the pattern, the standard formula is, for $L \gg d$,

$$y_m = m \frac{\lambda L}{d} \qquad (1)$$

where “d” is the spacing of the double slit, “L” is the distance between the double slit and the screen, and “$y_m$” is the distance of the m^th^ fringe from the position of the primary maximum.

The intensity $I$ is proportional to the time average of the square of the total electric field $E$. For the small angle $\theta$, the intensity is

$$I \propto \langle E^2 \rangle = I_0 \cos^2 \left( \frac{\pi d}{\lambda L} y_m \right) \qquad (2)$$

Thus, according to the standard wave descriptions, there is an interference pattern with one maximum intensity when $L \gg d$. In the double slit experiment, the pattern is studied in the far field.

## 2.2. Photon chamber, zones, particle pattern, transition pattern and interference pattern

To study the experiments, we propose an apparatus and several terms.

### 2.2.1. Photon chamber

The photon chamber is a transparent container filled with a mixture of water and fine powder. The dimensions of the photon chamber are 60 x 60 mm (Figure 5(b)). We refer to the side of the photon chamber facing the screen as the far side, and the side facing the double slit as the near-side.

<figure><img src="image_8.png" /><figcaption>Figure 5. Schematics of the Double Slit Experiment with a Photon Chamber</figcaption></figure>

The photon chamber has been placed near the screen in the double slit experiments [19-22]. Next, we utilize the photon chamber to study the patterns near the double slit.

### 2.2.2. Zone

For convenience in the following discussion, let us divide the space between the source and screen into four zones (or areas) (Figure 6):

(1) **Zone-0**: between the source and the double slit, in which the pattern is non-wave, which has been experimentally confirmed [16];
(2) **Zone-1**: near the double slit, in which the pattern is the image of the diaphragm and is *non-interference*, referred to as the **particle pattern**;

(3) **Zone-2**: transition Zone, between zone-1 and zone-3, in which the particle pattern evolves to the orthogonal interference pattern, referred to as the *transition patterns* that are also the non-interference pattern.

<figure><img src="image_9.png" /><figcaption>Figure 6. Four Zones</figcaption></figure>

(4) **Zone-3**: near the screen, in which the patterns are orthogonal *interference patterns*;

**2.2.3. Particle pattern, transition pattern and orthogonal interference pattern: definitions** [16-20]

(1). **particle pattern** (Figure 7): classical particles going through a double slit will form the pattern that has exactly the same shape as the cross sections of the photon track-1 and photon track-2 of Figure 7. Thus, we define the pattern of two photon tracks as “particle pattern” that indicates that the light behaves as particles in Zone-1.

<figure><img src="image_10.png" /><figcaption>Figure 7. Photon Tracks --- particle patterns in Zone-1</figcaption></figure>

Figure 7(a) and 7(b) are top view and cross-section view of the particle pattern respectively. The cross-section view of the particle pattern is the image of the diaphragm. In this experiment, it is a double slit.

(2). **Transition pattern** (Figure 8):

<figure><img src="image_11.png" /><figcaption>Figure 8. Transition pattern in Zone-2</figcaption></figure>

The shapes of transition patterns are in between the particle patterns in Zone-1 and the orthogonal interference patterns in Zone-3. When the particle pattern gradually transitions to the orthogonal interference pattern, they are neither particle pattern nor wave pattern and thus, the light behaves not as a wave in Zone-2. We call them the “transition patterns”.
The transition pattern is the non-interference pattern. In Zone-2, the particle pattern transit to orthogonal interference pattern.

**(3). Interference pattern** (Figure 9): Figure 9 shows the orthogonal interference pattern.

Note that the boundaries between zone-1 and zone-2, and between zone-2 and zone-3 are not clear cut.
Patterns in one zone gradually transform to the patterns in another zone.

<figure><img src="image_12.png" /><figcaption>Figure 9. Interference pattern in Zone-3</figcaption></figure>

To study the evolution of the patterns between different zones, we utilize the convex lens to study
the cross section of the patterns.

**2.3. Non-interference pattern: photon chamber placed near double slit (Zone-1)**

In Section 2.3, all Figures are top views.

It is difficult to utilize the top views shown by a photon chamber to study the evolution of the
patterns. However, it is those top views of the patterns that actually lead to the novel phenomena, near
the double slit, that the patterns are no longer the interference pattern.

**Experiment-1** (Figure 10):

Placing the photon chamber with the far side at 65 mm from the diaphragm of the double slit, Figure 10(a)) shows two photon tracks in the photon chamber, which indicates that from the diaphragm to the far side of the photon chamber, the light propagates as photons along the straight-line photon tracks (trajectories). The pattern is non-interference. Two photon tracks represent two primary maximum densities. Figure 10(b)) shows the interference pattern on the screen in the same experiment.

<figure><img src="image_13.png" /><figcaption>Figure 10. Non-interference pattern: 65 mm away from the double slit</figcaption></figure>

**Experiment-2** (Figure 11):
Placing the photon chamber with the far side at 100 mm from the double slit, we observed two photon tracks (Figure 11(a)), which indicates that from the diaphragm to the far side of the photon chamber, the light propagates as photons, not as waves. The pattern is non-interference.

<figure><img src="image_14.png" /><figcaption>Figure 11. Non-interference pattern: 100 mm Away from Double Slit</figcaption></figure>

On the screen, we observed the standard interference pattern simultaneously. The interference pattern (Figure 11(b)) has no change, which is the same as that in Figure 10(b).

Figure 11(a) also shows the two light spots at the two slits of the double slit, the two light spots corresponding to two photon tracks.

**Experiment-3** (Figure 12):

Placing the photon chamber with the far side at 150 mm from the diaphragm of the double slit, we observed two photon tracks, which indicates that from the diaphragm to the far side of the photon chamber, up to 150 mm, the light propagates as photons, not as waves. The pattern is a non-interference pattern. Two photon tracks represent two primary maximum fringes.

<figure><img src="image_15.png" /><figcaption>Figure 12. Non-interference pattern: 150 mm Away from Double Slit</figcaption></figure>

**Discussion:** Experiments 1, 2 and 3 show, for the first time, that (1) within a certain macroscopic distance from the diaphragm, the patterns are non-interference and contain two equal maximum intensities (photon tracks), which indicates that the standard double slit experiments violate the
standard wave interpretations, e.g., Equation 1 and Equation 2, in Zone 1 near the diaphragm; and (2) the light beams behave as photons near the double slit. While, on the screen, we simultaneously observe the standard interference pattern (e.g., Figure 10(b)). The characteristics of the interference pattern do not change, but are dimmer due to the photon chamber.

The photon chamber may be placed at any position between the double slit and the screen. Photon chamber was placed in Zone-1, Zone-2 and Zone-3 respectively in the following experiments.

Experiments-1, -2 and -3 show the top view of photon track-1 and photon track-2 in photon chamber placed near the double slit, and we refer to two photon tracks as the “particle pattern”. Experiments-1, -2 and -3 are schematically shown in Figure 13. The photon chamber shows the existence of the non-interference pattern with two maximum intensities in the double slit experiment (Figure 10 to Figure 12).

<figure><img src="image_16.png" /><figcaption>Figure 13. Non-interference pattern of standard double slit experiments (near double slit)</figcaption></figure>

## 2.4. Orthogonal interference pattern: photon chamber placed near screen (Zone-3)

**Experiment-4** (Figure 14): top view

Figure 14(b) shows the top view of the interference pattern in photon chamber-1 placed in Zone-3.

Light propagates along photon tracks/trajectories, and photon tracks are distributed as waves [16-20].

<figure><img src="image_17.png" /><figcaption>Figure 14. Photon tracks showing light propagating as particles in Zone-3</figcaption></figure>

The interference patterns are shown in the photon chamber-1 and on the screen simultaneously. The interference pattern has no change, as shown in Figure 10(b) and Figure 11(b).

## 2.5. Non-interference pattern: photon chamber in Zone-2

**Experiment-5** (Figure 15):

Figure 15 shows the top view of the transition pattern in photon chamber-1 placed in Zone-2.
<figure><img src="image_18.png" /><figcaption>Figure 15. Light behaving as particles in Zone-2</figcaption></figure>

The transition patterns (non-interference) in Zone-2 are blurred.

We propose three Postulates to study how the non-interference patterns evolve to the interference patterns.

### 3. Postulates: precise rules of convex lens

Hereafter, we use the term “diaphragm” to represent the single slit, double slit, cross double slit, ring, 1D grating and 2D grating. In the experiments, the diaphragm stays at the same location. The light coming out of the slits has the certain pattern. However, we will show that the pattern changes with the distance from the diaphragm. The convex lens moves and thus, the patterns arriving at the input surface of the convex lens change. Namely, the light patterns arriving at the input surface of the convex lens are different. Let us define two terms, input and output surfaces, for the convex lens (Figure 16).

<figure><img src="image_19.png" /><figcaption>Figure 16. Convex lens enlarges the image arriving at its “input surface”</figcaption></figure>

We suggest the following Postulates.

**First Postulate:** the convex lens enlarges the input image that arrives at the input surface (Figure 16).

**Second Postulate:** The convex lens does not change the nature and characteristics of the input pattern.

**Third Postulate:** The convex lens breaks/stops the evolution of the patterns.

**Example-1 of First Postulate:** For a regular object, the shape of the image of the object does not change. Thus, the input image that arrives at the input surface of the convex lens is the same image of the object. Namely the image of an object is not the distance dependent.

**Example-2 of First Postulate:** For the wave experiments, the input image that arrives at the input surface of the convex lens is distance dependent and thus, the shapes of the input images are different, even in the same experiment.

**Experiment of Second Postulate:** After passing through a convex lens, the pattern keeps the same nature: e.g.,

(a) if an input pattern is a particle pattern, the output pattern is still the particle pattern;

(b) if an input pattern is a transition pattern, the output pattern is still the transition pattern;

(c) if an input pattern is an interference pattern, the output pattern is still the interference pattern.
**Example of Third Postulate:** as a consequence of Second Postulate, the input image and the output image of the convex lens are the same, and the output image keep the same nature and characteristics of the pattern as that of the input image; namely the evolution is stopped.

Experiments in Section 4 are based on three Postulates and experimentally confirm them.

Note that the boundaries between Zone-1 and Zone-2, and between Zone-2 and Zone-3 are not clear cut. Patterns in one zone gradually transform to the patterns in another zone.

To study patterns in a zone, we utilize the photon chamber and/or convex lens.

## 4. Non-interference pattern in Zone-1 evolving to interference pattern in Zone-3

Hereafter, we refer to all wave patterns, i.e., interference patterns and diffraction patterns, as the orthogonal interference patterns, since they are perpendicular the slits of the diaphragms. All of experiments in this section have the same setup (Figure17), except with different diaphragms.

It is challenging to describe the evolutions shown in those experiments.

**Experimental setup** (Figure 17):

<figure><img src="image_20.png" /><figcaption>Figure 17. Experimental setup</figcaption></figure>

The convex lens is placed between the diaphragm and the screen. The distance between the diaphragm and the convex lens is L. We start experiments from $L = 10$ mm and increase L.

The diaphragms in Figure 18 show: the diaphragms of the single slit, double slit, triple slit, cross double slit, disc ring, 1D grating and 2D grating respectively.

<figure><img src="image_21.png" /><figcaption>Figure 18. Diaphragms</figcaption></figure>
4.1. Single slit: horizontal slit of width 0.04 mm (supplement-1)

Figure 19 shows the standard diaphragm and pattern of a single slit. The pattern is orthogonal to
the single slit.

<figure><img src="image_22.png" /><figcaption>Figure 19. Standard single slit experiment</figcaption></figure>

**Experiment-6** (Figure 20) (for more detail, see supplement-1): the horizontal single slit of Figure 18 is placed at the distance L from the single slit. To study the evolution of the pattern, the L is increased from 10 mm to 1000 mm respectively.

<figure><img src="image_23.png" /><figcaption>Figure 20. Evolution of pattern of single slit experiment</figcaption></figure>

Figure 20 shows the cross-section views of the evolution of the patterns, which show how the
horizontal non-interference patter (start from L = 10 mm) evolves to the orthogonal interference pattern
at (L ≥ 1000 mm). The patterns are distance-dependent. We observe the evolution of the patterns. The pattern at L = 50 mm is the typical particle pattern which is the image of the single slit.

## 4.2. Double slit experiment: vertical slits

### 4.2.1. Wider spacing: spacing: 1 mm, width: 0.15 mm (supplement-2)

<figure><img src="image_24.png" /><figcaption>We have shown the top view of the non-interference pattern in Experiment-1 (see below).</figcaption></figure>

Next we show the cross-section view of the patterns evolving from non-interference to interference.

**Experiment-7** (Figure 21): utilizing the vertical double slit of Figure 18. Placing the convex lens at different distance L from the diaphragm. We have the following cross-section views of the evolution of the patterns placed at different distances L from the diaphragms.

<figure><img src="image_25.png" /><figcaption>Figure 21. Evolution of patterns of double slit experiment (1)</figcaption></figure>
From $L = 10 - 150$ mm, the vertical patterns are the images of the double slit and clearly the particle pattern, the non-interference pattern. Then, when $L > 200$ mm, the vertical pattern gradually evolves to the horizontal orthogonal interference pattern at $L \ge 800$ mm.

The observations of Experiment-1, -2, -3 and -7 are consistent.

### 4.2.2. Narrow spacing: spacing 0.25 mm, width 0.15 mm (supplement-3)

The feature of the patterns is dependent on the parameters of the double slit.

**Experiment-8** (Figure 22): utilizing the double slit of Figure 18. Placing the convex lens at different distance L from the diaphragm. We observe the following evolution of the patterns.

<figure><img src="image_26.png" /><figcaption>Figure 22. Evolution of patterns of double slit experiment (2)</figcaption></figure>

From $L = 60 - 70$ mm, the vertical patterns are clearly the particle pattern, the non-interference pattern. Then, when $L > 150$ mm, the pattern gradually evolves to the horizontal orthogonal interference pattern $L \ge 1000$ mm.

### 4.3. Triple slit experiments: vertical slits (supplement-4)

**Experiment-9** (Figure 24): utilizing the triple slit of Figure 18.

<figure><img src="image_27.png" /><figcaption>Figure 23. Vertical triple slits and its horizontal pattern</figcaption></figure>
Figure 23 show the diaphragm of the triple slits and its standard pattern.

Placing the convex lens at different distance L from the diaphragm of the triple slit. We observe
the following evolution of the patterns.

<figure><img src="image_28.png" /><figcaption>Figure 24. Evolution of patterns of triple slit experiment</figcaption></figure>

From $L = 40 - 90$ mm, the vertical patterns are clearly the particle pattern, the non-interference patter. Then, when $L > 130$ mm, the vertical pattern gradually evolves to the horizontal orthogonal interference pattern at $L \ge 1000$ mm.

**4.4. Cross-double slit experiment**

**4.4.1. Two double slits crossing at angle (supplement-5)**

**Experiment-10** (Figure 26): utilizing the cross double slit of Figure 18.

<figure><img src="image_29.png" /><figcaption>Figure 25. Cross double slits and its cross pattern (1)</figcaption></figure>

Figure 25 shows the diaphragm of the cross double slits and its standard cross pattern.

Placing the convex lens at different distance L from the diaphragm of the cross double slit. We observe the following evolution of the patterns.
<figure><img src="image_30.png" /><figcaption>Figure 26. Evolution of patterns of cross double slit experiment (1)</figcaption></figure>

From $L = 40 – 70$ mm, the patterns are the images of the cross double slit are clearly the particle pattern, the non-interference pattern. Then, when $L > 100$ mm, the pattern gradually evolves to the interference pattern at $L \ge 1000$ mm.

### 4.4.2. Two double slits crossing at right angle (supplement-6)

**Experiment-11** (Figure 28): utilizing the cross double slit of Figure 18.
<figure><img src="image_31.png" /><figcaption>Figure 27. Cross double slits and its cross pattern (2)</figcaption></figure>

Figure 27 shows the diaphragm of the cross double slits and its standard cross pattern.

Placing the convex lens at different distance L from the diaphragm of the cross double slit. We observe the following evolution of the patterns (Figure 28).

<figure><img src="image_32.png" /></figure>
<figure><img src="image_33.png" /><figcaption>Figure 28. Evolution of patterns of cross double slit experiment (2)</figcaption></figure>

From $L = 40 – 70$ mm, the patterns are clearly the particle pattern, the non-interference pattern. Then, when $L > 90$ mm, the pattern gradually evolves to the interference pattern at $L \ge 1000$ mm.

**4.4. Disc ring experiment** (supplement-7) [27]

**Experiment-12** (Figure 30): utilizing the disc ring of Figure 18. Placing the convex lens at different distance L from the diaphragm of the ring. We observe the following evolution of the patterns.

<figure><img src="image_34.png" /><figcaption>Figure 29. Disc ring and its pattern</figcaption></figure>

Figure 29 shows the diaphragm of the disc ring and its standard pattern.

Placing the convex lens at different distance L from the diaphragm of the disc ring. We observe the following evolution of the patterns (Figure 30).

<figure><img src="image_35.png" /></figure>
<figure><img src="image_36.png" /><figcaption>Figure 30. Evolution of patterns of disc ring experiment</figcaption></figure>

From $L = 50 - 60$ mm, the patterns are clearly the particle pattern, the non-interference pattern. Then, when $L > 60$ mm, the pattern gradually evolves to the interference pattern at $L \ge 150$ mm.

4.6. 1D grating: 40 slits/cm (supplement-8)

**Experiment-13** (Figure 23): Utilizing the commercial 1D grating with 40 slots/cm.

<figure><img src="image_37.png" /><figcaption>Figure 31. 1D grating and its pattern</figcaption></figure>

Figure 31 shows the diaphragm of the 1D grating and its standard pattern.

Placing the convex lens at different distance L from the diaphragm of the 1D grating. We observe
the following evolution of the patterns (Figure 32).

<figure><img src="image_38.png" /></figure>
<figure><img src="image_39.png" /><figcaption>Figure 32. Evolution of patterns of 1D grating experiment</figcaption></figure>

At $L = 150$ mm, the vertical pattern is the image of the grating and is the particle pattern, the non-interference pattern. Then, when $L > 150$ mm, the pattern gradually evolves to the orthogonal interference pattern at $L \ge 700$ mm.

### 4.7. 2D grating: 40 slits/cm (supplement-9)

**Experiment-14** (Figure 34): Utilizing a commercial 2D grating with 40 slits/cm.

<figure><img src="image_40.png" /><figcaption>Figure 33. Standard pattern of 2D grating experiment</figcaption></figure>

Figure 33 shows the diaphragm of the 2D grating and its standard pattern.

Placing the convex lens at different distance L from the diaphragm of the 2D grating. We observe the following evolution of the patterns (Figure 34).
<figure><img src="image_41.png" /><figcaption>Figure 34. Evolution of patterns of 2D grating experiment

At $L = 75$ mm, the pattern is the particle pattern, the non-interference patter. Then, when $L > 75$ mm, the pattern gradually evolves to the interference pattern at $L \ge 700$ mm.</figcaption></figure>

**5. Discussion and summary**
In this article, we proposed three Postulates as the precise rules of convex lens for the first time, which is then confirmed experimentally.

**First Postulate:** the convex lens enlarges the input image that arrives at the input surface (Figure 12).

**Second Postulate:** The convex lens does not change the nature and characteristics of the input pattern.

**Third Postulate:** The convex lens breaks the evolution of the patterns.

We place the convex lens in Zone-1, Zone-2 and Zone-3 respectively. Then we show that in different Zones, the photons behave differently and produce the non-interference patterns, the transition patterns and orthogonal interference patterns respectively.

Based on Postulates, we utilize a convex lens in three Zones to study the experiments including single slit, double slit, triple slit, cross double slit, disc ring, 1D grating and 2D grating experiments.

We show, for the first time, the following novel universal phenomena of photons:

(1). within a certain macroscopic distance from the diaphragm, i.e., in Zone-1, light behaves as photons and produces non-interference pattern;

(2). the non-interference pattern evolves to the orthogonal interference pattern gradually and naturally in the same experiment.

(3). the non-interference pattern and orthogonal interference pattern co-exist in the same experiment.

(4). the nature and characteristics of the patterns are distance dependent: in the wave experiments, the non-interference patterns indicate that the nature of light is photons; while the interference patterns indicate that the photons distribute as waves.

(5). The optical Equation (1) and (2) cannot describe the above-mentioned universal phenomena; It is a challenge to find the mechanism/physical interpretation and the mathematical description of this phenomenon. The phenomena violate the existing wave theories describing the wave experiments.

(6) The Bohr's complementarity principle is experimentally violated.

We suggest that a complete theory should be able to interpret simultaneously the non-interference pattern, the interference pattern, and the evolution from one pattern to other.

The experiments provide profound phenomena/data in optics/physics for further development of theory, for exploring the mystery of the double slit, and for exploring the nature of the light. It is really a mystery that, light behave as photons near the diaphragm and near the screen, but distribute as wave on the screen.

<table><caption>Table 2: Comparison of Afshar, You-Kuan-Zhang, Textbooks and author's experiments</caption><thead><tr><th></th><th>Afshar [9,10]</th><th>S. You, C. Kuang, B. Zhang [13]</th><th>Textbook [14,15]</th><th>Author</th></tr></thead><tbody><tr><td>Experiment</td><td>yes</td><td>yes</td><td>none</td><td>yes</td></tr><tr><td>purpose</td><td>Testing Bohr's complementary principle via which way experiments</td><td>Studying how the slit width affects the claimed resolution</td><td>Establishing the math formulas to calculate the pattern</td><td>Showing evolution of patterns from non-interference pattern to orthogonal interference pattern in same experiment</td></tr><tr><td>Observation/ conclusion</td><td>Violation of Bohr's complementary principle</td><td>the slit width has minimal influence when the illuminating light is polarized parallel to the slits.</td><td>none</td><td>(1). Non-interference pattern evolving to orthogonal interference pattern in same experiment; (2). Lens stops evolution of patterns; (3) Bohr's complementary principle is violated.</td></tr><tr><td>Position of lens</td><td>fixed</td><td>fixed</td><td>fixed</td><td>Positions are varied in Zone-1, Zone-2, Zone-3</td></tr><tr><td>Type of experiment</td><td>Two pinholes</td><td>Double slit</td><td>Single slit, double slit, multi-slits</td><td>Single slit, double slit, multi-slits, cross double slit, disc ring, 1D grating, 2D grating</td></tr></tbody></table>
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