Photon in Double Slit

Beginning of controversy: First of all, two models are proposed based on observations: one states that light is made up of particles, and the other states that light is a wave. In the era of Isaac Newton, there was a great debate among the scientific community about the nature of light. Some believed that light is made up of particles and simply follows collision rules, similar to other particles when striking any object. On the other hand, some believed that it is a wave. Surprisingly, both communities are totally right because phenomena like the photoelectric effect and the Compton effect provide enough evidence that light has particle-like behavior. In contrast, phenomena like interference and diffraction prove that light is a wave, not a particle. This was the most famous controversy in the era of the 16th to 18th century.

Many scientists came and gave their opinions on light. Newton also tried to explain the nature of light and gave his corpuscles theory. According to Newton, light is made up of particles called corpuscles, and it behaves just like colliding particles. He argued that for explaining phenomena such as reflection or refraction, we must assume light as a particle. Newton's corpuscles theory states:

Every source of light emits large numbers of tiny particles known as corpuscles in a medium surrounding the source.

These corpuscles are perfectly elastic, rigid, and weightless.

Later, a scientist named Huygens came and gave his own wave theory of light. In the same era, a new phenomenon known as double refraction of light was discovered. Huygens easily explained the phenomenon of double refraction of light in crystals with his wave theory. Unfortunately, nobody paid any attention to his wave theory for over a hundred years because of Newton's simplified theory and his influence on the physics community.

Then, Young performed his famous double-slit experiment and discovered that when light strikes a screen after passing through slits, it forms an interference pattern. He discovered another phenomenon named diffraction there, and these experiments could not be explained by assuming the particle theory of light. Therefore, Newton's theory went into the background, and the wave theory of light came into the spotlight, and everyone began to accept it until Albert Einstein gave his theory where he assumed light as a quantum of packet called a photon. Again, this conflict started, but later it was accepted that light has a dual nature, particle as well as wave. In this article, we are going to understand the Young double-slit experiment in detail.

Experiment:









In 1801, Young performed an experiment to prove that light is a wave and that it also forms an interference pattern, just like other waves. He also calculated the wavelength of sunlight, which is very close to the modern measured value. In his experiment, he used light from a distant monochromatic source, and the light that interfered on the screen was in the same phase. Firstly, he passed monochromatic light through a single slit (S). After passing through the single slit, it spread into a circular wave due to diffraction and struck the double slit kept in front of the single slit. After passing through the double slit, when we observe the screen beyond the double slit, we will observe continuous maxima (bright regions) and minima (dark regions present between two adjacent bright regions) one after another, and this is called an interference pattern. Maxima are regions formed due to constructive interference of light on the screen, and minima are regions formed due to destructive interference of light waves on the screen.

Locating the fringes: For the formation of interference on the screen (C), the distance of separation between slits must be much smaller than the distance between the slit and the screen. So for locating the fringes, we will draw a central line from the center of two slits to the screen. Let's assume a point P on which a fringe is formed at an angle (theta) to the central axis. P is the point on which two rays, r1 (a ray from the bottom slit), and r2 (a ray from the top slit), intercepted and produced fringes. The waves passing through the slit to incident on point P have the same phase difference due to the same origin (sources). However, once they have passed through the slit, they have traveled different distances to reach point P, and this difference in distance covered by the wave is called path difference. Due to this path difference, it led to the phase difference of two waves. Now, if we consider two waves after passing through slits incident on point P with zero path difference, then they will arrive with exactly the same phase difference, and hence, they interfere fully constructively. If that is true for the waves of rays r1 and r2, then point P is part of a bright fringe. When, instead, 2L is an odd multiple of half a wavelength, the waves arrive at the common point exactly out of phase, and they interfere fully destructively there. If that is true for the waves of rays r1 and r2, then point P is part of a dark fringe.

When waves from the two slits arrive at a point on the screen in phase (crest meets crest or trough meets trough), they undergo constructive interference, reinforcing each other and creating a bright fringe. Conversely, when the waves arrive out of phase (crest meets trough), destructive interference occurs, leading to a dark fringe.

Mathematical Framework: The location of fringes in the double-slit experiment can be determined using the mathematical framework developed by Augustin-Jean Fresnel and further refined by George Biddell Airy. The mathematical expressions involve the wavelength of the incident particles or light, the distance between the slits, and the distance from the slits to the screen.

Formula for Fringe Separation: The fringe separation, or the distance between adjacent bright or dark fringes, can be calculated using the formula:

fringe separation = λL/d

where:

λ is the wavelength of the incident particles or light.

L is the distance from the slits to the screen.

d is the distance between the slits.

B. Application to Different Wavelengths:




This formula demonstrates that the fringe separation is inversely proportional to the distance between the slits and directly proportional to the wavelength of the incident particles or light. Therefore, changing the wavelength or adjusting the distance between the slits can significantly impact the location and visibility of the fringes.




Coherent and Incoherent Source: The interference pattern observed in the double-slit experiment is possible only when the light waves arriving on the screen have a phase difference that does not vary in time. Hence, the waves forming an interference pattern on the screen have a constant phase difference, and sources emitting these waves are called coherent sources. Similarly, sources emitting waves whose phase difference continuously varies with time are incoherent sources.




Interference and Intensity: Intensity Defined: Intensity is like the spotlight on the stage of light. It measures the brightness or power of light waves. The higher the intensity, the brighter the light.




Relationship with Interference: Intensity and interference are closely linked. In regions of constructive interference, where waves team up, the intensity is high, creating bright spots. Conversely, in regions of destructive interference, where waves cancel out, the intensity is lower, resulting in darker areas.

Mathematical Choreography: Understanding the Equations:

Constructive Interference Equation:

The intensity of light in regions of constructive interference can be calculated using the equation:

I(constructive) = I(1) + I(2) + 2rootI1*I2*cos(theta)

where:

I(constructive) is the intensity in the constructive interference region,

i(1) and I2) are the individual intensities of the interfering waves,

(theta) is the phase difference between the waves.

B : Destructive Interference Equation:




For destructive interference, the intensity equation is:

I(distructive) = I(1) + I(2) - 2rootI1*I2*cos(theta)

The cosine term accounts for the collaboration or cancellation between the waves.




Copenhagen Interpretation:

The Copenhagen interpretation, formulated by Niels Bohr and Werner Heisenberg, posits that particles exist in a superposition of states until observed, at which point the act of observation causes the system to collapse into one of the possible states. This interpretation emphasizes the probabilistic nature of quantum mechanics and the inherent uncertainty in measuring particle properties.




Many-Worlds Interpretation:

Proposed by Hugh Everett III, the many-worlds interpretation takes a different approach to the double-slit experiment. According to this theory, when a measurement is made, the universe splits into multiple branches, each corresponding to a different outcome of the measurement. In this framework, the interference pattern persists in a parallel universe where the measurement is not made, while another universe emerges where the particles behave as discrete entities.


Pilot-Wave Theory: Louis de Broglie's pilot-wave theory offers a deterministic perspective on quantum mechanics. In this interpretation, particles have both particle and wave-like properties, and the pilot wave guides the particle's motion. The double-slit experiment, according to this theory, is a result of the interaction between the particle and its accompanying wave.




Beyond Light: Electrons and Other Particles: The double-slit experiment is not limited to the realm of light. Electrons, initially considered as classical particles, were later found to exhibit wave-like behavior as well. When electrons are fired through a double slit, they create an interference pattern, similar to the pattern produced by light. This discovery reinforced the idea that the wave-particle duality is a fundamental aspect of the quantum world.




Technological Advancements and Modern Applications: As technology has advanced, scientists have been able to perform the double-slit experiment with increasing precision and explore its implications across various domains. From electron microscopy to quantum computing, the principles derived from the double-slit experiment have paved the way for groundbreaking technological developments.




Quantum Entanglement and Bell's Theorem: The double-slit experiment also has profound implications for our understanding of quantum entanglement. Entangled particles, when separated by large distances, can instantaneously influence each other's properties. Bell's theorem, formulated by physicist John Bell in 1964, provided a means to test the validity of quantum mechanics against classical theories. Experiments based on Bell's theorem have consistently supported the predictions of quantum mechanics, further reinforcing the enigmatic nature of the quantum world."



















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