Soumendra Nath Thakur¹
¹Tagore's
Electronic Lab.
23 AUG 2023
Abstract:
This research paper
explores the intricate interplay between photons and mirrors, shedding light on
the processes that occur during photon-mirror interactions. We delve into the
absorption of photons by electrons on a mirror's surface, which leads to energy
gain and movement of electrons to higher energy levels. This interaction, akin
to photoelectric absorption, is fundamental to understanding the behavior of
light and mirrors. The paper investigates the principles of mirror
reflectivity, highlighting the optimization of reflectivity by minimizing
energy absorption (ΔE) to maintain high reflectivity. We also examine the
angles of incidence and reflection, emphasizing their equal values and the
related sum of angles.
Through careful analysis,
we establish that the energy difference between incident and reflecting
photons, denoted as ΔE, corresponds to a time delay (Δt) between the photons.
This unique relationship between energy and time delay introduces the concept
of infinitesimal time delay during reflection, contributing to a time
distortion in the behavior of light. The research culminates in the assertion
that the constancy of motion of a photon of light is disrupted when it is
reflected by a mirror due to the introduced time delay.
Introduction:
The interaction between photons and
mirrors is a fundamental phenomenon with profound implications for our
understanding of light and its behavior. In this research, we delve into the
intricate details of photon-mirror interactions, energy absorption, and the
subsequent time delay introduced by the interaction.
Photon-Mirror Interaction and Energy Absorption:
When a photon collides with an atom on
a mirror's surface, it has the potential to be absorbed by an electron within
the atom. This absorption results in the electron gaining energy (hf) and
transitioning to a higher energy level. This process, analogous to
photoelectric absorption, is central to the interaction between photons and
mirrors. The mirror's reflectivity is optimized by minimizing energy absorption
(ΔE), ensuring that high reflectivity is maintained. The energy of the
reflected photon, denoted as hf-ΔE, represents the energy loss within the
mirror.
Angle of Incidence and Reflection:
The angles of incidence and reflection
play a pivotal role in photon-mirror interactions. The relationship between
these angles is such that the angle of incidence (θi) is equal to the angle of
reflection (θr). This relationship is also expressed in terms of angles in
degrees (θi and θr), where θi+θr=180°. This symmetry in angles contributes to
the predictable behavior of reflected photons.
Photon Energy Absorption and Time Delay:
The difference in energy between the
incident photon (γi) and the reflecting photon (γr) is represented as ΔE, which
signifies the energy absorbed by the mirror. Remarkably, this energy difference
also corresponds to a time delay (Δt) between the incident and reflecting
photons. This intriguing relationship between energy and time introduces the
concept of infinitesimal time delay during reflection, leading to a time
distortion in the behavior of light.
Equations and scientific foundations:
When a photon (hf) interacts with an
atom on a mirror's surface, it can indeed be absorbed by an electron in the
atom. This interaction results in the electron gaining energy (hf) from the
absorbed photon. This increase in energy can cause the electron to move to a
higher energy level within the atom, farther away from the nucleus.
Photoelectric absorption takes place. Mirrors are made to minimize absorption (ΔE)
in order to maintain high reflectivity.
Optimize reflectivity (hf- ΔE) and minimize light absorption (ΔE). The
reflected photon will have energy (hf- ΔE). The reflected photon will have
energy of (hf−ΔE).
The angle of incidence (θi) is equal to the angle of reflection (θr). Since, the angle of incidence (θi) is equal to the angle of reflection (θr), θi = θr; and, the sum of the angles of incidence (θi) and reflection (θr) always equals 180°, θi + θr = 180°. Therefore, if the angle of incidence (θi) = 180°, so the, angle of reflection (θr) = 180°.
The reflected photon having energy (hf- ΔE) travels in the opposite direction of the interacting photon with energy (hf), the angle of incidence is equal to the angle of reflection. This means that the direction of the reflected photon is related to the direction of the incident photon but is not necessarily opposite to it.
Briefly, incident photon energy (γi) = hf; reflecting photon energy (γr) = (hf−ΔE); photon energy absorption (γi - γr) = (ΔE);
So, when a photon of light at the speed of light strikes or collides with a mirror wall, initially, the photon is absorbed by electrons in the mirror's surface atoms. In effect, the collision causes another photon to detach from an electron in an atom on the mirror surface, and the detached photon travels at the speed of light but in the opposite direction to the colliding photon. As a result, some of the energy of the colliding photons is lost in the collision with the mirror surface.
The reflected photon having energy (hf- ΔE) travels in the opposite direction of the interacting photon with energy (hf), at a 180° angle, when the angle of incidence was 180°.
Briefly, when a photon collides with a mirror surface, it is initially absorbed by electrons in the mirror's surface atoms. The collision causes another photon to detach from an electron in an atom on the mirror surface. The detached photon travels at the speed of light but in the opposite direction to the colliding photon. Some energy of the colliding photons is lost in the collision with the mirror surface.
The energy of the incident photon is hf, where h is Planck's constant and f is the frequency of the photon. The energy of the reflecting photon is hf−ΔE, where ΔE represents energy loss due to interactions within the mirror. The difference in energy between the incident and reflecting photons is ΔE. This difference represents the energy absorbed by the mirror and not reflected.
The photon energy absorption = (γi - γr), the difference in energy between the incident and reflecting photons = ΔE.
Assuming, the incident photon frequency = f1; when, the incident photon energy = (γi); and, the reflecting photon frequency = f2; when, the reflecting photon energy = (γr); the change in energy between incident photon and reflecting photon = ΔE;
The change in energy (ΔE) is equal to the time delay (Δt) between the incident photon and the reflecting photon. This suggests a relationship between the energy difference of the incident and reflecting photons and the difference in frequencies (f1 and f2) of those photons., presented by the equation,
Given Equations:
- ΔE = γi−γr
= Infinitesimal loss in wave energy
- f1 =
incident photon frequency
- f2 =
reflecting photon frequency
- T(deg)
= T/360 = (1/f)/360 = Δt
- f =
E/h = 1/360*T(deg)
- T(deg) = 1/f*360 = Δt
So, the relationships are -
- ΔE
=γi−γr
- Δt=f1−f2
Hence,
- ΔE = Δt. *(Update below)
Therefore when, there is an infinitesimal time delay (Δt) between the colliding photon (γi) and the diffusing photon (γr) to change direction of travel. Therefore, the constancy of motion of a photon of light is broken when it is reflected by a mirror.
Conclusion:
This research paper explores the intricate interactions between photons and mirrors, revealing the processes of energy absorption and time delay. We have shown that the energy absorbed by a mirror during photon-mirror interaction is intricately tied to the time delay between incident and reflecting photons. This relationship challenges our conventional understanding of the constancy of motion of light, as the introduced time delay disrupts this constancy during reflection. By investigating these phenomena, we gain deeper insights into the behavior of light and its interactions with mirrors, contributing to our broader understanding of the fundamental principles of physics.
References:
[1] Elert, G. (n.d.). Photoelectric effect. The Physics Hypertextbook. https://physics.info/photoelectric/
[2] Einstein, A. (1905) On a Heuristic Viewpoint Concerning the Production and Transformation of Light. Annalen der Physik, 17, 132-148 https://doi.org/10.1002/andp.19053220607
[3] Filippov, L. (2016) On a Heuristic Point of View Concerning the Mechanics and Electrodynamics of Moving Bodies. World Journal of Mechanics, 6, 305-322. doi: http://dx.doi.org/10.4236/wjm.2016.69023
[4] P. Ewart 1. Geometrical Optics - University of Oxford Department of Physics. Geometrical Optics. https://users.physics.ox.ac.uk/~ewart/Optics%20Lectures%202007.pdf
[5] Planck, M. (n.d.). On an Improvement of Wien’s Equation for the Spectrum. M. Planck . http://www.ub.edu/hcub/hfq/sites/default/files/planck_1900_llei%281%29.pdf
[6] Louis-Victor de Broglie (1892-1987). (1925). On the Theory of Quanta: Recherches sur la théorie des quanta. (Ann. de Phys., 10e serie, t. III). Janvier-F evrier https://fondationlouisdebroglie.org/LDB-oeuvres/De_Broglie_Kracklauer.pdf
[6] Thakur, Soumendra Nath; Samal, Priyanka; Bhattacharjee, Deep (2023). Relativistic effects on phaseshift in frequencies invalidate time dilation II. TechRxiv. Preprint. https://doi.org/10.36227/techrxiv.22492066.v2
* Updated 08 Sep 2023 :
ΔE = hΔf; where, h is Planck's constant. Δf = 1/Δt; (Fourier transform); Δt = h / ΔE
