Wave-Particle Duality and Propagation of Light

Light exhibits wave-particle duality, behaving as both a wave and a particle.
The wave model is useful for explaining phenomena such as interference, diffraction, and polarization.
The particle model is useful for explaining phenomena such as the photoelectric effect and Compton scattering.

Light propagates as an electromagnetic wave, consisting of oscillating electric and magnetic fields.
These fields are perpendicular to each other and to the direction of propagation.
Light waves can travel through a vacuum, as they do not require a medium to propagate.
The speed of light in a vacuum is a fundamental constant, approximately 299,792,458 meters per second.
In a medium, the speed of light is reduced, depending on the properties of the medium.
The energy of a light wave is proportional to the square of the amplitude of the electric field.
Light also propagates as particles called photons.
Photons are discrete packets of energy, and the energy of a photon is proportional to its frequency.
The higher the frequency, the more energy the photon carries.
The intensity of light is proportional to the number of photons per unit area per unit time.

Reflection occurs when light bounces off a surface.
There are two types of reflection: specular and diffuse.
Specular reflection occurs when light reflects off a smooth surface, such as a mirror.
In specular reflection, the angle of incidence equals the angle of reflection.
The angle of incidence is the angle between the incident ray and the normal to the surface.
The angle of reflection is the angle between the reflected ray and the normal to the surface.
Diffuse reflection occurs when light reflects off a rough surface, such as paper.
In diffuse reflection, the light is scattered in many directions.
The law of reflection (angle of incidence equals angle of reflection) still holds locally, but the surface irregularities cause the overall scattering.
From a particle perspective, reflection can be viewed as the photon bouncing off the surface, conserving energy and momentum.
The surface atoms absorb and re-emit photons, resulting in the reflected light.

Refraction occurs when light bends as it passes from one medium to another.
The bending of light is due to the change in the speed of light as it enters a different medium.
The refractive index of a medium is a measure of how much the speed of light is reduced in that medium.
Snell's law describes the relationship between the angles of incidence and refraction: n1sinθ1 = n2sinθ2.
n1 is the refractive index of the first medium.
θ1 is the angle of incidence.
n2 is the refractive index of the second medium.
θ2 is the angle of refraction.
When light passes from a medium with a lower refractive index to a medium with a higher refractive index, it bends towards the normal.
When light passes from a medium with a higher refractive index to a medium with a lower refractive index, it bends away from the normal.
Total internal reflection occurs when light is traveling from a medium with a higher refractive index to a medium with a lower refractive index, and the angle of incidence is greater than the critical angle.
The critical angle is the angle of incidence at which the angle of refraction is 90 degrees.
From a particle perspective, refraction can be understood as the photons interacting with the atoms in the new medium.
This interaction causes the photons to be absorbed and re-emitted, resulting in a change in speed and direction.

The wave model explains propagation through electromagnetic waves and concepts like wavelength and frequency.
It describes reflection and refraction by considering the change in wave speed and the Huygens' principle.
The particle model explains propagation through photons and their energy, momentum.
It describes reflection and refraction by considering photons interacting with matter.
Wave model better explains: interference, diffraction, polarization.
Particle model better explains: photoelectric effect, Compton scattering.
Wave-particle duality acknowledges that light exhibits both wave-like and particle-like properties, depending on the experiment.
Both models are necessary to fully understand the behavior of light.
Neither model is perfect on its own, but together they provide a comprehensive understanding.
The choice of which model to use depends on the specific phenomenon being studied.