The particle and wave-like behavior of light is modeled by two sets of equations and accompanying perspectives on the nature of light and its interaction with matter.
Wave-like behavior is based on oscillating electric and magnetic fields propagating through space. These electromagnetic fields interact with charged particles of matter, such as electrons. This wave-like behavior of light is summarized and described by Maxwell’s equations.
Another perspective about the nature of light has to do with particles called photons. Some experiments indicate light behaves as photons that exist on energy levels founded on Planck’s Constant. The equation E = hc/y describes the inverse relationship between a photon’s energy “E” and the wavelength of electromagnetic radiation that characterizes it “y”. Numerator components h and c, Planck’s Constant and the speed of light, respectively, do not change and provide a “pivot” around which the wave-like nature of a photon and its accompanying discrete energy, rotate.
This wave-particle duality is present not just in light, but also in matter. The photoelectric effect illustrates this fact and hints at a deeper property of matter and light which is, for now, difficult to understand.
Approximations of light’s behavior using particle and wave models don’t always agree with observed phenomena. Certain cases defy traditional explanations relying on either the wave-like or particle-like behavior of light.
This breakdown is not an isolated case. Momentum and gravitational effects on an object increasingly deviate from Newtonian predictions due to relativistic effects at near-light speeds. Gravitational relativistic effects, though always present, make a very trivial impact on the behavior of a system in most circumstances. However, as with wave/particle approximations, extreme conditions defy predicted behavior.
In textbooks, the quantized nature of light is not as emphasized as much as its wave-like properties. On the other hand, the quantized and discrete nature of matter, especially when interacting with electromagnetic radiation at the atomic/molecular scale of electron energy levels, is usually presented more prominently at the expense of the wave-like aspects of matter. Thus, light is primarily portrayed as wave-like, while matter as quantized, though neither perspective is completely accurate.