The intensity of light can be described using either the amplitude squared or the number of photons, depending on the context.
In classical physics, the intensity of a wave, such as light, is indeed proportional to the square of the amplitude. This is known as the intensity-amplitude relationship. Mathematically, the intensity (I) is proportional to the square of the amplitude (A):
I ∝ A^2
This relationship holds for classical waves, where light is treated as an electromagnetic wave. In this case, the intensity of light is related to the energy carried by the wave.
However, in the quantum theory of light, known as quantum electrodynamics (QED), light is considered to be composed of discrete packets of energy called photons. Each photon carries a specific amount of energy proportional to its frequency. The intensity of light can also be described in terms of the number of photons, which is directly related to the photon flux.
In the photon picture, the intensity of light is proportional to the number of photons per unit area per unit time. Mathematically, the intensity (I) is related to the number of photons (N) by:
I = N * E
where E is the energy carried by each individual photon. This equation shows that the intensity is directly proportional to the number of photons.
So, in classical physics, the intensity is proportional to the square of the amplitude, while in quantum physics, the intensity is related to the number of photons. Both descriptions are valid and can be used depending on the specific context and the level of detail required in the analysis.