In this lecture from MIT, the professor defines the intensity of a wave as the square of the amplitude of the wave. But, at the same time, the professor defines the intensity of light as the number of photons per second. Are these definitions equivalent?
I know that light has both properties of a particle and properties of a wave, but the two different definitions of intensity have different units, which seems confusing to me.
Additionally, when I searched up intensity on Wikipedia, I was unable to find a definition of intensity that matched the definition provided in the lecture. Some of the definitions of intensity that I did find on Wikipedia were "power per unit area," "power per unit solid angle," and "luminous flux per unit solid angle."
Thus, my question is: what do the terms "intensity," "intensity of light," and "intensity of a wave," mean? What are their definitions?