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?
Best Answer
For a collimated light beam, the most relevant intensity measure is the irradiance, i.e. how much energy passes through a unit cross-sectional area in unit time (i.e. power per unit area), and for a plane wave with electric-field amplitude $E_0$, the irradiance is given by $$ I = \frac{\epsilon_0c}{2}E_0^2. $$ The (average) number of photons that pass through that area per unit time, $R=dN/(dt\:dA)$, is then obtained from the irradiance via $$ R = \frac{I}{h\nu}, $$ i.e. by dividing the energy flux by the energy of each photon as given by the Planck relation $E=h\nu$ from the light's frequency $\nu$.
As the Wikipedia page for irradiance explains in detail, there exists a huge range of radiometric measures of light intensity, depending on whether you care about the angle of emission or the spectral distribution over different frequencies or wavelengths, and so on. From these, the irradiance is the most natural measure, and (once you put in the suitable constants) all three versions of it are equivalent.