# How does the amplitude on a EM wave graph correspond to the number of photons?

## Main Question or Discussion Point

Hello all! I am trying to understand ER on a more intuitive level. I can see the relationship between energy and frequency. The relationship between amplitude and photon number is less clear. So far I have E = hf. I understand that the intensity of light is a function of the number of photons. Can this be correlated to amplitude? If so, then how? Thank you.

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Drakkith
Staff Emeritus
What amplitude are you referring to?

Physics Monkey
Homework Helper
curiousatlarg,

I assume by amplitude you mean the magnitude of the electric field, let's call it E. In fact, E is related to the average number of photons via $N \sim E^2$. Please note also the very important word average. A macroscopic electric field does not correspond to an exact number of photons but instead to something called a coherent state of photons (we can discuss this later if you want).

My claim above can be understood as follows. Let's think about a EM wave of fixed frequency. If you accept that the energy of one photon is $h f$ then the energy of N photons is $N h f$ and the rate of energy flow, which is proportional to the intensity, is $I \sim c N h f$ ($c$ is the speed of light i.e. how fast the photons are going). Now you also know that the intensity is given by $I \sim E^2$ in a classical EM wave, so by equating these two forms you find that $E^2 \sim N$ up to lots of factors that you can work out or look up somewhere.

Hope this helps.

Thanks. I was referring to both the electric and the magnetic fields. What you gave me so far is what I was looking for. I will work with it some.