Energy of light

1. Sep 9, 2015

UncertaintyAjay

So, I've learnt in school that the energy of a wave is proportional to the square of its amplitude. I've also learnt that the energy of light is given by E= hv. I'm confused. Could someone clarify?

2. Sep 9, 2015

blue_leaf77

More precisely, energy of a photon with frequency $\nu$. For classical lightwave, the energy is the sum of all these quanta present in there.

3. Sep 9, 2015

UncertaintyAjay

And hence proportional to intensity? Thanks a bunch.

4. Sep 9, 2015

blue_leaf77

What is proportional to the intensity? The energy?, Electromagnetic wave's energy is in general not proportional to its intensity, instead it's the integral of intensity over space and time.

5. Sep 9, 2015

UncertaintyAjay

I'm having a bit of trouble visualising exactly what you mean by over space and time. Could you give me an example?

6. Sep 9, 2015

blue_leaf77

$$E = \int \int |\mathbf{E}(\mathbf{r}_\perp,t)|^2 d\mathbf{r}_\perp dt$$.
where $\mathbf{r}_\perp$ are coordinates in the transverse plane. This is the energy passing through a transverse plane on which the vector $\mathbf{r}_\perp$ lies during certain time interval specified by the limits of the intgral over time.

7. Sep 9, 2015

UncertaintyAjay

E(r,t) is some function of the two right? If you're taking the mod sqaured of it, is it the amplitude as a function of space and time? And would it be too much to ask for a derivation?

8. Sep 9, 2015

UncertaintyAjay

Thanks btw,this is shaping up to be a fun topic