How can wave energy and photon energy both be correct?

[UncertaintyAjay]

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

 

[blue_leaf77]

I've also learned that the energy of light is given by E= hv. I'm confused

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

 

[UncertaintyAjay]

And hence proportional to intensity? Thanks a bunch.

 

[blue_leaf77]

And hence proportional to intensity?

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.

 

[UncertaintyAjay]

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

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

 

[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.

 

[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?

 

[UncertaintyAjay]

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