# Light intensity and index of refraction

Nikitin
Hi. Will the amplitude of Poynting's vector change if the electromagnetic wave goes from one medium to another?
Shouldn't the amplitude remain constant due to conservation of energy? I.e. the photon-density and velocity will change, but their total intensity remains the same.

I could always do the calculations from maxwell's equations, but it seems like too much bother right now if one of you guys already know this (I'm tired).

Thanks

Mentor
Shouldn't the amplitude remain constant due to conservation of energy?
Why? If the wave propagation gets slower, the energy density goes up (because the flow stays constant if we can neglect losses).

Nikitin
But if the wave propagation gets slower, less photons are going thru the surface in question.

Btw, im talking about linear mediums only!

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Mentor
less photons are going thru the surface in question.
No. Why do you think that?
Btw, im talking about linear mediums only!
Yes I expected that.

Nikitin
No. Why do you think that?
Yes I expected that.

If the velocity of the photons is less, then fewer photons, per second, are passing thru the surface. So you could say that the photon flow gets "denser" if the light enters a medium with higher index of refraction than whence it came.

Sorry, I neglected to add the per second bit

Mentor
If the velocity of the photons is less, then fewer photons, per second, are passing thru the surface.
No. All photons that go in will go out (this is exactly the "no absorption" assumption). If their speed gets lower, their density increases, but flow (here: photons per second) stays constant.

Nikitin
No. All photons that go in will go out (this is exactly the "no absorption" assumption). If their speed gets lower, their density increases, but flow (here: photons per second) stays constant.
Yes this is basically what I was saying with "doesn't the amplitude of Poynting's vector stay constant?".

So the intensity remains unchanged, right?

Nikitin
No. All photons that go in will go out (this is exactly the "no absorption" assumption). If their speed gets lower, their density increases, but flow (here: photons per second) stays constant.

Didn't you imply that the intensity does not remain constant for the light beam, in the beginning?

Mentor
Power per area stays constant. I don't know how the Poynting vector is defined in a medium.