# Amplitude - photon correspondence

## Main Question or Discussion Point

Hello,

I've got a number of questions about physics. None of my physics friends have given me clearly defined answers, so I thought maybe asking here.
For now, I'll just ask one simple question.

So, if I have a laser pointer, which has a weak battery, it will shine with less number of photons than if I had a strong battery. Correct? The only difference, with a strong battery, would be more photons. Correct?
If you look at the laser pointer's electromagnetic light wave the change you would see, with the stronger battery, is that the amplitude of the wave increased.

If this is the case, then there is a correspondence between the number of photons, and the amplitude of the light wave.
Meaning that each photo corresponds to a specific amount of amplitude.
Do you know what this specific amount of amplitude per photon?

Thank you,
Veniamin

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Drakkith
Staff Emeritus
Sure, we can calculate it. For example, you can measure the induced voltage in a radio antenna, and knowing the frequency, and thus the energy of each photon you can calculate the approximate number of photons per unit of time. At least I think we can lol.

For example, you can measure the induced voltage in a radio antenna, and knowing the frequency, and thus the energy of each photon you can calculate the approximate number of photons per unit of time.
As an experiment, sure you can measure the induced voltage in a radio antenna, but some of that power will be lost in heat.

I gather however that this has already been done. I assume there is some kind of formula for this, given a frequency. No?

If this is the case, then there is a correspondence between the number of photons, and the amplitude of the light wave.
Meaning that each photo corresponds to a specific amount of amplitude.
Do you know what this specific amount of amplitude per photon?
You'll have to calculate it, but it should be fairly easy to do it in the following way, as long as you have the necessary information:

Assuming you know the electromagnetic field amplitude and frequency corresponding to the light from your laser pointer, you can calculate the energy per unit of time that passes through a unit area perpendicular to the direction of the laser.

At the same time, you obviously also know the frequency of the laser, so you can calculate the energy of a single photon by using the simple formula E=hf, vhere h is Planck's constant and f is frequency.

By comparing the two values, you can determine how many photons pass the unit area per second on average to make up your laser light.

Then you can divide the amplitude of the laser light EM field by the number of photons to get the amount of amplitude contributed per photon. I.e. you'll get something like "N photons per second in a certain cross-sectional area corresponds to an EM amplitude of X". Therefore "1 photon per second passing the same cross-sectional area would contribute X/N to the measured amplitude".

sophiecentaur