In one experiment, 6000 photons are detected in a 0.10-mm-...

In one experiment, 6000 photons are detected in a $0.10-\mathrm{mm}-$ wide strip where the amplitude of the electromagnetic wave is 200 V/m. What is the wave amplitude at a nearby 0.20-mm-wide strip where 3000 photons are detected?

Key Concepts

Electromagnetic Wave Intensity

This concept explains that the intensity of an electromagnetic wave is proportional to the square of its amplitude. In other words, if the amplitude of the wave is altered, the intensity changes by the square of that factor. This relation (I ? E²) is fundamental in understanding the energy distribution in any region of the wave.

Photon Energy and Intensity Connection

Photons are quantum packets of energy, and the total energy carried by an electromagnetic wave is proportional to the number of photons it contains multiplied by the energy per photon. If the energy per photon remains constant, then the number of photons is a useful measure of the energy or intensity of the wave, linking photon counts to the amplitude through the intensity relationship.

Area Dependence of Intensity

When measuring light over different spatial regions, the intensity is understood as the energy per unit area. If the same wave is spread over a larger area, the energy density (and thus the intensity) decreases accordingly. This concept is critical when comparing regions of different sizes, as the detected number of photons must be normalized by the area to correctly understand changes in amplitude or intensity.

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