# Are number of photons in an incident radiation proportional to its intensity?

Does number of photos emitted depends upon frequency of light source (or light color)?

I don't think so but one of the questions I attempted today suggests so. When the number of photons is proportional to the frequency of the radiation?

I think it should only depend on intensity of light. How can one relate the number of photons in an incident radiation to its intensity ?

Intensity is the total amount of energy falling on (or going through) a surface/region per unit area $$A$$ per unit time $$t$$ and therefore measured in $$\rm J/(m^2\,s)$$.

For monochromatic radiation, the total energy emitted equals the number of photons $$n$$ times the energy of one photon, $$h\nu$$.

Hence intensity $$I$$ is given by $$I=\frac{hn\nu}{At}$$

For constant area and time, $$I \propto n\cdot\nu$$

This is a very important result. You can increase the intensity of the radiation by either increasing the number of photons in it or increasing energy of each photon, or both.

The number of photons does not necessarily increase when the frequency of the radiation increases; only the energy of each photon increases.

However, for constant intensity, $$n \propto \frac{1}{\nu}$$

Light intensity is a classical measure , proportional to the square of the electric field in the electromagnetic wave equation.

Photons are elementary particles which carry $$E=h{\nu}$$ and build up in confluence the classical wave.

The number of photons comes from dividing the classical energy by the single photon energy. For the same classical beam energy, the higher the frequency the fewer the photons, from this simple algebra.