7.0 Photon Density

It is defined as the number of photons per unit volume. Consider a Uniform cylindrical light beam of cross-sectional area $S$ and power $P$.

Total volume covered in $1s$ by these photons= $S(c \times 1) = Sc$

$$\begin{equation} \begin{aligned} {\text{The total number of photons crossing cross - sectional area }}S,\quad N = \frac{{I\lambda }}{{hc}} \times S \\ \\\end{aligned} \end{equation} $$

Thus, photon density,

$${\rho _{ph}} = \frac{N}{{Sc}} = \frac{{I\lambda }}{{h{c^2}}} = \frac{\phi }{c}$$

$${\rho _{ph}} = \frac{\phi }{c}$$