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How many photons are emitted by a light source? To answer this question we need to evaluate the following simple formula at every wavelength in the spectral range of interest and add the values up:

(1) $\begin{equation*} \frac{\text{Power of Light in }W/m^2}{\text{Energy of Average Photon in }J/photon} \end{equation*}$

The Power of Light emitted in $W/m^2$ is called Spectral Exitance, with the symbol $M_e(\lambda)$ when referred to units of energy. The energy of one photon at a given wavelength is

(2) $\begin{equation*} e_{ph}(\lambda) = \frac{hc}{\lambda}\text{ joules/photon} \end{equation*}$

with $\lambda$ the wavelength of light in meters and $h$ and $c$ Planck’s constant and the speed of light in the chosen medium respectively. Since Watts are joules per second the units of (1) are therefore $photons/m^2/s$ . Writing it more formally:

(3) $\begin{equation*} M_{ph} = \int\limits_{\lambda_1}^{\lambda_2} \frac{M_e(\lambda)\cdot \lambda \cdot d\lambda}{hc} \text{ $\frac{photons}{m^2\cdot s}$} \end{equation*}$

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