A photo sensor located $10m$ away from a $200 W$ lamp emitting wavelength $600nm$ is exposed for a certain amount of time. How many photons enter the sensor per second if the sensor has an opening that is $20mm$ in diameter?

The energy of a photon of light is

$$\begin{gathered} E=\frac{hc}{\lambda }=\frac{\left(6.626\times {10}^{-34}\right)\left(3\times {10}^8\right)}{600\times {10}^{-9}} \\ =3.31\times {10}^{-19} \mathrm{J} \end{gathered}$$

The power of the source is $200W$; the number of photons emitted per second is therefore,

$n=\frac{200}{3.31\times {10}^{-19}}=6.04\times {10}^{20} \mathrm{photons}/\mathrm{s}$

The emitted photons move out in spherical symmetry.

Number of photons per unit area per second reaching the surface of a sphere of radius $R$, with source at its centre is $=\frac{\left(6.1\times {10}^{20}\right)}{4\mathrm{\pi }\left({10}^2\right)}$

The exposed area of sensor is $=\mathrm{\pi }{\left(0.010\right)}^2$

So the number of photons striking the sensor per second,

$N=\frac{\left(6.04\times {10}^{20}\right)\mathrm{\pi }{\left(0.010\right)}^2}{4\mathrm{\pi }\left({10}^2\right)}=1.51\times {10}^{14} \mathrm{photons}/\mathrm{s}$