1 \begin{problem*}{28.6} % photon energy
2 The average threshold of dark-adapted (scotopic) vision is
3 $4.00\E{-11}\U{W/m$^2$}$ at a central wavelength of $500\U{nm}$. If
4 light having this intensity and wavelength enters the eye and the
5 pupil is open to its maximum diameter of $8.50\U{mm}$, how many
6 photons per second enter the eye?
10 The total power into the eye is
12 P = IA = \pi r^2 I = \frac{\pi d^2 I}{4} = 2.27\U{fW} \;,
14 and the energy per photon is
16 E = hf = \frac{hc}{\lambda} = 2.48\U{eV} = 3.97\E{-19}\U{J} \;,
18 so the number of photons entering per second is
20 \Phi_p = \frac{P}{E} = \ans{5710} \;.