Question

An owl has good night vision because its eyes can detect a light intensity as small as 5.0 × 10-13 W/m2. What is the minimum number of photons per second that an owl eye can detect if its pupil has a diameter of 8.1 mm and the light has a wavelength of 528 nm?

Answer 1

Suppose, N = min number for photons of wavelength 528 nm, then

N * Ephoton = 5.0 x 10^-13 W/m^2 * Area_of_Pupil * 1 sec

Ephoton = h * c / w
where h =Planck Constant, c = speed of light, w=wavelength of light = 528 nm = 528x10^-9 m

Area_of_Pupil = pi * r^2 = pi * (d/2)^2 = pi/4 * d^2 = pi/4 * (8.1x10^-3m)^2

N = 5.0 x 10^-13 W/m^2 * Area_of_Pupil * 1 sec / Ephoton

N = 5.0 x 10^-13 W/m^2 * (pi/4 * (8.1x10^-3m)^2 ) / (h * c / 528x10^-9 m)

= 5.0 x 10^-13 W/m^2 * (pi/4 * (8.1x10^-3m)^2 ) / (6.63x10^-34 * 3.0x10^8) / 528x10^-9 m)
= (257.52x10^-7) / (0.0377x10^-17)

= 6830.77 x 10^10 = 6.83 x 10^13 photons/sec.