Question

Consult Interactive LearningWare 29.1 for background material relating to this problem. 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 564 nm?

Answer 1

Given:

light intensity, I_min = 5.0 x 10^-13 W/m²

pupil has a diameter, d = 8.1 mm = 8.1x10^-3 m

thus, radius of the owl eye, r = 4.05x10^-3 m

thus, area of the eye = A = ?r² = (3.14)(4.05x10^-3)² = 51.53x10^-6 m²

thus,

P_min = I_min A = (5.0 x 10^-13 W/m²)(51.53x10^-6m² )

        = 257.65x10^-19 W

thus, minimum number of photons is given by the formula

N_min = P_min / E

where , E = (hc/?) = (6.63x10^-34)(3x10⁸)/(564x10^-9)

                = 3.53x10^-19 J

thus,

N_min= 257.65x10^-19 / 3.53x10^-19 ~ 72.99 photons per sec