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 8.4 mm and the light has a wavelength of 594 nm?

Answer 1

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

pupil has a diameter = d = 8.4 mm = 8.4x10^-3m

thus, radious of the owl eye = r = 4.2x10^-3m

thus, area of the eye = A = ?r² = (3.14)(4.2x10^-3)²

A = 55.3896 x10^-6m²

thus,

P_min = I_min A =(5.0 x 10^-13 W/m²)(55.3896 x10^-6m² )

        = 276.948 x10^-19 W

thus, Minimu No . of photons is given by the formula

N_min = P_min / E

where , E = (hc/?) = (6.63x10^-34)(3x10⁸)/(594x10^-9)

                = 0.033x10^-17   J

thus,

N_min= 276.948 x10^-19 /  0.033x10^-17  

          ˜ 83.9 photons pre sec