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 8.2 mm and the light has a wavelength of 595 nm?

Answer 1

As we know that;

If N = min number for photons of wavelength 595 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 = 595 nm = 5.95x10^-7m

So,

Area of Pupil = pi * r^2

= pi * (d/2)^2 = pi/4 * d^2

= pi/4 * (8.2 * 10^-3m)^2

Then,

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

= N = 5.0 * 10^-13 * (pi/4 * (8.2 * 10^-3)^2 ) / (6.626 * 10^-34 * 3 * 10^8 / (5.95 * 10^-7))

= N = 79.03 photons/s

The number of photons per seccond are 79.03 photons/s.