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 8.5 mm and the light has a wavelength of 548 nm?

Answer 1

Answer:

Thus, the minimum number of photons per second is 77.34

Explanation:

Light intensity, $I_{min}$ =  $5\times 10^{-13} W/m^{2}$

Pupil has a diameter, d = 8.5 mm

                                      = 8.5 x $10^{-3}$ m

Radius of the eye, r = 4.25 x $10^{-3}$ m

∴ Area of the eye, A = $\pi .r^{2}$

                                 = $3.14\times \left ( 4.25\times 10^{-3} \right )^{2}$

                                = $5.6\times 10^{-5} m^{2}$

Let $P_{min}$ be the minimum number of photons.

Therefore, $P_{min}$ = $I_{min}$ x A

                                              = $5\times 10^{-13}$ x $5.6\times 10^{-5}$

                                             = $2.8\times 10^{-17}$ W

Thus the minimum number of photons is given by

$N_{min}=P_{min}/E$

where E = $hc/\lambda$

             = $\left (6.63\times 10^{-34}\times 3\times 10^{8} \right )/548\times 10^{-9}$

            = $3.62\times 10^{-19} J$

Therefore, $N_{min}$ = $\frac{2.8\times 10^{-17}}{3.62\times 10^{-19}}$

                                              = 77.34 photons per second

Thus, the minimum number of photons per second is 77.34