Question

The human eye can barely detect a star whose intensity at the earth's surface is 1.6 * 10-11 w/m2. If the dark-adapted eye has a pupil diameter of 7.0 mm, how many photons per second enter the eye from the star? Assume the starlight has a wavelength of 550 nm.

Answer 1

To find the number of photons entering the eye from the star, calculate the area of the pupil, the energy per photon, and use these to determine the power entering the eye. Then divide the power by the energy per photon to get approximately 1.71*10^3 photons per second.

Step-by-step explanation:

To determine how many photons per second enter the eye from a star, we can follow this procedure:

Calculate the area of the pupil's opening where the starlight enters. A = (πd^2)/4, where d is the pupil diameter in meters.

Calculate the energy per photon using the formula E = hc/λ, where h is Planck's constant, c is the speed of light, and λ is the wavelength of the light.

Use the given intensity of the star (I) and the pupil area (A) to find the power entering the eye: P = I * A.

Finally, divide the power entering the eye by the energy per photon to get the number of photons per second.

First, the area of a 7.0 mm diameter pupil is A = (π*(7.0*10^-3)^2)/4 = 3.85*10^-5 m^2. The energy per photon for the light with a wavelength of 550 nm is E = (6.626*10^-34 Js * 3*10^8 m/s) / (550*10^-9 m) = 3.61*10^-19 J. With the given intensity (I = 1.6*10^-11 W/m^2), the power entering the pupil is P = I * A = 1.6*10^-11 W/m^2 * 3.85*10^-5 m^2 = 6.16*10^-16 W. Therefore, the number of photons entering the eye per second is P/E = 6.16*10^-16 W / 3.61*10^-19 J = 1.71*10^3 photons/second.