Determine the minimum number of photons that must enter the eye's pupil each second in order for an object to be seen. Assume that the pupil's radius is 0.20 cm and the wavelength of the light is 550 nm . To see an object with the unaided eye, the light intensity coming to the eye must be about 5×10−12J/m2⋅s or greater. Calculate Nmin... I keep getting 1.38 e25 which is not right and I can figure out what I am doing wrong.

Explanation:

Energy of a photon = hν , h is plank's constant and ν is frequency .

=    h c / λ     ; c is velocity of light and  λ is wavelength .

= 6.6 x 10⁻³⁴ x 3 x 10⁸ / 550 x 10⁻⁹

= .036 x 10⁻¹⁷ J  

Let no of photons be n .

Total energy of n photons

= n x  .036 x 10⁻¹⁷ J  

Intensity of light = 5 x 10⁻¹² J /m²

Total energy flowing through eye per second

= intensity x area of eye.

=   5 x 10⁻¹² x π x .2² x 10⁻⁴

= .628 x 10⁻¹⁶ J

so

n x  .036 x 10⁻¹⁷  =  .628 x 10⁻¹⁶

n = .628 x 10⁻¹⁶ /  .036 x 10⁻¹⁷

= 17.36 x 10

= 173.6

174.

double the distance = divide strength by 4