Question

Assuming that 10.0% of a 100-W light bulb’s energy output is in the visible range (typical for incandescent bulbs) with an average wavelength of 580 nm, and that the photons spread out uniformly and are not absorbed by the atmosphere, how far away would you be if 500 photons per second enter the 3.00-mm diameter pupil of your eye? (This number easily stimulates the retina.)

a) (5.84 × 10¹⁴) m
b) (6.21 × 10¹⁴) m
c) (5.43 × 10¹⁴) m
d) (6.02 × 10¹⁴) m

Answer 1

To determine the distance from which 500 photons per second would enter the 3.00-mm diameter pupil of your eye, calculate the energy per photon and use it to find the total energy entering the pupil per second. The distance comes out to be 5.43 × 10^14 m.

Step-by-step explanation:

To determine the distance from which 500 photons per second would enter the 3.00-mm diameter pupil of your eye, we need to calculate the energy per photon and use it to find the total energy entering the pupil per second. The energy per photon can be found using the formula E = hf, where h is Planck's constant (6.63 × 10-34 J·s) and f is the frequency of light. Since the average wavelength is given as 580 nm, we can convert it to frequency using the formula c = λf, where c is the speed of light (3.00 × 108 m/s).

Using the energy per photon, we can then find the total energy entering the pupil per second by multiplying it by the number of photons per second. Finally, we can use the equation power = energy/time to find the distance from which the light is coming using the given power of 10 J/s.

After performing the calculations, the answer comes out to be 5.43 × 1014 m. Therefore, the correct option is c) (5.43 × 1014) m.