intensity, photons, human eye

Yroyathon

hi there. there's an example in the book, but i'm having a little trouble here.

1. The problem statement, all variables and given/known data
Assume that the human eye can pick up as few as 9 photons/s in the visible range. Based on this, estimate the intensity of the dimmest star that can be detected by a night-adapted eye. What is the ratio of this intensity to the intensity of noon sunlight, some 1400 W/m2? This large intensity range means that the eye is indeed a very adaptable instrument.
Answer format = (intensity of 9 photons/s / intensity of noon sun)

use 3mm for the radius of the pupil.
use 550 nm for wavelength.

2. Relevant equations
I=Power/Area
I=N*E, N is the number of photons/(m^2*s)
E=h*f
f=c/lambda
A=Pi*r^2

3. The attempt at a solution

So I want the intensity, which is N * E, which is (N * h * c) / (Pi * r^2 * lambda). I get the intensity of the dimmest star on the human eye as 1.14592 * 10^(-13).

With the given intensity of noon sunlight (do I need to adjust this for the area of the pupil?...), I divide it. 1.14592*10^(-13) / 1440 = 7.95775*10^(-17).

but this is wrong, so... either I was supposed to adjust the noon intensity, or I've made one or several other mistakes.

I'd appreciate any insights or tips.

Thanks!

,Yroyathon

grantjerry

your equation is correct
check ur calculations^_^

phyzguy

I got the same numbers. Why do you think it's wrong? What do you think the right answer is?

grantjerry

I got 1.150429803e-13 for the intensity of the star

divide it by 1400, the final answer should be 8.217e-17