A From how far away is radiated energy of photons effective?

[windowofhope]

I'm faced with a problem here and would really appreciate anyone's help. The question is paraphrased as follows:
The eye can respond to single photons but there are certain requirements from the eye: it must receive at least 100 photons/s to process it. Assume the eye to have an area of 4E-6 m^2, from how far away can the eye pick up the radiated energy of a 400 nm wavelength photon from a 200W light bulb?

So I know that the photon flux is equal to the poynting vector (in W/m^2) divided by the energy of each photon i.e |S|/hf=S*Area*lambda/(hc).. I do (200W/m^2)*(4E-6 m^2)*(400E-9m)/(6.63E-34Js)(3E8m/s) = 1.6E15 photons/s which is clearly greater than the required 100 photons/s required for the eye to register the light. However, the formula doesn't say anything about distance away from the source.. All I know is that the surface of the eye picks up 1.6E15 photons/s but have no information as to what distance that is from and how much mroe distance until it gets reduced down to 100 photons/s. Any help would be really awesome!

thank you

 

[jfizzix]

So, you know the total number of photons radiated per second, and you know that they are radiated outwards equally in all directions.

What the question is asking is how far away do you have to be so that the number of photons hitting your eye is a small enough fraction compared to the total number of photons in all directions so that you'll barely register seeing anything from that source.