At What Distance Does the Sun Become Invisible to the Human Eye?

[UMich1344]

[SOLVED] Sensing Light at Great Distances

Homework Statement

In perfect darkness, human eyes might be able to sense a point source of light if roughly 10 photons/second strike the retinas. The sun, which is currently 1.5 x 10^11 meters from earth, emits about 10^45 photons/second. Assuming that the pupils of a pair of eyes have a combined area of 1.0 square centimeters, at what distance would the sun become invisible to the unaided human eyes?

Homework Equations

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The Attempt at a Solution

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I've been given this problem in my physics class and have absolutely no clue as to what step needs to be taken first. There are more parts to this question, but figuring out the distance is the first thing that needs to be done. Can anybody offer me any hints as to what I can do to solve this problem?

 

[Avodyne]

Imagine a big sphere of radius R around the sun. How many photons are passing through it each second? (Hint: no calculation need be done here, and the answer does not depend on R.)

OK, now, how many are passing through each square centimeter on the surface of this sphere? (This DOES depend on R.)