Distance between photons travelling from a bulb to your eye

[Jenkz]

Homework Statement

On a dark night, most people can see a 100W light bulb from at least 1 km away.
Given that a 100W light bulb emits about 5W of visible light, and assuming that
the wavelength is 500 nm, calculate the number of photons per second entering each
eye (pupil diameter 0.7 cm) of an observer 1 km from the bulb.

What is the average distance between photons en route from the bulb to the eye?

The Attempt at a Solution

Energy of a photon= hc/lambda = 3.98 x 10 ^-19 J
Number of photons from 5w = 1.25x 10 ^19 per second.
area of eye = 3.85 x 10 ^-5 m^2
area of virtual sphere from bulb = 1.26 x 10 ^7m^2

Ratio of area of eye and virtual sphere = 3.06 x 10 ^-12
Total number of photons entering one eye = 3.85 x10^7 per second.

Now I'm not too sure what to do to get the average distance. Please help?

 

[kuruman]

I have not checked your numbers - I assume they are correct for the time being. Can you figure out how many photons are in the beam from the source to the eye at any given time? Hint: How many seconds does a photon take to travel from the source to the eye?

 

[Jenkz]

Speed of a photon 3x 10 ^8 ms^-1 , distance of 1000m

So time it takes to travel is 3.33x10^-6 s

In one second there are 3.85 x10^7 photons, so in total there are 128 photons in 3.33x10^-6 s along the beam?

If its 1000m long then 1000/128 = 7.81m between each photon.

That sounds weong to me..

 

[kuruman]

Speed of a photon 3x 10 ^8 ms^-1 , distance of 1000m

So time it takes to travel is 3.33x10^-6 s

In one second there are 3.85 x10^7 photons, so in total there are 128 photons in 3.33x10^-6 s along the beam?

If its 1000m long then 1000/128 = 7.81m between each photon.

That sounds weong to me..

Why? It's the correct method and, if the numbers that go in it are correct, the answer is correct. So recheck your numbers.

 

[Jenkz]

It just sounds rather large to me, but taking into account how long the distance is, it seems ok.

Thank you for the hints.