Photon Intensity & Distance Calculation

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To determine how far from a 100 W light source emitting 600 nm wavelength light the photons can be detected, one must calculate the energy per photon using E = hc/λ. The challenge lies in relating the power output to the intensity at a distance, which can be conceptualized by imagining a sphere of radius r around the source. The energy per square meter at the surface of this sphere can then be calculated to find the photon density. By understanding how the intensity dissipates with distance, the distance at which 20 photons per second can enter a 7 mm diameter pupil can be determined.
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Homework Statement


Supopse that a 100 W source radiates light of wavelength 600 nm in all directions and that the eye can detect this light if only 20 photons per second enter a dark adapted eye having a 7 mm diameter pupil. How far from the source can the light be detected under these conditions?


Homework Equations


E = hf = hc/\lambda

The Attempt at a Solution



I am having a hard time finding a relationship between the 100 W source and a distance. At what rate do the photons die off?

I can calculate the energy per photon: E = hc\ 600nm but with that information, I still don't see a way factor distance in there.

Anyone have some hints?

how I can figure out at what rate it will dissipate over a distance.
 
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jesuslovesu said:
I can calculate the energy per photon: E = hc\ 600nm but with that information, I still don't see a way factor distance in there.

Hi jesuslovesu! :smile:

Hint: imagine a sphere of radius r round the source.

How much energy falls each square metre of its surface? :smile:
 

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