From how far away is radiated energy of photons effective?

In summary, the question is how far away can the eye detect the radiated energy of a 400 nm wavelength photon from a 200W light bulb, considering the eye's requirement of receiving at least 100 photons/s to process the light. Based on the given formula and information, it is determined that the eye can pick up 1.6E15 photons/s at the surface, but the distance at which this number reduces to 100 photons/s is unknown. Therefore, further help is needed to determine the distance at which the eye can barely register seeing anything from the light source.
  • #1
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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
 
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  • #2
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.
 

1. How does distance affect the effectiveness of radiated energy of photons?

The effectiveness of radiated energy of photons is inversely proportional to distance. This means that the further away the source of radiation is, the less effective it will be. This is because as the photons travel, they spread out and become more diluted, resulting in a lower intensity of radiation at further distances.

2. Does the type of radiation affect the distance at which it is effective?

Yes, different types of radiation have varying distances at which they are effective. For example, gamma rays have a much shorter effective distance compared to radio waves. This is due to their different energy levels and wavelengths, which determine how far they can travel and how easily they can penetrate materials.

3. What factors can impact the effectiveness of radiated energy of photons at a certain distance?

The effectiveness of radiated energy of photons at a certain distance can be impacted by several factors, including the type and energy of the radiation, the medium through which it is traveling, and any obstructions or barriers in its path. These factors can all affect how much energy is able to reach a certain distance.

4. Is there a maximum distance at which radiated energy of photons can still be effective?

There is no definitive maximum distance at which radiated energy of photons can still be effective. However, as the distance increases, the intensity of the radiation decreases significantly, making it less effective. At a certain point, the intensity may become too low to have any noticeable effects on objects or materials.

5. How does the concept of the "inverse square law" relate to the effectiveness of radiated energy of photons?

The inverse square law states that the intensity of radiation is inversely proportional to the square of the distance from the source. This means that as the distance increases, the intensity decreases exponentially. Therefore, the concept of the inverse square law directly relates to the effectiveness of radiated energy of photons, as it explains why the effectiveness decreases as the distance increases.

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