Distance between photons travelling from a bulb to your eye

In summary, a 100 watt light bulb emits about 5 watts of visible light. This light travels at a speed of 3.33x10^-6 seconds, and it takes 7.81 seconds for one photon to travel the 1000 meter distance.
  • #1
Jenkz
59
0

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?
 
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  • #2
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?
 
  • #3
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..
 
  • #4
Jenkz said:
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.
 
  • #5
It just sounds rather large to me, but taking into account how long the distance is, it seems ok.

Thank you for the hints.
 

Related to Distance between photons travelling from a bulb to your eye

1. What is the distance between photons travelling from a bulb to my eye?

The distance between photons travelling from a bulb to your eye can vary depending on the specific lighting conditions and the distance between the bulb and your eye. On average, photons can travel up to 186,282 miles per second, so the distance between the bulb and your eye can be calculated by multiplying the time it takes for the photons to reach your eye by the speed of light.

2. How long does it take for photons to travel from a bulb to my eye?

The time it takes for photons to travel from a bulb to your eye is incredibly fast, as they move at the speed of light. On average, photons can travel from a bulb to your eye in just a fraction of a second, depending on the distance between the two. For example, if the bulb is 1 meter away from your eye, it would take approximately 0.0000033 seconds for the photons to reach your eye.

3. Does the distance between a bulb and my eye affect the brightness of the light?

Yes, the distance between a bulb and your eye can affect the brightness of the light. This is because the further away you are from the bulb, the less intense the light will appear. This is due to the fact that the photons spread out as they travel, making the light beam wider and therefore less intense the further it travels.

4. How do photons travel from a bulb to my eye?

Photons travel from a bulb to your eye in a straight line until they are absorbed or reflected by objects in their path. When photons are emitted from a light source, they travel through space as electromagnetic waves until they reach your eye. Once they enter your eye, they are then converted into electrical signals that are interpreted by your brain as light.

5. Can the distance between a bulb and my eye affect my vision?

No, the distance between a bulb and your eye does not have a direct impact on your vision. However, if the light is too bright or too dim, it can cause strain on your eyes and potentially affect your vision in the short term. It is important to ensure that the lighting conditions are optimal for your eyes to reduce any strain or discomfort.

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