Light Intensity Model: Showing Minimal Difference at Off Point

In summary, the conversation discusses a question about modeling the intensity of light at a point on a desk with a light bulb above it, and whether turning off one light will make a significant difference in the overall intensity. It is determined that the inverse square law applies and the result will depend on the distance between the lights and the desk. A link is provided for further explanation and math formulas are used to explain the concept.
  • #1
S.1.B
3
0
Can someone assist with a simple model for the following question? I have looked on the net but cannot find anything on it.

Say you are sat at a desk with the light bulb directly above you switched off and the rest on; so:

on - on - on
on - off - on
on - on - on

Each at distance r apart with the light intensity at each point the same (say I)

I wish to model the intensity of light at the off point and show that just switching the bulb at this point will have very little difference to the intensity of light here point regardless if the bulb at that piont was switched on or off.

I wish to double check my working to see if I am on the right track. Many thanks,
 
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  • #2
It depends on how far the desk is from the array of lights. If far away (compared to r) turning off 1 light reduces the illumination by 1/9. If close to array it will be more. Essentially you need to use the inverse square law.
 
  • #3
mathman said:
It depends on how far the desk is from the array of lights. If far away (compared to r) turning off 1 light reduces the illumination by 1/9. If close to array it will be more. Essentially you need to use the inverse square law.

Thank you for your reply. How did you come to this result? I am very rusty on my Physics at the moment.

Lets say the distance between the each light is fixed and at r distance apart. The height distance is h; if I have understood your reply and I failed to consider that aspect. I do not think that would be a major issue though.

Can you refer me to a link or a book that explains the above scenario. I cannot find one at present that explains what I am trying to solve,

 
  • #4
S.1.B said:
Can someone assist with a simple model for the following question? I have looked on the net but cannot find anything on it.

Say you are sat at a desk with the light bulb directly above you switched off and the rest on; so:

on - on - on
on - off - on
on - on - on

Each at distance r apart with the light intensity at each point the same (say I)

I wish to model the intensity of light at the off point and show that just switching the bulb at this point will have very little difference to the intensity of light here point regardless if the bulb at that piont was switched on or off.

I wish to double check my working to see if I am on the right track.Many thanks,

S.1.B said:
Thank you for your reply. How did you come to this result? I am very rusty on my Physics at the moment.

Lets say the distance between the each light is fixed and at r distance apart. The height distance is h; if I have understood your reply and I failed to consider that aspect. I do not think that would be a major issue though.

Can you refer me to a link or a book that explains the above scenario. I cannot find one at present that explains what I am trying to solve,

Just search on "Inverse Square Law" for light. mathman's point is that if the ceiling with the lights is 10cm over your head, switching on the middle bulb 10cm over your head will increase the light for you quite a bit. If the ceiling is several meters away, you will see a smaller increase in intensity.
 
  • #5
Intensity of each light source is proportional to [itex]\frac{1}{d^2}[/itex]. Total illumination is sum over all sources. Overhead [itex]d^2=h^2[/itex], four nearest to overhead - each [itex]d^2=h^2+r^2[/itex], four corners - each [itex]d^2=h^2+2r^2[/itex].
 
  • #6
Thanks both for your help.
 

1. What is a light intensity model?

A light intensity model is a mathematical representation of the relationship between the intensity of light and its distance from a source. It helps us understand how light behaves and changes as it travels through different mediums.

2. How does the light intensity model work?

The light intensity model uses the inverse square law to describe the relationship between light intensity and distance. This law states that the intensity of light is inversely proportional to the square of the distance from the source. In other words, as the distance from the source increases, the light intensity decreases exponentially.

3. What is the purpose of showing minimal difference at off point in the light intensity model?

The off point in a light intensity model refers to the distance at which the light source is no longer detectable. Showing minimal difference at this point is important because it allows us to determine the maximum distance at which the light source can still be detected. This information is useful in various applications, such as designing lighting systems or understanding the visibility of objects in space.

4. How is the light intensity model used in real-life situations?

The light intensity model is used in many different fields, including astronomy, photography, and lighting design. For example, in astronomy, the model helps us understand the brightness of stars and their distances from Earth. In photography, it can be used to adjust camera settings for the best exposure. In lighting design, the model can be used to determine the placement and intensity of light sources for optimal illumination in a space.

5. Are there any limitations to the light intensity model?

While the light intensity model is a useful tool, it does have some limitations. It assumes that light travels in a straight line and does not take into account factors such as atmospheric conditions or the reflective properties of surfaces. Additionally, the model may not accurately represent the behavior of light in certain situations, such as when the light source is not a single point or when the medium through which the light travels is not uniform.

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