Why when you move twice as far away from a light source is its luminosity decreased by a factor of 4
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Why when you move twice as far away from a light source is its luminosity decreased by a factor of 4

[From: ] [author: ] [Date: 12-08-05] [Hit: ]
I think gravity follows this same principle, as well as all other types of energy.-Its the inverse square law.It applies to radiation as it does to gravity, or anything that radiates in 3 dimensions.In 2 dimensions it would be proportional: twice as far would be twice as weak,......
And 3 times as far away by 9, and 4 times as far away by 16? I forgot what the specific name for this.

But, why does the luminosity of light in comparison to the distance you are away from it follow as an inverse square relationship? I think gravity follows this same principle, as well as all other types of energy.

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It's the inverse square law. It applies to radiation as it does to gravity, or anything that radiates in 3 dimensions. In 2 dimensions it would be proportional: twice as far would be twice as weak, etc. But in 3 dimensions, twice as far is four times as weak. It's easiest to picture it as, well, a picture:
http://c304977.r77.cf1.rackcdn.com/backe…

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Because at twice the distance the same amount of energy, in this case electromagnetic radiation, is spread out over a sphere of twice the diameter, which means it has four times the surface area. A gramme of dust on the surface of a balloon 20 cm in diameter occupying one square centimetre will occupy four square centimetres if the balloon is inflated to 40 cm diameter, so a square centimetre of that dust would then only have a mass of a quarter of a gramme.

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This is not because of some special property of light or even of energy. It is the math of geometry, and the formula works for anything dependent on a central point. It works for gravity, the heat and light from the Sun or a light bulb and it works for sound (if the sound is being sent out in all directions.)
If you had a machine that shot golf balls (in space, to avoid falling to the ground) in random directions; the balls would hit a nearby object a certain number of times per hour (on average). If you moved the object twice as far away (x2), the number of hits per hour would decrease to 1/4 (inverse of 2x2).

It is called the inverse square law.

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As Lodar said its because its three dimensions.

Consider, if we only had one dimension the intensity would be constant regardless of distance. Because the light could only go in a straight line (there are no other directions).

With two dimensions (which means when looking at the light it is coming towards you, but spreading out left/right as well) intensity would be divided by distance.

But with three dimensions it is coming towards you but spreading out left/right(first division) AND up/down(second division) so its divided twice. Intensity divided by distance and then divided by distance again.

We simplify that by dividing by distance²

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the why question is a very hard question to answer, watch how richard feynman explains why the "why" question is sometimes not possible to answer.

http://www.youtube.com/watch?v=36GT2zI8l…
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