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