I’m pretty sure the answer is yes, but I’d like to know for sure. Can the Inverse Square Law for light be undone or avoided by the use of lenses, mirrors, fiber optics etc. Or is the law still at work despite these efforts?
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$\begingroup$ avoiding the law = the law is violated? $\endgroup$– ShingMar 28, 2018 at 21:22
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1$\begingroup$ A lens can stop the divergence of light. $\endgroup$– LambdaMar 28, 2018 at 21:32
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2$\begingroup$ When you refer to "the inverse square law", what exactly do you mean? $\endgroup$– David ZMar 28, 2018 at 21:34
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1$\begingroup$ That EM radiation spreads out as it leaves its source $\endgroup$– LambdaMar 28, 2018 at 22:46
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1$\begingroup$ "the Inverse Square Law for light" - perhaps you should state this law as you understand it? $\endgroup$– Alfred CentauriMar 28, 2018 at 23:10
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1 Answer
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The "inverse square law" is not a law, and the answer is not "yes" or "no". The actual law is the law of conservation of energy.
For any object radiating energy into space, that energy must be conserved. For energy such as light or sound, the geometry of the physical situation controls how that energy decreases as one moves away from the energy source. For a point source of energy, if there are no reflections involved, the energy moves away from the source in spherical wave fronts. All points that are equidistant from that energy source experience the same level of energy intensity, and all points that are equidistant from the energy source describe a sphere in space. Since the area of a sphere is $A=4\pi r^2$, a sphere that has twice the radius of a "standard" sphere (e.g., you are taking a measurement twice as far away as you did initially), has 4 times the area. For a constant power level (energy per second), the same amount of energy has to cover 4 times the area in this case, meaning that the energy intensity is 1/4 of what it was originally. Thus, the geometry of the situation causes the energy intensity to follow the $1/r^2$ relationship.
Likewise, for the case of a very long and straight energy source (think of an extremely long florescent light), all points that are the same distance from the energy source describe the walls of a cylinder with the energy source located at the center of the cylinder. The equation for the area of the walls of this cylinder is $A=2\pi rL$, where L is the length of the cylinder. This means that if I double the distance from the energy source, the area of the new cylinder is twice the area of the original cylinder, and the energy intensity for this geometry decreases as 1/r, meaning that if I move twice as far away from this energy source, the energy intensity is 1/2 of what it originally was.
Thus, the geometry of the physical situation controls how the energy is decreasing as I move away from the source.
answered Mar 29, 2018 at 2:01