Talk:Inverse-square law

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Point sources?[edit]

Inverse-square laws are about point sources, and yet it sounds like point sources can't actually exist. (Doesn't the Planck length, among other things, imply that things must have a certain minimum size?) In light of this apparent paradox, can someone explain why inverse-square laws are to any extent successful? Perhaps there are empirically-derived bounds along the lines of "if two masses both have volumes less than Vsmall, then Newton's gravitation law will give results that shall not deviate by more than 1x10^(-8) newtons from the true value"? --Ryguasu 17:31 Feb 6, 2003 (UTC)

Partly it's something along those lines. Notice that one of Newton's laws says that if no force acts on an object it continues at the same velocity, but one may object that there has never been an object on which no force acted, and the objection is somewhat parallel to what you're saying. Newton demonstrated mathematically that if the earth has uniform density then its gravitational field outside of the sphere in which its mass exists, is the same as if all the mass were concentrated at the center. So that's another reason. Michael Hardy 00:23 Feb 7, 2003 (UTC)

For example, Sol "provides" 9140W at the distance of Mercury (0.387AU); but only 1370W at the distance of Earth (1AU)

It would be useful if the formula to get the above values (9140 and 1370) were given too.

It does not make sense to use watts as the unit here. Perhaps watts-per-square-meter or something like that was intended instead? If so, it needs to say so. Michael Hardy 22:58, 12 Jan 2004 (UTC)

Looking at the Principia Mathematica first edition -- it may BE Robert Hooke who advance the Inverse-Square in relation to gravity first... - Sparky 06:01, 18 January 2004
Do you mean Philosophiae Naturalis Principia Mathematica? QuentinUK (talk) 23:01, 6 January 2012 (UTC)

The diagram[edit]

I just looked at the diagram I drew again and I realised it doesn't look terribly good. I am going to redraw it. Does anybody have some suggestions as to how I can make it better? -- Borb 00:39, 31 December 2005 (UTC)

Looks good to me. If you were specific about what you think needs improvement in it, maybe I could say more. Michael Hardy 02:44, 31 December 2005 (UTC)
It doesn't look very high quality, I was going to draw it again anyway, I just wondered if there was a different way I should draw it. A diagram could be either showing a quarter of the lines going through the same sized square, as in my diagram, or it could be showing the same number of lines going through a square 4 times the size of the original. Does anybody have a preference on which type I should draw? Also, technically the "squares" should be part of a sphere so I might try making them look like that. -- Borb 20:14, 2 January 2006 (UTC)
If you can access a copy of Edgar Allan Poe's Eureka, you will find a perfectly clear visual illustration of this law.Lestrade 15:21, 12 February 2006 (UTC)Lestrade
The diagram is wrong. Look at the red lines, one of them is actually going the wrong way, and end up in a completely new place in the 3r area. Irios 11:28, 3 March 2010


The first diagram I ever saw of the inverse square law was better, in my opinion. It showed ...

Nevermind, I found some similar ones: [1] [2]Omegatron 18:16, 19 February 2006 (UTC)

What about lasers?

- I agree on the diagram comment. Looking at the two linked images here the first did not work. The second is a great diagram. Displaying the four and then nine squares at each of the given distance values displays how the light is being spread out over greater distance.

p. 47 of Bill Bryson's A Short History of Nearly Everything explains that Halley (of Halley's Comet fame) was the one who went to Newton to ask him about a math problem concerning the inverse square law. Halley and Hooke were acquaintances and were involved in a bet to see who could solve the problem first. After Newton started publishing books with his findings, Hooke said he had already discovered the answer and accused Newton of plagiarism.

Light and other electromagnetic radiation[edit]

It would be appropriate to add the word "Interestingly" to the start of this section, I am perplexed attempting to explain connection Omeganumber (talk) 02:26, 1 March 2008 (UTC)


how do you cite it? —Preceding unsigned comment added by (talk) 18:34, 7 March 2008 (UTC)

New Diagram![edit]

Well I finally got around to drawing a new diagram of the inverse square law. Comments/Suggestions etc? It's not the easiest law to illustrate... -- Borb (talk) 14:05, 2 April 2008 (UTC)

Hi If you could show the first square as a more intense shade of yellow, and the third as a very pale shade of yellow, that might help to illustrate the fact that intensity has diminished by to one-quarter and then one-ninth. — Preceding unsigned comment added by (talk) 20:10, 7 August 2013 (UTC)

Acoustics section[edit]

This is intended as constructive criticism regarding the "acoustics" entries on the inverse square law page. I don't like to see popular misconceptions perpetuated. I guess if I knew how to present what I feel is the correct information on the page I would have edited it rather than posing a comment here, but I am an absolute novice when it comes to Wikipedia editing. But to get to the point…

The propagation of sound *does* obey the inverse square law in exactly the same way as electromagnetic radiation does. Sound *pressure* is not a valid equivalent to electromagnetic radiated power as a source – you are not comparing like with like. As the distance from the source increases, the acoustic *power* fall as the inverse square of the distance – double the distance means a quarter of the power, or 6·02dB; this equates to (and is the cause of) a halving of sound *pressure*, since pressure is proportional to the square root of power times radiation resistance, the latter being constant.

If my knowledge of acoustics is faulty, then please disregard the foregoing comments, if not, then maybe you might consider editing the relevant sections of the page accordingly.

S Sycamore (talk) 19:16, 8 August 2008 (UTC)

Above copied from User_talk:Borb -- Borb (talk) 20:58, 8 August 2008 (UTC)

If anything, the section as written is confusing to the layperson, both physically and mathematically. The section reads "In acoustics one usually measures the sound pressure at a given distance r from the source using the 1/r law. Since intensity is proportional to the square of pressure amplitude, this is just a variation on the inverse-square law." On its face, this seems to suggest that this whole section does not belong on this page at all, as it is inversely proportional and not inverse-square. Could someone clarify (for the layman) the difference between "pressure" and "intensity," as that seems to be the sticking point? NewkirkPlaza (talk) 19:19, 22 October 2014 (UTC)
I removed acoustics section - it may be correct, but not explained to a depth that makes it fit (understandable) into the article. I think it would be hard or impossible to fix that, because much depends on the use of dB in that section, which makes the numbers hard to understand. Also, the reader would need to understand the relation of sound power, amplitude, pressure and loudness (or most of it) to make sense of the calculations in terms of perceived sound intensity. (Oh, and the dB is usually referring to a standardized psychoacoustic weighting of frequencies, which complicates it some more.) — Preceding unsigned comment added by Volker Siegel (talkcontribs) 14:10, 29 July 2016 (UTC)

Light Emitting Diodes (LEDs)[edit]

Is it possible that the LED device .. designed to remove infrared radiation (IR) from the white light spectrum does not follow the Inverse-square law as is? Sorta meaning IR helps carry light through distance?Greg0658 (talk) 16:42, 9 February 2009 (UTC) More clearly put .. does LED light fall-off at a different rate than full spectrum electromagnetic waves and white light?Greg0658 (talk) 13:58, 13 May 2009 (UTC)

No the inverse square law is a spreading function and is independent of the spectrum of radiation. The typical LED has a built in reflector and lenses that direct the light in one direction. Inverse square still applies but it's as if the point source was originated somewhere far to the rear of the actual LED so the fall of is less per unit distance after the LED surface. (talk) 17:15, 15 April 2010 (UTC)

If the light spreads out over some space as it moves away from the source, it spreads over the same amount of space regardless of whether it's from a light-emitting diode or from some other kind of source. Michael Hardy (talk) 17:34, 15 April 2010 (UTC)

accuracy - Point Source Approximation[edit]

From ISBN 0-9658356-9-3 Ryer, A, "The Light Measurement Handbook", 1997 : p.26. (The chapter is also available online here[3])

Under the heading "Point Source Approximation" Ryer describes 1) some practical limitations of the inverse square rule, 2) a more accurate and encompassing alternative formula which includes non-point sources.

If I have interpreted correctly: for illuminance from a non-point-source - ie where the diameter of the light source is more than 1/5th of the distance - the following formula may be more useful: E = Lr2/(r2 + d2); where r= source radius and d= distance.

This would certainly seem like a valid addition to the Inverse-square_law#Light_and_other_electromagnetic_radiation section. Perhaps it would also be applicable in other contexts ? --Redbobblehat (talk) 14:07, 10 February 2009 (UTC)

Watts Versus Candles[edit]

I was trying to look up a solution to a problem I had run into regarding Inverse Square law calculations given a distance variable of 0 (which would involve division by 0, which is unallowed), although I see someone has made a comment referring to limitations of inverse square law, and that may be one of them.
However, much of the work I am doing involves simulated sunlight, and I noticed the potentially useful mention of the relative illumination of the sun at the surfaces of Mercury and the Earth; but I was a bit puzzled as to why this is presented in watts? Watts are a measurement of energy consumption, not illumination: for that reason, it's impossible to convert between watts and candles since energy consumption given an illuminative power is variable: in other words, different lights produce varying amounts of illumination given the same energy consumption. So I can't convert the value to a useful illuminative power. Perhaps this should be given in candles instead? LSmok3 Talk 12:10, 7 December 2009 (UTC)

A clearer summary definition for the layman is needed[edit]

This article could greatly benefit by the addition of a clear summary for the layman appended near the beginning. I came away with not much greater an understanding of the concept of the inverse-square law than I had before I read this. Not enough, I had to go to several other web sources to acquire a basic understanding. I am a well-educated person without much mathematics (which is a large demographic). Someone with a thorough grasp of the term and its applications, as well as related concepts, should write a brief non-technical, non-specialist definition and place it near the beginning of the article. The depth and breadth of Wikipedia articles is commendable and very useful, but just as often readers seek to gain a basic grasp of a thoroughly unfamiliar subject. We can do both here, it just needs 50-100 words of cogent definition added.Googlyelmo (talk) 19:06, 22 October 2010 (UTC) Googlyelmo (talk) 19:06, 22 October 2010 (UTC)

Kepler's beliefs[edit]

Hi there Wikipedians- I removed the part of the sentence under 'gravitation' which read " instead of the guess of Johannes Kepler at inverse distance dependence"

I'm researching pre-Newtonian gravitation and can't find any other mention that Kepler accepted a 1/d law for gravity. He certianly used a 1/d relation for orbital velocity- but that's not the same thing at all as gravitational attraction. If someone finds a reference then I think it could be reintroduced. In the meantime it shouldn't be there as it's unsubstantiated. (talk) 17:33, 26 November 2010 (UTC)

Hello I wonder if Kepler merits inclusion as it does work out that the inverse of the square of the velocity of a planet is directly proportional to its radius. Uglysses

The Flux Visualisation[edit]

I just noticed an error in the introductional picture about the flux behaviour. The intersection points of the three central rays with the third distance sphere are obviously wrong (compared to the first two spheres). If you klick on the image it is presented correctly, so it should be an easy matter to change this. Anyways, i have no idea how to do that. Greetings to all fans of the inverse square law. — Preceding unsigned comment added by (talk) 11:37, 10 September 2011 (UTC)

To do: some mathematics[edit]

The article should present a mathematical discussion of the force field of four special cases.

  1. The outside of a spherical charge distribution (equal to a point charge)
  2. The inside of a spherical charge distribution (zero)
  3. Infinitely long linear charge. (inverse to distance)
  4. Infinitely large planar charge. (constant at all distances from plane.)

The force should be derived – not only from the flux, but also by integrating over an even distribution of charges. -- Petri Krohn (talk) 22:52, 17 January 2012 (UTC)

Entropy and energy density[edit]

What is the relation of the ISL to space-time? --TheLastWordSword (talk) 17:37, 3 August 2015 (UTC)