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Prove or conversely disprove the inverse square law.

Extracts from this document...


Adam Hodgkinson


My aim of this experiment is to prove or conversely disprove the inverse square law, which simply states that the intensity of any point source, which spreads its influence equally in all directions without a limit to its range, will decrease in intensity inversely proportional to the square of the distance.

Background information


As first proposed by Isaac Newton when proposing his universal law of gravitation it became clear to him that the intensity of gravity would decrease according to the inverse of the square of the distance.  This is the heart of the inverse square, which states for any point source, which spreads its influence equally in all directions without a limit to its range, will obey the inverse square law.    Quite simply the inverse square law states that for sources emitted from a point the intensity will be deduced as the inverse of the square of the distance.     You double the distance you reduce the intensity by a factor of ¼.    This has applications in electric fields, light, sound, gamma radiation, and gravity.    All of these are expressed in the medium of a field.     To explain the properties involved in a field it is useful to use the idea of flux.    When water flows form a ‘source’ to a sink it is transferred at a certain rate, or flux.   The flux density will be the mass of water per second crossing a unit area perpendicular to the flow.   We can think of energy density in a similar way.     Energy flux density is normally referred to as intensity.    Field strength and energy flux density are related.    The strength of a field will fall off proportionally.

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Also what must be decided is the range of distances I will work across and the increments by which I will increase my distance.    I feel the best distance to measure across will be from zero distance, through to 15 cms.    And I also feel it is advisable to increase in stages of 5mm.   I believe if we plot distance against 1/√c then a straight line will be described, so a sufficient number of results are necessary to accurately plot this.

Light experiment

Practical issues

The practical issues at hand here, are far less complicated than that of the Gamma radiation experiment.    We have a limited amount of resources available.

I could have constructed an LDR circuit attached to a ohm meter, this would gage the changing resistance of the circuit as the light source is moved away.   However this is impractical, and although would prove an inverses square relationship it doesn’t deal in the basic units.    In order to get a direct reading of the changing lux readings it would be sensible to use a light sensor and a  large analogue meter meter.    I will use a Griffin and George ray box with 12v bulb as the source of light.      The only real decision to be made here is what form of measurement device is to be used to measure the distance of the source for the dector.     I have decided to measure roughly over 25 cm, this means I simply cannot use either the digital, or sight-read vernier callipers, as they have a range only up to 15 cm.    So I must use a metre rule.


The experiment is very similar to the Gamma experiment, in that you are moving a point source away from a dector at steady intervals.

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20 = 8 X 100 = 800%


This is obviously an unacceptable level of error, however is not as bad as it sounds as it is a systematic error so will affect each result the same amount, so relative to each other the results will not be perverse.   The only difference it will make will be to the gradient of a line.    I feel that it is responsible for the fact that in my logarithm graph the gradient is -0.86 rather than 2.   The other people doing the same experiment also got a gradient of around –0.8 so I feel my reasoning here is justified.  

But this is the glaring error, and should I do the experiment I would either try to have direct measurement from actual source to actual dector to eliminate this error.   Or find out the value of the error and add it to the measured distance, in a similar way we work out the background radiation count, and then subtract it from our radiation count.

In conclusion it is hard to give an overall percentage error in my result.  This is because as the distance of the source from the dector changes, so does the relevance of the error.   As distance increases any inaccuracy in measurement decreases.  However I will give a total percentage error at the distance of 10mm.

Error of measurement +- 0.5mm –  +- 5%  

Error due to timing +- 0.8 seconds –  +-1.3%

Error due to unknown position of source and dector 20mm – 200%

So the total error would be 206.3%

However I will choose to ignore the last one, because unlike the others it is not plus or minus, it is constant at present in all results so the final percentage error is;

+- 6.3%

In conclusion I feel I have proved that both gamma and Light radiation Obey the inverse square law, I feel this is sufficient data to say that all members of the electro-magnetic spectrum obey the inverse square law.

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