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Investigating the effect of distance from a lamp on its brightness: results

Answers to questions

  1. The voltage is decreasing.
  2. Since DrDAQ is measuring the p.d. between itself and the point where the bulb holder makes contact with the potentiometer wire, a decreasing voltage means that the distance is also decreasing.
  3. DrDAQ's datalogging routine was started. It then took a few seconds to place the lighted bulb onto the wire and begin moving it. This accounts for the strange start to the graph. Once the bulb had reached the end of its travel it was removed from the wire [still lit] and then the dataloging was stopped - hence the end part of the graph. [There are many experiments where useful readings are not immediately available when an experiment commences - obvious examples are those involving heat, where a steady state has to be reached first.]
  4. Brightness increases more steeply as the distance decreases. This tells us that the relationship between the two quantities is non-linear.
  5. Plot a graph of brightness against distance.
    When this is done for the above data set, the following graph is obtained:
Brightness vs p.d

Further question:

Q: As the distance increases to infinity it is reasonable to expect that the light level would fall to zero. This is clearly not going to be the case. Why do you suppose this is so?

A: Background illumination present in the laboratory.

Discussion of further work

The light emitted by the bulb spreads out through three dimensional space. At some distance 'r' from the bulb the surface area that the light has to pass through [has to illuminate] is equal to:

A = 4πr2

at twice this distance, 2r, the area will be:

= 4π[2r]2

= 4A

In other words, as the distance increases the area illuminated increases with the square of the distance. The greater the area to be illuminated, the less the apparent brightness of the bulb becomes.

Hence if the area increases with the square of the distance, the brightness decreases with the inverse-square of the distance.

This is a property of three dimensional space, not of the light and it applies equally to electric, magnetic and gravitational field strengths for exactly the same reason.

Using this idea, the spreadsheet was used to calculate 1/r2 for each distance and these were plotted on the x-axis against brightness.

This graph is shown below and demonstrates that the experimental results agree with the inverse-square theory. The graph also allows the value of the background illumination to be estimated. If this was subtracted the graph would then pass through the origin.

Note that the brightness will then be zero when 1/r2 is zero. This latter statement means the distance r is infinity.

Brightness vs Inverse square p.d.

Teachers’ notes

DrDAQ proved to be very sensitive to fluctuations in light level, easily capable of detecting the mains flicker on fluorescent tubes. It is similarly sensitive to fluctuations in p.d. For these reasons a stabilised power supply was used both for the lamp and the potentiometer wire. If a suitable power supply is not available then three 1.5 volt dry cells would be equally suitable.

The original experiment was conducted in the lab, with lights off but no attempt made at blacking out the room, hence the relatively high background illumination. Perhaps this could be related to background radiation in studying radioactivity, and has to be taken into account in the same way.

Note that this experiment was performed as a pilot to establish the suitability of DrDAQ for purpose. Various changes were made, mainly to the way in which electrical contact was achieved between the base of the bulb and the potentiometer wire. Whilst the photograph of the arrangement shows the final design it could be made more aesthetically pleasing [and probably more robust] by screwing the bulb onto a wooden block [or piece of Lego] and by gluing the conducting end of the plug to its underneath.

The ‘manual’ experiment was conducted in a much darker room, hence the lower background. The ideal situation would be to perform the experiment in a dark-room.

Despite using clean wire the variation of p.d., as the bulb was moved along it, remained quite jerky [see original datalog graph]. A ‘manual’ version of the experiment was performed using Picoscope. The wire was disconnected from the power supply and the lamp was placed at different known distances from the sensor. The light intensity was measured at each position.

Picoscope was set as a meter:


The light levels and bulb position were recorded manually and entered into a spreadsheet.

The graphs obtained are shown below.

The discussion about results applies equally here, so is not repeated.

brightness vs distance

Brightness vs Inverse Square of distance

Credits, comments and further info

This experiment was written by Dr. R. Robinson, Maesydderwen Comprehensive, Ystradgynlais, SA9 1AP.


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