Why does this inverse square calculation fail to predict actual data?

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• JimLub
In summary, during the conversation it was discovered that the inverse square calculations used to predict the dimming of light over a test distance of 168 mm were not accurate. This was due to the fact that the matrix of LEDs being used was not a point source and emitted light unequally in all directions. The speaker also mentioned that the ISL fails when using two point incoherent sources, except when they are equidistant from the detector. As the distance between the sources increases, the departure from ISL becomes less significant.
JimLub
TL;DR Summary
A simple test using solar cell and LEDs - shows dramatic differences between predictions and actual data. Test results are shown in attached file.
The test data and notes are attached - showing that the inverse square calculations fail to reasonably predict the actual dimming of light over a test distance of 168 mm. Did I err in my test design or my calculations?

Attachments

• Inverse Proportional Square Questions.docx
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A matrix of LEDs is not a point source - not even a good approximation at short distances. At 3/4" square, it is bigger than the distance to the detector at the closest distance. There is no way that this is going to give you an inverse square dependence of the intensity. I don't suppose it's even emitting light equally in all directions.

It's an easy calculation to show where the ISL fails, using two point incoherent sources, spaced at a certain distance and with a detector at some distance away. The resulting intensity will be
1/R12 +1/R22
which is not 2/R2
except when R1 = R2
i.e. along a normal to mid point of the line of centres.
Edit: as R increases, the departure from ISL is less and less.

Last edited:

1. Why is the inverse square calculation not accurate in predicting actual data?

The inverse square calculation is based on the assumption that the source of the data is a point source, meaning it emits radiation equally in all directions. However, in real-world scenarios, sources are often extended and not point sources, causing the calculation to be inaccurate.

2. Can the inverse square calculation be used for all types of data?

No, the inverse square calculation is only applicable to data that follows the inverse square law, which states that the intensity of radiation decreases with the square of the distance from the source. If the data does not follow this law, the calculation will not be accurate.

3. How does distance affect the accuracy of the inverse square calculation?

The inverse square calculation becomes less accurate as the distance from the source increases. This is because the intensity of radiation decreases with distance, and the calculation assumes that the intensity remains constant.

4. Are there any other factors that can cause the inverse square calculation to fail?

Yes, other factors such as atmospheric conditions, absorption, and scattering of radiation can also affect the accuracy of the inverse square calculation. These factors can cause the intensity of radiation to vary, making the calculation inaccurate.

5. Is there a way to improve the accuracy of the inverse square calculation?

Yes, the accuracy of the calculation can be improved by taking into account the factors that affect the intensity of radiation, such as the size and shape of the source, as well as environmental conditions. Additionally, using more advanced mathematical models and techniques can also improve the accuracy of the calculation.

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