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

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SUMMARY

The inverse square law (ISL) fails to accurately predict light intensity from a matrix of LEDs at a distance of 168 mm due to the non-point source nature of the light emission. The test design inadequately approximates the light source, as the LED matrix dimensions exceed the distance to the detector, leading to significant deviations from expected ISL behavior. The calculations demonstrate that the intensity from two incoherent point sources is represented by the formula 1/R1² + 1/R2², which diverges from the ISL equation of 2/R² unless the sources are equidistant from the detector. As the distance increases, the discrepancies from the ISL diminish.

PREREQUISITES
  • Understanding of inverse square law (ISL) in light intensity calculations
  • Familiarity with LED characteristics and light emission patterns
  • Knowledge of point source vs. non-point source light behavior
  • Basic principles of geometric optics and intensity calculations
NEXT STEPS
  • Explore the effects of non-point sources on light intensity predictions
  • Investigate LED matrix design and its impact on light distribution
  • Learn about incoherent light sources and their intensity calculations
  • Study the mathematical derivation of the inverse square law in various contexts
USEFUL FOR

Optical engineers, physicists, lighting designers, and anyone involved in light intensity modeling and analysis will benefit from this discussion.

JimLub
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TL;DR
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?
 

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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:

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