Light variation around a point source I'm trying to use LED's as a point source of light for a project I have. a crucial idea is that the intensity of the light of the led falls off as 1 over the distance squared as we move away from it. i.e. it should obey the inverse square law. I ran some measurements on an LED and tried to fit the results on a curve but did not get that result,(the intensity was more proportional to
1/d^3
). my measurements could be non-accurate.
I haven't found any helpful sites that point out that LEDs actually follow the inverse square law, but I'm still skeptic that it does.
so my question is, can an LED be used to some extent as a point source? how does an LED light vary with distance and with direction? if unfit, what other light emitting circuit components can be used instead if any?
engineering exchange didn't help much, thought asking here would be better.
 A: The first possibility is that the response of the probe is non-linear?
Another possibility is that there is an error in the way that you have interpreted the distance you measured between the led and the probe.
What I mean is that is that there may possibly be a constant error at the probe end because you do not exactly where the sensor is you have measured to a point on the probe which is not quite where the sensor is.
At the other end there may be a larger error of the same type.
Looking at some data sheets for single LEDs it would seem that the full width beam angle (a measure of how much the rays spread out) can be $60^\circ$ although for high power LEDs it can be down to $00^\circ$.
The production of such a beam is done by sometimes having a concave reflector behind the actual source and the use of a converging external surface at the front end of the led.
This would mean that the apparent position source of the light (back producing the diverging beam emerging from the led) is not at the same place as the actual source.
A standard way of dealing with such a constant uncertainty in the distance between the source and the detector is to measure the distance between a well defined point on the source and a well defined point on the source $d$.
If the actual distance between where the light appears to come from and position of the detector is $D$ then one can write $D=d+e$ where $e$ is a constant error.
You wish to show that the intensity $I$ is proportional to the reciprocal of the distance squared $I \propto \frac {1}{D^2} \Rightarrow I = \frac {k}{D^2}$
Substituting for $D$ and rearranging the equation one gets $d = \sqrt{k}\cdot \frac{1}{\sqrt I} -e$.
So perhaps you should see what happens if you draw a graph of $d$ against $\frac {1}{\sqrt I}$?
A: LEDs can be pretty directional, so right there they are not point sources. A small incandescent filament should be a pretty good point source if the detector isn't too close and the glass around it doesn't add distortion.
I  wouldn't expect the brightness vs distance to change that much because of this, but having strong variation of brightness vs angle and a finite size detector are complications. Can you try scattering the light with something like tissue paper, or looking at a diffuse reflection of the LED off a white surface like paper? 
