Understanding the Spatial Accuracy of Track Detectors

[McCuack]

Hi

please forgive me if you find that this is not the correct place, but since my work is of experimental nuclear physics and I didn't find a sub.forum in math neither engineering I decide to post here.

Here is the question:

in any track detector, the spatial accuracy of the detector is σ=pitch/sqrt(12) where the pitch is the separation between two wires/fibers/etc, but where the sqrt(12) comes from?

I know that should come from some statistics analysis but I have an absolute blockout.

Thank you

 

[humanino]

The uniform distribution !
$$\mu = \frac{1}{b-a}\int_a^b \text{d}x\,x = \frac{a+b}{2}$$
$$\sigma^2 = \frac{1}{b-a}\int_a^b\text{d}x\, (x-\mu)^2 = \frac{(b-a)^2}{12}$$

 

[McCuack]

thank you very much!