Spatial Detector accuracy

1. Nov 30, 2011

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

2. Nov 30, 2011

humanino

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

3. Dec 2, 2011

McCuack

thank you very much!!