A proportional wire chamber contains an array of

parallel wires that are used to detect the $x$ coordinate

of a particle that passes through the chamber. $($The

axis of each wire is along the $y$ direction.$)$ The

chamber is used to detect particles that pass through

at random locations. An electrical signal is detected

on the wire closest to which the particle passes. The

measurement of the particle $x$ coordinate is the $x$

coordinate of the wire with the electrical signal. If the

wire spacing is $1mm,$ what is the position resolution

$()$ of the chamber?