Answer
$17.1m$
Work Step by Step
First we look at equation (36-14) and use a small angle approximation to obtain :
$\theta_R= \frac{1.22\lambda}{d}=\frac{D}{L}$
We are given a wavelength of $\lambda=1.40*10^{-9}m$, a wire diameter of $d=0.200*10^{-3}m$, a target distance of $L=2000*10^3m$, and we are asked to find the diameter of the central beam at the target, $D$.
$\frac{1.22\lambda}{d}=\frac{D}{L}$
$D=\frac{1.22\lambda}{d}L$
$D=\frac{1.22*1.40*10^{-9}m}{0.200*10^{-3}m}2000*10^3m$
$D=17.1m$
