= Solution
The speed of one rocket in the other's rest frame is obtained by <relativistic velocity addition>:
$$
u=\frac{c/2-(-c/2)}{1-(c/2)(-c/2)/c^2}=\frac{4c}{5}.
$$
The <Lorentz factor> is $\gamma=(1-u^2/c^2)^{-1/2}=5/3$. By <length contraction>, the spatial length measured at simultaneous times in that rocket's rest frame is
$$
\boxed{L=L_0/\gamma=3L_0/5}.
$$
This is the inertial-frame length measurement; a visual image assembled from light arriving at one instant is a different measurement.
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