= Solution
In the regime of <weak-field Zeeman splitting>, $J,m_J$ remain good labels and $\Delta E=\mu_B g_Jm_JB$. For the 393.4 nm line, $J_u=3/2$ in $4p\,{}^2P_{3/2}$ and $J_l=1/2$ in $4s\,{}^2S_{1/2}$. The <Landé g-factors> are $g_u=4/3$ and $g_l\simeq2$. Apply $\Delta m_J=0,\pm1$ to the four upper and two lower sublevels. The allowed pairs $(m_u,m_l)$ are
$$
(3/2,1/2),\ (1/2,1/2),\ (-1/2,1/2),\
(1/2,-1/2),\ (-1/2,-1/2),\ (-3/2,-1/2).
$$
Their <frequency> displacements in units of $\mu_BB/h$ are respectively $1,-1/3,-5/3,5/3,1/3,-1$, so none coincide. Looking perpendicular to the field permits both the $\pi$ radiation from $q=0$ transitions and the $\sigma$ radiation from $q=\pm1$ transitions. Consequently
$$
\boxed{\text{six distinct components: two }\pi\text{ and four }\sigma.}
$$
A linear <polarizer> parallel to the field isolates the two $\pi$ components; a transverse <polarizer> selects the four $\sigma$ components. Without <polarization> selection both sets are present. This count assumes a field small compared with <fine structure> coupling and neglects isotope-dependent <hyperfine structure>; the strong-field <Paschen-Back effect> or a resolved nonzero-spin isotope would require a different model. The spectral spacings are unnecessary for the count, but the distinct shifts verify that counting allowed transitions does not inadvertently count degenerate lines twice.
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