  Suppose that $h$ is a Gaussian free field (GFF) on a planar domain. Fix
$\kappa \in (0,4)$. The SLE$_\kappa$ light cone ${\mathbf L}(\theta)$ of $h$
with opening angle $\theta \in [0,\pi]$ is the set of points reachable from a
given boundary point by angle-varying flow lines of the (formal) vector field
$e^{i h/\chi}$, $\chi = \tfrac{2}{\sqrt{\kappa}} - \tfrac{\sqrt{\kappa}}{2}$,
with angles in $[-\tfrac{\theta}{2},\tfrac{\theta}{2}]$. We derive the
Hausdorff dimension of ${\mathbf L}(\theta)$.
  If $\theta =0$ then ${\mathbf L}(\theta)$ is an ordinary SLE$_{\kappa}$ curve
(with $\kappa < 4$); if $\theta = \pi$ then ${\mathbf L}(\theta)$ is the range
of an SLE$_{\kappa'}$ curve ($\kappa' = 16/\kappa > 4$). In these extremes,
this leads to a new proof of the Hausdorff dimension formula for SLE.
  We also consider SLE$_\kappa(\rho)$ processes, which were originally only
defined for $\rho > -2$, but which can also be defined for $\rho \leq -2$ using
L\'evy compensation. The range of an SLE$_\kappa(\rho)$ is qualitatively
different when $\rho \leq -2$. In particular, these curves are
self-intersecting for $\kappa < 4$ and double points are dense, while ordinary
SLE$_\kappa$ is simple. It was previously shown (Miller-Sheffield, 2016) that
certain SLE$_\kappa(\rho)$ curves agree in law with certain light cones.
Combining this with other known results, we obtain a general formula for the
Hausdorff dimension of SLE$_\kappa(\rho)$ for all values of $\rho$.
  Finally, we show that the Hausdorff dimension of the so-called SLE$_\kappa$
fan is the same as that of ordinary SLE$_\kappa$.
