  The most extreme cluster mergers can lead to massive cluster-wide travelling
shock waves. The CIZA J2242.8+5301 ('sausage') and 1RXS J0603.3+4213
(`toothbrush') clusters ($z\sim0.2$) host enormous radio-emitting shocks with
simple geometry. We investigate the role of mergers and shocks in shaping the
H$\alpha$ luminosity function, using custom-made narrow-band filters matching
the cluster redshifts mounted on the INT. We surveyed $\sim0.28$ deg$^2$ for
each cluster and found $181$ line emitters in the `sausage' (volume of
$3.371\times10^3$ Mpc$^3$ for H$\alpha$ at $z=0.1945$) and $141$ in the
`toothbrush' ($4.546\times10^3$ Mpc$^3$ for H$\alpha$ at $z=0.225$), out of
which $49$ (`sausage') and $30$ (`toothbrush') are expected to be H$\alpha$. We
build luminosity functions for the field-of-view down to an average limiting
star formation rate of $0.14$ M$_{\odot}$ yr$^{-1}$, find good agreement with
field luminosity functions at $z=0.2$, but significant differences between the
shapes of the luminosity functions for the two clusters. We discover extended,
tens-of-kpc-wide H$\alpha$ haloes in galaxies neighbouring relics, which were
possibly disrupted by the passage of the shock wave. By comparing the `sausage'
cluster with blank fields and other clusters, we also uncover an order of
magnitude boost (at $9\sigma$ level) in the normalisation $\phi^*$ of the
luminosity function in the relic areas. Our results suggest that cluster
mergers may play an important role in the evolution of cluster galaxies through
shock-induced star formation.
