  We present H-alpha and [O III] (5007 Angstroms) images of the nebula powered
by the jet of the black hole candidate and microquasar Cygnus X-1, observed
with the 2.5m Isaac Newton Telescope (INT). The ring-like structure is luminous
in [O III] and there exists a thin outer shell with a high [O III] / H-alpha
flux ratio. This outer shell probably originates in the collisionally excited
atoms close to the front of the bow shock. Its presence indicates that the gas
is shock excited as opposed to photoionised, supporting the jet-powered
scenario. The shock velocity was previously constrained at 20 < v < 360 km/s;
here we show that v >= 100 km/s (1 sigma confidence) based on a comparison of
the observed [O III] / H-alpha ratio in the bow shock with a number of
radiative shock models. From this we further constrain the time-averaged power
of the jet: P_Jet = (4 - 14)*10^36 erg/s. The H-alpha flux behind the shock
front is typically 4*10^-15 erg/s/cm^2/arcsec^2, and we estimate an upper limit
of ~8*10^-15 erg/s/cm^2/arcsec^2 (3 sigma) to the optical (R-band) continuum
flux of the nebula. The inferred age of the structure is similar to the time
Cyg X-1 has been close to a bright H II region (due to the proper motion of the
binary), indicating a dense local medium is required to form the shock wave. In
addition, we search a > 1 square degree field of view to the south of Cyg X-1
in H-alpha (provided by the INT Photometric H-alpha Survey of the Northern
Galactic Plane; IPHAS) for evidence of the counter jet interacting with the
surrounding medium. Two candidate regions are identified, whose possible
association with the jet could be confirmed with follow-up observations in [S
II] and deeper observations in [O III] and radio.
