It has been argued that F-R I radio galaxies and BL Lac objects are in
trinsically the same. The strong emission seen in BL Lac objects may b
e the result of beaming of radiation from the galactic nucleus. We see
a BL Lac object when our line of sight lies within the beam. If this
is correct, then F-R I radio galaxies also have very luminous beams of
radiation, which are directed away from our line of sight. Many F-R I
galaxies are found in the centers of clusters of galaxies, and many c
lusters contain cooling flows. The high gas densities in these regions
imply small but significant electron scattering optical depths. We sh
ow that the cooling flow gas will scatter the beamed emission and make
it visible even when the beams are directed away from our line of sig
ht. We derive the surface brightness of the scattered light for beams
of polarized and unpolarized radiation and determine the polarization
properties of the scattered light. Assuming typical angles for the bea
ms, a typical BL Lac spectrum and apparent luminosity, and typical coo
ling flow properties, we derive the expected scattered light surface b
rightness from radio to X-ray wavelengths. The surface brightness of s
cattered light is compared to that of the direct emission from the gal
axy and its environment, assuming typical cD galaxy properties. We fin
d that the scattered emission will be most easily detected at radio, i
nfrared, and blue/UV wavelengths. Such observations could provide an i
mportant means of detecting the parent population of high-luminosity A
GNs. We compare our models to recent observations of lobes of excess,
polarized blue light in Cyg-A, and observations of lobes of UV light i
n the central regions of the cD galaxies in A1795 and A2597. These lob
es are aligned with the radio axis. Our models predict scattered surfa
ce brightnesses in reasonable agreement with those observed. If these
lobes are indeed scattered light, this would show that F-R I radio gal
axies do possess beams of radiation with apparent luminosities similar
to BL Lac objects, that these beams are double and that the radiation
is actively beamed and not merely obscured by a torus of dust around
the nucleus.