1. An apparatus for determining a presence of fog in an atmosphere around a vehicle, comprising: image capturing means mounted on the vehicle for capturing an image around the vehicle; first determining means for determining a sky region in the image; second determining means for determining a far-flung road region in the image; first acquiring means for acquiring a brightness of a sky around the vehicle based on the sky region of the image; second acquiring means for acquiring a brightness of the far-flung road region based on the far-flung road region of the image; judging means for judging whether or not an underexposure phenomenon is occurred in the far-flung road region of the image; and third determining means for determining whether or not fog is present in an atmosphere based on the brightness of the far-flung road region when a nonoccurrence of underexposure phenomena in the far-flung road region and the brightness of the far-flung road region and the brightness of the sky when an occurrence of the underexposure phenomena in the far-flung road region.