If you are using the Nikon original flashes SB-N5 or SB-N7 then the Nikon 1 V1 camera will recognize the flash unit and will prevent you from selecting shutter speeds outside the flash sync speed limitations, which is maximum 1/60s if you are using the electronic shutter, or 1/250s if you are using the mechanical shutter.
If on the other hand you are using the V1-F1A flash adapter and a suitable external flash or a radio trigger, then the camera will not recognize the adapter, the radio trigger or the flash and will let you use any shutter speed selectable on the camera. This is normally not a problem as long as the shutter speed is below the flash sync speeds. If however shutter speeds outside that limit are selected then the recorded image will record the shutter mechanism movement, or the electronic shutter simulated movement. This happens because the camera will always trigger the flash, regardless of selected shutter speed. This is the way the camera is designed and is not a fault of the adapter or the camera. On the other hand, the user must be aware of this, since the user must keep track of selected shutter speed.
The effects of this phenomenon can be more or less disturbing, but should be generally avoided because the black band you get on the bottom of the image with mechanical shutter used, or the top of the image with electronic shutter is not just a shadow, there is no image under the black band so you cannot recover what was there when you took the image. Also, the more the difference is between the maximum flash sync speed and the one selected on the camera, the wider the black band becomes. This is only causing problem if you are using higher shutter speeds, lower than the flash sync shutter speeds cause no problems.
This behavior is normal and is not an error in the camera or the adapter.
Some example images
Electronic shutter used, camera set to 1/60s, flash triggered using a radio trigger and there is no black band, the whole image area is evenly lit.
Electronic shutter used, camera set to 1/80s, flash triggered using a radio trigger and there is a clearly visible black band at the top. The slight increase in shutter speed above the specified shutter speed causes the band.
Electronic shutter used, camera set to 1/100s, flash triggered using a radio trigger and the black band at the top increased even more.
Mechanical shutter used, camera set to 1/250s, flash triggered using a radio trigger and there is no black band, the whole image area is evenly lit.
Mechanical shutter used, camera set to 1/320s, flash triggered using a radio trigger and there is a clearly visible black band at the bottom of the image. The slight increase in shutter speed above the specified shutter speed causes the band.
It does not matter which flash is used, I have tested this with several and they all cause the same banding. This behavior is normal, the specifications of the camera are not changed if the V1-F1A flash adapter is used.
About using a TTL flash or radio trigger
Please note also that iTTL is not possible, even if you are using an iTTL compatible radio trigger and an iTTL compatible flash. You must disable the iTTL function when you are using the V1-F1A flash adapter. Contact your manuals regarding how to disable that function. I don't have any iTTL compatible radio trigger, and testing of all possible combinations of flashes and radio triggers is not possible for me to do. If your radio trigger does not allow you to disable the iTTL function then you must use the PC contact on the side of the V1-F1A flash adapter to trigger your flash or you must buy another kind radio trigger.
The V1-F1A adapter used for taking the above flash sync sample images is now available. Read about the details here: