Is the periscope view obscured by water? Are you in bad weather? If so, you might have to come up a meter or two in depth to clear the wave tops with your optics. Or are you attempting to use the periscope at "high" speed and have the h.sie and/or Stiebler realism patches enabled on the SH3.exe file? If so, slow down to Ahead One Third and try looking through the scope.
In situations like this, when you have troubles, a picture is worth a thousand words. A screen grab posted on an image site and linked here would help immensely in a "diagnosis" for you. Listing any mods you might have activated, or stating if you are using just the Stock game is also helpful.