The only thing like an optical tool Columbus would have used is a quadrant... which doesn't necessarily use a tube at all. Usually they just had two holes you would look through to line them up. Once you lined them up, a plumb bob hanging in front of a quarter circle (from whence the quadrant gets its name) with angle markings would give the angle to whatever you're looking at. It was used for primitive celestial navigation, and from all accounts, Columbus was terrible at it, even by the standards of the time.
Mostly he navigated by dead-reckoning, which basically means plotting your location by calculating hourly vectors for speed and direction. Direction was measured with the compass, and speed was measured by tossing flotsam overboard, and counting how long it took to pass it. Accuracy, needless to say, was rather low.
The likely explanation for the image you have of him looking through an optical device is anachronism. Artists of later eras who wished to romanticize his image would have likely included navigational tools (telescope, sextant) of later times. That's why they were artists, and not navigators.
Last edited by Dude; 10/23/12 07:52 AM. Reason: eye cants tipe