Linear or Circular Polarizer, How Can You Tell?
Modern auto-focus cameras require the use of circular polarizers rather than linear. It may not be easy, though, to be able to tell which you've got, if it's not labeled.
One way to tell is to look at it in a mirror. Hold the polarizer so you can look through it and see the reflection of the polarizer in the mirror. A linear polarizer will appear light gray. If you flip the filter over such that the side that was facing the mirror is now facing you, it will still appear light gray. A circular polarizer, on the other hand, will be light gray if you look through it one way, but noticeably darker if not almost black when reversed.
Why does this work? Looking through a linear polarizer, the light gets polarized. It then reflects off of the mirror and retains its polarization. It then passes back through the polarizer relatively unchanged since its orientation already matches that of the polarizer.
A circular polarizer though re-scrambles the linearly polarized light by means of a "quarter-wave retarder." Imagine that the filter is oriented with the retarder facing you rather than the mirror. When you look through it, the light is first scrambled by the retarder, then polarized, then reflected off the mirror, after which it will pass back through the filter exactly as it does with a liner polarizer, except that it is again scrambled by the retarder on the way back out. If the polarizer is reversed though, the light is first polarized, and then scrambled by the retarter. Reflecting off the mirror, it then gets further scrambled by its second pass through the retarter. This time through the filter though, only light that has the correct orientation will make it through, meaning that significantly less light will make it back to your eye than with a linear polarizer, or a circular one facing the other way.
Even if you know what kind you have, this can be an interesting experiment in order to help understand more how polarizers work.