How can I tell whether I have a circular or a linear polarizer? I have a polarizer which has CIRCULAR PL written on it. This suggests it is a circular polarizer even though I am supposed to have a linear one.
My question is how can I tell whether the polarizer I have is a linear or a circular polarizer?
 A: There is a number of ways you can find out whether you are dealing with a polarizer of a given kind, this is because 1) light reflected off surfaces is partially linearly polarized, 2) polarizers of a certain kind polarize your light and you can use that to compare with your polarizer, and 3) LCD screens emit linearly polarized light. As a result, you can do the following to tell which polarizer you have


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*Take a glass surface such as your window, and take a look at some reflection on it at about a $45^°$ angle through your polarizer. Now start rotating the polarizer. If the reflection is dimming and brightening as you rotate the polarizer, your polarizer is a linear one. If nothing happens, your polarizer is a circular one. (For more, see Brewster angle.)

*If you have polarized sunglasses or a polarizer for your camera lens, it is a linear one exactly because it tends to dim reflections. (Not all sunglasses and camera lens' are polarized though, you have to be sure that they are!) Put your polarizer and your camera polarizer behind each other, look through them, and start rotating your polarizer. If the image is periodically dimming and brightening, you have a linear polarizer, a circular one if nothing happens.

*LCD displays emit linearly polarized light. Take a look at an LCD display through your polarizer and rotate it. Again, if it dims and brightens, it is a linear polarizer, if not, it is circular.



EDIT: The meaning of the word "circular polarizer" as I use it in the first part of the answer above is an optical element which filters out the light of a given circular polarization and leaves only the complementary one. (In practice this could be for instance achieved by a combination of a quarter-wave plate, a linear polarizer, and a 3/4-wave plate.)
However, I have just learned that in photography, the word "circular polarizer" is actually used for a linear polarizer with a quarter wave-plate. In other words, "circular polarizer" in photographic equipment means an optical element which ideally does the following:


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*It filters out the light of one linear polarization. I.e., the light leaving this first step is linearly polarized in the complementary direction.

*Turns the rest of the linearly polarized light into circularly polarized. (This is achieved by introducing a phase-shift between the magnetic and electric part of the electromagnetic wave.)


Apparently, this piece of equipment gets rid of complications a simple linear polarizer causes with (partially) reflective parts inside the camera. 
Nevertheless, the second step, the quarter-wave plate, works exactly as described above only for one fixed wavelength of light $\lambda_0$ (this could be e.g. the wave-length of orange light). For other wavelengths (other colors of light), it introduces a slightly different phase shift. 
I.e., if linearly polarized light of various wavelengths enters the quarter-wave plate, it will emerge from it with various degrees of elliptical polarization (essentially a mix of linear+circular polarizations) from it, dependent on its wavelength. 
If you use the polarizer in the way it was designed, it doesn't really matter, because your eyes are unable to detect polarization anyways. However, it changes if you flip it around. Then the light from a linearly-polarized source such as an LCD display gets first shifted in a color-dependent way, and then, based on this shift, filtered out by the linear polarizer. As a result, the flipped photographic "circular polarizer" applied to linearly polarized light will filter out some colors more and some colors less.
In other words, if you ordered a photographic polarizer, it will be most likely either be a linear polarizer, or a linear polarizer with a quarter-wave plate. Both of them should dim and brighten an LCD screen when rotated and used in the designed direction, but you can tell between the two when you flip it. Then the simple linear polarizer will work exactly the same, but the circular one will work different; it should show less dimming/brightening when rotated and possibly some color variations to the light when flipped.
A: A circular polarizer is often a combined $\lambda$/4- retardader, and a linear polarizer having its transmision axis at 45 deg with the optical axis of the retardader. A linear polarizer cannot transmit light having the electric field vibrating perpendicular to its transmision axis.
On one hand, You can distinguish between the two as the linear polarizer cancels light reflected in a surface at the Brewster angle of incidence, i.e, you cannot see the reflexion. The transmission axis should be in the vertical direction. On the other hand, the circular polarizer differentiates circular polarized light that rotates counterclockwise or clockwise direction. Circular polarizers are often used as antireflection coatings in displays screens, as the light impinging in the display is circularly polarized rotating in one direction when previously transmitted by the circular polarizer, but after reflection then rotates in the opposite direction, and the circular polarizer cancels transmission to the observer.
You can learn more about polarization reading Hecht's textbook "Optics, 5th ed" (Pearson education, 2016, or previous editions), or a more especiliazed texts such as that from Goldstein "Polarized ligh" (Marcel Dekker, 2003), as well as the more recent from Jose Jorge Gil and Ravizgor OssiKovski "Polarized light and the Mueller matrix approach" (CRC press, 2016)
