How can I determine if a retarder is quarter or half wave?

An easy way to determine if a retarder is a ¼λ of a ½λ is to use the set-up outlined below. First, transmit linearly polarized light through the retarder. This light can either come from a light source that is already linearly polarized or be randomly polarized light that is sent through a linear polarizer. After the light is passed through the retarder, it can have one of two characteristics: if the retarder is ¼λ, then the light is circularly polarized; if the retarder is ½λ, then the light is linearly polarized, but at a different angle than the incident light.

Finally, you can use a second linear polarizer (typically called an "analyzer") to determine which retarder you possess. Place the analyzer in the path of the light coming from the retarder and rotate it. If, at certain angles of rotation, the light being emitted from the analyzer gets more intense and then is completely blocked out, you have a ½λ retarder. If the light emitted is of similar intensity no matter how the analyzer is rotated, then you have a ¼ wave retarder. Please note that there are other types of retarders than ¼λ of a ½λ, and this test does not take that into consideration.