For some years I have troubled experts in physics and optics with this phenomenon.
Still I don’t have a good answer.

As known polarized sun glasses filters away light reflexes which are partly polarized.

Similar methods are used for watching 3D movies and LCD (Liquid Crystal Displays)

The phenomenon discussed here is illustrated by this picture. 

With two disks, a and b, together the transmission can be controlled by turning one of them as shown.
Changing from a maximum to a minimum transmission is obtained by  rotating one disc 90 degrees.

Now turn the discs to a minimum transmission and introduce a third similar disk c between the two. What happens?

You will find that when turning the middle disc the rotation span between max. and min.
is only 45 degrees.

(I think this can be explained by calculating with the vectors of the polarized light giving the mathematic expression [Transmission= const. x sin.v x cos.v ]  where v is the angle.)

The middle layer can be replaced by some clear plastic sheets "d" showing the same behaviour!

But these films do not show any signs of being linear polarized.

Many, but not all films, show this behaviour.
The thickness does not seem to be of any importance.
Also the distance between the layers does not change anything.

Some matters are known to rotate light. But then, in this case, rotating the the middle sheet should not make any difference. I therefore don’t think that can explain what happens.

Can you solve the mystery?