Originally posted by JohntheThird Thanks Rich for the clarification.
So in the mirror, it is the retarding layer / recirculating layer that blocks out the light, not the polarising layer?
Light goes through the polarizing part and becomes linearly polarized then through the quarter-wave plate to make it circularly polarized. That light hits the mirror and reflects back (the relevant reflected beams are the ones that reflect at an angle of reflection small enough that they will pass through the plane of the polarizer again). The mirror does not affect polarization, but does affect direction of propagation. Let's trace the rays and see how this leads to complete destructive interference, and hence, complete blackness.
You stand behind the polarizer. (Unpolarized) Light enters the filter and first becomes linearly polarized, say at 90º to the horizontal. Then it goes through the quarter wave plane and becomes circularly polarized; based on your perspective, it will be rotating clockwise. Then it hits the mirror and comes back; this doesn't change the polarization, but does change the direction of propagation. From your perspective, now the light will be rotating counterclockwise when it goes back through the quarter-wave plate. Coming through the other side, the plate will now transform in the opposite manner.
In (forward direction, from your perspective): 90º linear --> clockwise circular or -90º --> counterclockwise circular
Out (from your perspective): clockwise circular --> -90º linear, counterclockwise circular --> 90º linear
So our light exits the plate at 90º linear polarization. Now it heads through a linear polarizer that took unpolarized light and made it linearly polarized 90º light. So...reversing it means you get...-90º degree light. Between the quarter plate and the polarizer you have light at nearly identical amplitudes* with polarizations of the same direction that differ by 180º. Hence, they cancel in total destructive interference** and you see nothing.
*: The light reflected is not identical to the light that comes through, even if the scene is static. Even light can't be in two places at once (finite speed of propagation). But the two are so nearly identical due to the ridiculous speed of light compared to the distance that the light very nearly IS in two places at the same time. At the least, your eyes can't tell that it's different.
**: Of course, the filters aren't perfect and you won't have quite 180º phase mismatch, but it will be close. That's why you can see some light, but not a lot. The better the filter, the less you should see.