# Why two opposite circular polarization filters let light pass through?

I've been playing with 3D glasses. I punched out one of the filters, stacked them with some space in between and looked through both the filters without flipping anything over. I expected the interaction to be like between linear polarization filters at 90° angle - no light should pass. If they were linear polarization filters at 90° all light that passed throught the first filter would be polarized according to the first filter and would not be able to pass through the second. So I thought all light that was able to pass through the first circular polarization filter would have, lets say clockwise polarization and it will not be able to pass through the second filter, because the second would only let counter-clockwise polarized light through. But actually a lot of light passes through both the filters - it only changes its tint between blue and yellow depending on the angle I twist them at.

I know the equation describing the chance of a linearly polarized photon to pass through a linear filter, but I don't know any such equations about circular filters.

## 1 Answer

These glasses consist of two layers: an ordinary linear polaroid-type polarizer and a quarter-wave retarder plate. The $\lambda/4$ retarder is the front surface. It converts circularly polarized light to linear.

Whay happens then if you put a second analyzer for circular polarization behind the first one? The linearly polarized light from the first analyzer will then pass through a $\lambda/4$ retarder and be converted to circular polarized light. Half of this will be absorbed by the second linear polarizer, but half will pass through.

So the analyzers need to face eachother. One way to accomplish this without punching them out is to look at oneself in a mirror with these glasses.

• Thanks, I think that explains it, I did actually see myself in a mirror beforehand and that was how I figured the filters were circular, not linear, because I could only see the opposite eyes, my same-side eyes were dimmed, and I expected it to be the other-way around with linear polarization filters. But since the reflected light has opposite chirality I saw what I saw. What about the second part of the post? I know linear filters' chance of letting photons pass is $cos^2(\theta)$ where $\theta$ is the angle. What about circular and eliptical filters how do they handle linear polarization? – K. Kirilov Apr 19 '18 at 11:47
• @K.Kirilov In the 3d glasses that I have here, the linear polarizers have the same orientation, so it must be the $\lambda/4$ plates that have different orientations, with the fast axes perpendicular to eachother. This causes or removes a 90 degree phase shift between the linear components of circularly polarized light. – Pieter Apr 19 '18 at 11:55
• I might have asked wrong. The second part of the post is: What is the chance a linearly polarized photon would pass through a circular polarization filter? – K. Kirilov Apr 19 '18 at 12:03
• I tend to avoid speaking about this in terms of photons. Photons have helicity eigenstates, and single linearly polarized photons do not exist as I understand it. That would be a coherent superposition of two helicity eigenstates. Half the intensity, $\sqrt{2}$ of the (probability) amplitude, 50 % of the photons. – Pieter Apr 19 '18 at 13:04