Light propagation through polarizers

[Heirot]

A beam of unpolarized light falls upon a polarizer which polarizes the light in e.g. x - direction. After that polarizer, we put another one which polarizes it along the y - direction. Of course, no light is transmited. Now we put a third polarizer between the first two, so that the third one polarizes the light in the x + y direction (the diagonal). Is any light transmited form the y - polarizer and if so, why? If not, why?

 

[zhermes]

Why don't you give it a shot.

 

[Heirot]

I think that there will be some light because x-polarized light has a component in the x+y direction and also the x+y - polarized light has a component in the y-direction. So, putting in a third polarizer would act as a sorce of light. On the other hand, I always considered polarizers as some sort of filters so it confuzes me.

 

[Joseph14]

here is the experiment on youtube

 

[zhermes]

You're exactly right. And it is weird!---polarizers are a lot like filters, but this is a good example of quantum(like) behavior contradicting our intuition. Apparently polarizing filters are a little more complicated than normal filters---which simply remove one aspect, leaving everything but that aspect.

When light of one polarization passes through a polarizer, the amount of light that will be transmitted is proportional to the square of the cosine of the angle between the polarization and the polarization filter, i.e. $$\textrm{Prob} \propto \cos^2 \theta$$. Thus for any non-90 degree angle, some light will go through, regardless of the previous history of polarization.

 

[Heirot]

What about classical waves (on a string)? On second thought, this might also apply to them. It's hard for me to visualise things like this.

 

[DrChinese]

Take an X polarized beam. None of it will pass through a Y polarizer. Now run that beam through a 45 degree beam splitter and then recombine the outputs. That resulting beam will go through a Y polarizer at a 50% intensity.