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Assuming all photons have random states, what percentage of photons make it through a polarization filter with preferred axis $\newcommand{\bra}[1]{\left<#1\right|}\newcommand{\ket}[1]{\left|#1\right>}\newcommand{\bk}[2]{\left<#1\middle|#2\right>}\newcommand{\bke}[3]{\left<#1\middle|#2\middle|#3\right>} \ket{v} = 1\ket{\uparrow} + 0\ket{\rightarrow}$ ?

Does 100% of the light pass through and get polarized vertically? Or does 50% of the light pass through and get polarized vertically?

My knowledge of the subject suggests that 100% of the light passes and gets polarized vertically, but the answers I've found for my textbook say 50% get through.

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  • $\begingroup$ Note that if, instead of a filter, you use a birefringent material and a polarization rotator, it's possible to fun things with throughput. $\endgroup$ Commented Dec 10, 2021 at 14:32

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(See edit below)You can’t get a half photon. If a photon passes through a polarizer, It will be 100% and it will come out polarized parallel with the polarizer, no matter what polarization it had before it went in. EDIT: Because you changed your question, the answer would be 50% if the light is unpolarized and $\cos^2(\theta)$ if the light is polarized.

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  • $\begingroup$ I want to know what percentage of photons make it through. I will reword the question. $\endgroup$
    – Wadwamille
    Commented Dec 10, 2021 at 5:58
  • $\begingroup$ That doesn't make any sense. 50% of the light gets through or 100%? $\endgroup$
    – Wadwamille
    Commented Dec 12, 2021 at 4:20
  • $\begingroup$ @Wadwamille My last sentence says “the answer is 50% if the light is unpolarized.” That’s the answer to your reworded question. $\endgroup$ Commented Dec 12, 2021 at 6:03
  • $\begingroup$ Unpolarized means every photon has a random polarization? Or is that a state I am not familiar with? $\endgroup$
    – Wadwamille
    Commented Dec 12, 2021 at 13:00
  • $\begingroup$ @Wadwamille yes unpolarized light means every photon has a random polarization. You should watch a few videos like youtu.be/-ZUw1qJOflU some of them do a fair job of explaining the whole process. $\endgroup$ Commented Dec 12, 2021 at 16:56
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The percentage of photons of a wavelength depends on the design of the polarizer. If the slits are too wide for the specific wavelength, more than 50% of the photons will pass through. If the slits are too narrow, less than 50% or even no EM radiation will pass through.

Background. Each photon has exactly two possibilities when interacting with a polarizer. As you probably know, electromagnetic radiation in free space has an oscillating electric field component, whose oscillation direction is perpendicular to the direction of motion (and additionally a magnetic field component, perpendicular to the direction of motion and to the electric field component).

When interacting with the surface electrons of the slit, the photons are polarized with an orientation between -45° and 45° and 135° and 215° (i.e., all oriented at 0° and 180°, respectively). The other 50% of the EM radiation is absorbed by the polarizer. The specific angles depend, of course, on the orientation of the polarizer, but the principle should be clear.

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