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I believe your problem is that you want it to make sense. Pictures of it happening don't make sense of it. Mathematical descriptions of it happening don't make it make sense. Your problem is that physics has mostly given up on making sense. It dates to more than 100 years ago. People had some simple ideas about how light worked, that made reasonable sense,...


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Depends how deep you want to understand it. Mathematicaly, even a vertically linearly polarized light can be described by 2 diagonally lineraly polarized light beams. In that sense, it was always there, just "cancelled out". The retarder retards one diagonal component but not the other. Quantumly... i struggle with it a bit but this video from 3blue1brown ...


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I would proceed as follows \begin{align} \hat{k} =& k_x\hat{x} + k_y\hat{y} + k_z\hat{z}\\ \hat{e} =& e_x\hat{x} + e_y\hat{y} + e_z\hat{z} \end{align} \begin{align} \hat{e}\cdot\hat{e} =& e_x^2+e_y^2+e_z^2 = 1 \\ \hat{k}\cdot\hat{e} =& k_xe_x+k_y e_y+k_z e_z = 0 \end{align} We are always free to arbitrarily choose $e_y=0$ for one of the ...


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We have, for a free space plane wave, that $\hat{\boldsymbol{e}} \cdot \hat{\boldsymbol{k}} = 0$. This tells us that $\hat{\boldsymbol{e}}$ lies in the plane perpendicular to $\hat{\boldsymbol{k}}$. You are correct that in a fully general situation there is nothing else which determines the direction for $\hat{\boldsymbol{e}}$ within this plane. However, ...


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The dielectric susceptibility outside the ball is $\chi=0$ (if it's vacuum).


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It has to do with the structure of the material. Polarization, or polarization density, has to do with the size of dipole moments you can have in your material. The manner in which dipole moments are created depends on the material. In the example of water, each water molecule has it's own dipole moment. Macroscopically, they may form a net polarization if ...


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The most important factor for getting a large polarization in a solid is how close the material is to a distorted crystal structure which breaks inversion symmetry (e.g., a ferroelectric or piezoelectric instability). The closer a material is to being a ferroelectric etc., the larger the polarization because it is easier for the external electric field to ...


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When the light is travelling from the sun, we can see that the plane of unpolarised light is at an angle (90-θ) from the observer with reference to the horizontal line for the given angle. Now since the light is unpolarised, it vibrates in 2 directions, say X-axis and Y-axis in our case. So on passing through a polarizer (in a natural phenomena like this, a ...


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no , polarization in dielectric is throughout the medium but the net charge produced within bulk of material is $0$, so we consider only charges at surface (outside green box in above diagram)


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One has to start with Magnetization, as it is a striking result of magnetism, and see how it is defined : In classical electromagnetism, magnetization or magnetic polarization is the vector field that expresses the density of permanent or induced magnetic dipole moments in a magnetic material. The origin of the magnetic moments responsible for ...


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If $\mu_0$ was zero then there would be no magnetic field due to moving charges in the vacuum. $\epsilon_0$ and $\mu_0$ just determine the strengths of electric and magnetic fields in a vacuum, as $\epsilon$ and $\mu$ do in a dielectric. A medium isn't needed for permeability, or else magnetic fields would be zero in the vacuum in many cases.


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Polarization is, generically, a normalized vector in spin-space, i.e. the spin-state of a particle (When I say spin, I actually mean total angular momentum, spin+orbital angular momentum). Usually we take "fundamental" polarizations to be an orthonormal basis in spin-space. For scalars (spin-0), there is only a trivial polarization because the spin-space is ...


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