How does the reflection of light at different angles affect polarization?

[Maxo]

Homework Statement

Homework Equations

The Attempt at a Solution

I know that according to the Malus law formula, if the angle is 0 < θ < 90 then there is some transmission. But I need help understanding this physically. If we think of a polarizer/analyzer as a "lattice", i.e. kind of like this

then after having passed through such, the light waves should only be in one direction, right? So how can it then matter what other direction the next lattice (analyzer) is?

Are we supposed to think of the light waves as components in x and y direction? In that case, wouldn't a pure y-direction wave have no x-component? Wouldn't that then happen if you put the polarizer so that it transmits in y direction only? But then it comes back to my original question, why would the direction of the analyzer matter, why wouldn't it only allow transmission when θ = 0?

Please help me understand this further. I understand a lattice is not a perfect visualization of it. What would be a possible better image/object to visualize polarization with than a lattice?

 

[dauto]

You have three elements in this set up.
The 1st Polarizer produces a wave with no x component.
The insert decomposes this y-vector into two components along the y' and x' directions and blocks one of them - say x'. The analyzer decomposes the y'-vector into components along the y and x directions and blocks the y component. Some light comes through.
Even though a y-vector has not x-component, a y-vector does have a y'-component and the y'-component does have an x-component.

 

[Maxo]

You have three elements in this set up.
The 1st Polarizer produces a wave with no x component.
The insert decomposes this y-vector into two components along the y' and x' directions and blocks one of them - say x'. The analyzer decomposes the y'-vector into components along the y and x directions and blocks the y component. Some light comes through.
Even though a y-vector has not x-component, a y-vector does have a y'-component and the y'-component does have an x-component.

What do you mean with x' y'? How are they related to x y?

How can it be visualized what happends with the light as it goes through the filter? Since a "lattice" is not correct, what would be a correct analogy?

 

[dauto]

The picture you provided in the OP has a good visualization. y' is the axis of the insert which is rotated an angle θ from the axis of the 1st polarizer. The OP's picture has everything you need to see what's happening.

 

[Maxo]

Do you understand the word analogy?

 

[dauto]

The fence IS a good analogy.

 

[Maxo]

Why does sunlight get linearly polarized when reflected from water?

 

[dauto]

Why does sunlight get linearly polarized when reflected from water?

If you look at Fresnel equations for the reflection of light you will see that the two possible polarizations have different reflectances which leads to partially polarized light. for a specific angle called Brewster's angle the polarization is complete.