What are the Fresnel Equations and how do they relate to polarized light?

[heycoa]

Homework Statement

Use the Fresnel Equations to prove that light incident at θ_p=1/2*∏-θ_t
results in a reflected beam that is indeed polarized.

Homework Equations

N/A

The Attempt at a Solution

I cannot find a Fresnel equation that has θ_p in it. And even if I did, I wouldn't know weather to use the perpendicular or parallel reflection equation.

Please help me understand this. thank you

 

[Simon Bridge]

I cannot find a Fresnel equation that has θp in it. And even if I did, I wouldn't know weather to use the perpendicular or parallel reflection equation.

You have to start by understanding the problem that is in front of you in terms of physics and not in terms of plugging numbers into equations. $\theta_p$ is just the name they've given to this particular angle of incidence. They could have given it any letter in any language - the vast majority of which won't appear in any formulation of the Fresnel equation.

If you got rid of the subscript "p" in the relation so it reads:
$\theta = \frac{\pi}{2}-\theta_t$
... would that make it easier?

What is that relation telling you about this incident angle?
Sketch the situation ... what sort of reflection is happening here?

 

[heycoa]

• What is that relation telling you about this incident angle?

I sketched it, and if I'm right, the incident angle is equal to the the transmitted beam's non-incident angle (90°-θ_t).

• what sort of reflection is happening here

I'm not sure what sort of reflection is happening here.

 

[Simon Bridge]

transmitted beam's non-incident angle

What?
You mean the reflected ray is perpendicular to the transmitted one?

I'm not sure what sort of reflection is happening here.

... that's OK, you don't have to be sure. Being unsure means you have something to be unsure about. If you are drawing a total blank, though, then you just have to go back over your lessons in using the Fresnel equations and about reflection.

Notice that you have to prove that the reflected beam is polarized - this suggests an unpolarized incedent beam doesn't it?

 

[heycoa]

What?
You mean the reflected ray is perpendicular to the transmitted one?

Yeah, that would be a much better way of describing it. I believe that this is true in this scenario.

Notice that you have to prove that the reflected beam is polarized - this suggests an unpolarized incedent beam doesn't it?

Yeah, so the incident beam is unpolarized.

Oh wait, when the transmitted beam is perpendicular to the reflection of the incident beam then it is Brewster's angle.

So I need to use the parallel reflectance equation of Fresnel's and work it into the wanted result?

 

[Simon Bridge]

See - now you are thinking properly :)

 

[heycoa]

Except I am still stuck. I don't understand how I am supposed to prove that the reflected light is polarized. I know that the transmitted light is one component of the electric field, and I can also see that the reflected light is the other component of the electric field. But given the current information I have, I just do not know how to prove it.

 

[Simon Bridge]

The Fresnel equations are related to how much of each component gets transmitted and reflected. What you are looking for is the range of incident angles where the reflected light consists of only one polarization direction... specifically, for the relationship between the incident and transmitted angles.