Polarised light from fresnel's equation

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In summary, the question asks how to find the polarization of the reflected beam, if the question didn't give me the polarization of the incident beam. The answer is that you need to look at the E-field of the reflected beam, and use the Fresnel equations to find out what fraction of it is transmitted.
  • #1
quietrain
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Homework Statement



polarizationlight.jpg


The Attempt at a Solution


how do i interpret such a question? is there something wrong with the question?

in particular, the light is polarized at 45degrees wrt the plane of incidence(e.g x-y plane),

wouldn't that mean that

1) my E-field is orientated in the z=x line? (when we say light is polarized in a direction, it really means the E-field right?) [so what has this got to do with the E(parallel) and E(perpendicular)? since these E are wrt to the interface of the impact right?]

2) so how do i find the polarization of the reflected beam (E-field of reflected beam right?) , if the question didn't give me the polarization of the incident beam?

3)lastly, does fresnel's equation give me the polarising angle? because it seems that they only give me the incident and reflected and transmitted angles? thanks!
 
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  • #2
quietrain said:

Homework Statement



polarizationlight.jpg


The Attempt at a Solution


how do i interpret such a question? is there something wrong with the question?

in particular, the light is polarized at 45degrees wrt the plane of incidence(e.g x-y plane),

wouldn't that mean that

1) my E-field is orientated in the z=x line? (when we say light is polarized in a direction, it really means the E-field right?) [so what has this got to do with the E(parallel) and E(perpendicular)? since these E are wrt to the interface of the impact right?]

2) so how do i find the polarization of the reflected beam (E-field of reflected beam right?) , if the question didn't give me the polarization of the incident beam?

3)lastly, does fresnel's equation give me the polarising angle? because it seems that they only give me the incident and reflected and transmitted angles? thanks!
The plane of incidence is not the same thing as the plane of the glass interface. The plane of incidence is the plane in which the incident and reflected rays lie. In other words, it is the plane of the propagation (k) vectors. So, for example, if the directions are like so:
Code:
x                     
^                             
|                     
|    k vectors lie in this plane               
|                     
------->z       

y points out of the page
Then the glass interface is the x-y plane, whereas the plane of incidence is the "page" (the x-z plane)

Therefore E|| is the component of the E-field that lies in the page, and Eperp is the component that points out of the page. These two components are equal, meaning that the E-field makes a 45 degree angle with the "page." In other words, it makes a 45-degree angle in the plane of polarization which is the plane perpendicular to k (yet another plane!)

The Fresnel equations can tell you what fraction of E|| is transmitted, and what fraction of Eperp is transmitted. Obviously if these fractions are not the same, then the two components will no longer be equal, and hence the angle of total E-field in the polarization plane will have rotated.

EDIT: As an example, if the direction of the propagation k vector were just the z-direction (which would mean normal incidence), then E|| would be in the x-direction, since it must lie in the x-z plane (the plane of incidence) but still be perpendicular to k. Eperp would be in the y-direction, since it must be perpendicular to the page, and also perpendicular to k. In this example, the plane of polarization (the plane in which E-field lies) would just be the x-y plane.
 
Last edited:
  • #3
hmm... there's a plane of polarization too?


ok, from your example(k in z direction), since the question says 45degrees wrt plane of incidence, so it means my E-field is in the x-y plane right?

so, the rperp means the fraction of reflected light in the perpendicular direction wrt the plane of incidence right? (x-y plane again)

, similarly, rparallel is parallel to plane of incidence (x-z plane) ?

i think i am getting it, becos i got confused with the parallel and perpendicular components of E when i was deriving the fresnel's equations from the boundary conditions.

the boundary conditions' parallel and perpendicular E and B are wrt to the interface right? not the plane of incidence.

i watched prof walter lewin's lecture on waves and he is a great teacher :)
 

1. What is polarized light?

Polarized light is a type of light that has its electric field oscillating in a specific direction. This direction is known as the polarization direction and can be vertical, horizontal, or diagonal. Ordinary light contains waves with random polarization directions, but when it passes through certain materials, it can become polarized.

2. What is Fresnel's equation?

Fresnel's equation is a mathematical equation that describes the behavior of light when it passes through the interface between two materials with different refractive indices. It gives information about the reflectance and transmittance of light at the interface, which is affected by the polarization of the incident light.

3. How is polarized light affected by Fresnel's equation?

Fresnel's equation takes into account the polarization of the incident light and provides different values for reflectance and transmittance based on the polarization direction. This means that polarized light will behave differently when passing through an interface compared to unpolarized light, as the polarization direction will determine the amount of light that is reflected or transmitted.

4. What types of materials can produce polarized light according to Fresnel's equation?

Fresnel's equation can be applied to any material that can cause a change in the polarization of light. This includes materials like glass, crystals, and certain plastics. These materials have a refractive index that varies based on the polarization direction of the incident light, which results in different reflectance and transmittance values according to Fresnel's equation.

5. How is Fresnel's equation used in scientific research?

Fresnel's equation is a fundamental tool used in various fields of scientific research, such as optics, materials science, and quantum mechanics. It is used to understand and predict the behavior of light at interfaces, which is essential in the development of new optical devices, coatings, and materials. Fresnel's equation is also used in the study of polarized light and its applications in fields like astronomy, microscopy, and telecommunications.

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