Deriving the Fresnel Equations for E Field in Plane of Incidence

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In summary, The conversation is about deriving the Fresnel equations for the E field perpendicular to the plane of incidence. The person is having trouble with a transformation and is looking for help understanding how the equations were derived. They also ask what class the topic is for.
  • #1
Cummings
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I am trying to derive the Fresnel equations for the E field perpendicular to the plane of incidence.

There is one transformation, I assume involves some general math, that I am having a mental blank on.

It can be found here http://physics.tamuk.edu/~suson/html/4323/prop-em.html if you scroll down to Equation 7.17, they simply state that combining it with Equation 7.14 you can achieve 7.18, the fresnel equation.

I assuming this is just some substitution and re araging but for the life of me I am unable to figure out how they did. it.

Enlighten me.
________
Cummings
BSc: Photonics
BEng: Telecommunications and Internet Technologies.
 
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  • #2
I can't open that link. Will you double-check ?
 
  • #3
Gokul43201 said:
I can't open that link. Will you double-check ?

hmm.. the link works for me.


sorry, can't help ya, but may i ask, what class is this for? EM II or optics or something? fairly interesting.
 

FAQ: Deriving the Fresnel Equations for E Field in Plane of Incidence

What is the Fresnel equation?

The Fresnel equation is a mathematical formula that describes the reflection and transmission of light at the interface between two different media. It takes into account the incident angle, polarization, and refractive indices of the two media.

What are the applications of the Fresnel equation?

The Fresnel equation is commonly used in optics and photonics to calculate the amount of light reflected and transmitted at a boundary between two materials. It is also used in the design of optical coatings and anti-reflective surfaces.

How is the Fresnel equation derived?

The Fresnel equation is derived from Maxwell's equations, which describe the behavior of electromagnetic waves. It takes into account the conservation of energy and the boundary conditions for electromagnetic fields at the interface between two materials.

What is the difference between the Fresnel equations for s and p polarized light?

S and p polarized light refers to the orientation of the electric field of the incident light. The Fresnel equations for s and p polarized light take into account the different reflection and transmission coefficients for these two types of polarization.

How can the Fresnel equation be applied to real-world problems?

The Fresnel equation can be applied to various real-world problems, such as designing optical coatings for lenses and mirrors, calculating the reflectance and transmittance of light through different materials, and predicting the behavior of light in different optical systems. It is also used in the study of thin film interference and surface plasmon resonance.

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