Electromagnetic Waves

In summary, the conversation discusses a plane electromagnetic wave incident on a lower index medium at an angle greater than the critical angle. The expressions for the complex transmitted electric field vector (E) and magnetic field vector (H) for the case of s polarized electric field are requested, possibly involving the formulas E = Eo e^i(kr-wt) and H = Ho e^i(kr-wt). It is suggested that the individual should first review the corresponding section in their book before seeking further assistance.
  • #1
TimNguyen
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A plane electromagnetic wave is incident from a higher index medium on a lower index medium at an angle that is greater than the critical angle.
a) For the case of s polarized electric field, obtain an expression for the complex transmitted electric field vector, (E).
b) For the case of s polarized electric field, obtain an expression for the complex transmitted magnetic field vector, (H).

For this, could I just say that E = Eo e^i(kr-wt) and H = Ho e^i(kr-wt) or do I have to do something with the expression?
 
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  • #2
You need to start by carefully reading this section in your book and then making an attempt at the problem. It's clear that you haven't done that, or else you wouldn't ask the question that you asked. We're happy to help, but no one here has time to teach you from scratch.
 
  • #3


I would like to provide a more detailed response to the given scenario.

Electromagnetic waves are a form of energy that propagate through space in the form of oscillating electric and magnetic fields. These waves are characterized by their wavelength, frequency, and amplitude. When an electromagnetic wave encounters a change in the refractive index of the medium it is traveling through, it undergoes a phenomenon known as refraction.

In the given scenario, we have a plane electromagnetic wave incident from a higher index medium onto a lower index medium at an angle greater than the critical angle. This means that the wave will be refracted and undergo a change in direction as it enters the lower index medium. In addition, the polarization of the electric field is known as "s-polarization," which means that the electric field is perpendicular to the plane of incidence.

a) To obtain an expression for the complex transmitted electric field vector (E), we can use the Fresnel equations. These equations describe the behavior of electromagnetic waves at the interface between two different media. For s-polarized waves, the Fresnel equations are given by:

rs = (n1cosθi - n2cosθt) / (n1cosθi + n2cosθt)

and

ts = (2n1cosθi) / (n1cosθi + n2cosθt)

where rs is the reflection coefficient and ts is the transmission coefficient. In these equations, n1 and n2 are the refractive indices of the incident and transmitted media, respectively, θi is the angle of incidence, and θt is the angle of refraction.

The complex transmitted electric field vector (E) can then be expressed as:

E = tsEi

where Ei is the incident electric field vector. Substituting the value of ts from the Fresnel equations, we get:

E = (2n1cosθi / (n1cosθi + n2cosθt)) Ei

b) Similarly, to obtain an expression for the complex transmitted magnetic field vector (H), we can use the Fresnel equations for s-polarized waves, which are given by:

rs = (n2cosθi - n1cosθt) / (n1cosθt + n2cosθi)

and

ts = (2n1cosθi) / (n1cosθt + n2cos
 

What are electromagnetic waves?

Electromagnetic waves are a type of energy that is created by the movement of electrically charged particles. They consist of electric and magnetic fields that oscillate at right angles to each other and to the direction of the wave's propagation.

How do electromagnetic waves travel?

Electromagnetic waves do not require a medium to travel through, unlike other types of waves such as sound waves. They can travel through empty space and are able to travel long distances without losing their energy.

What are the different types of electromagnetic waves?

The different types of electromagnetic waves are radio waves, microwaves, infrared radiation, visible light, ultraviolet radiation, X-rays, and gamma rays. They differ in their wavelengths and frequencies, which determine their properties and uses.

What is the electromagnetic spectrum?

The electromagnetic spectrum is the range of all possible frequencies of electromagnetic radiation. It includes all types of electromagnetic waves, from the longest radio waves to the shortest gamma rays.

What are the practical applications of electromagnetic waves?

Electromagnetic waves have a wide range of practical applications, such as in communication technologies (e.g. radio, television, and cell phones), medical imaging (e.g. X-rays and MRI), and cooking (e.g. microwaves). They also play a crucial role in understanding the universe through astronomical observations.

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