# Fresnel Reflection and Transmission Coefficients

• whitenight541
In summary, the Fresnel coefficients are used to determine the magnitudes of the incident, reflected, and transmitted waves in a medium. It is possible for the transmission coefficient to be greater than the reflected one, as the energy density of a field is dependent on both the magnitude of the electric and magnetic fields and the permittivity and permeability of the medium. In situations with multiple interfaces, the Generalized Reflection and Transmission Coefficients should be used. The Fresnel coefficients can also account for phase changes in the transmission and reflection off of boundaries.
whitenight541
Hi all,

The relation between the magnitudes of the incident, reflected and transmitted waves are obtained using Fresnel coefficients.

If a field moves from air to a more denser medium, which field should have a greater magnitude (reflected or transmitted)? I thought that it would be the reflected one but I found that the transmission coefficient is greater than the reflected one. So the transmitted wave magnitude is greater than the reflected one ? Am I making any sense? If what I said is true, how come is that possible?

If a field moves from air through a wall of concrete of thickness t, I calculated the transmitted field after the first boundary, but when I tried to calculate the transmitted field at the second boundary, I found out that the transmission coefficient is greater than 1? Is that possible?

A transmission coefficient greater than one is ok, it doesn't necessarily violate the conservation of energy. One thing to keep in mind is that the energy density of a field is dependent upon both the magnitude of the electric and magnetic fields and the permittivity and permeability of the medium. If you pass from air to a dielectric, then the electric field can decrease (the normal electric flux density is continuous across boundaries, so the normal part of the electric field must decrease when entering a region of higher permittivity). When you go from concrete to air, you can expect a slight increase in the electric field for the same reason. If you are dealing with multiple regions, you should look at the Generalized Reflection and Transmission Coefficients. These coefficients take into account all the reflections between interfaces and gives you the complete reflection and transmission coefficients. If you have a single interface, you only have a single reflection and transmission, but if you have multiple interfaces, like with your concrete slab, then you have secondary, tertiary, and so on-ary reflections and transmissions. This comes about from the fact that the field that reflects off of the second interface will strike the first interface and transmit and reflect again. I would assume that Balanis' textbook deals with this but I do not have it front of me at home. Again I know that Chew's Fields and Waves textbook has it.

Also, the Fresnel coefficients do not just give the magnitude of the coefficients, the coefficients can be complex to reflect a phase change that occurs in the transmission and reflection off of the boundaries.

Hello,

Thank you for your question. The Fresnel coefficients, also known as reflection and transmission coefficients, are used to describe the behavior of electromagnetic waves at the interface between two media with different refractive indices. These coefficients can help us understand the magnitude of the reflected and transmitted waves in different scenarios.

To answer your first question, it is true that the transmission coefficient can be greater than the reflection coefficient when a field moves from air to a denser medium. This is because the transmission coefficient takes into account both the amplitude and phase changes of the transmitted wave, while the reflection coefficient only considers the amplitude change of the reflected wave. In some cases, the phase change of the transmitted wave can result in a higher magnitude compared to the reflected wave.

In the case of a field passing through a concrete wall of thickness t, it is possible for the transmission coefficient to be greater than 1. This can happen if the wall is made of a material with a high refractive index, which can cause a phase shift in the transmitted wave that results in a higher magnitude. However, it is important to note that a transmission coefficient greater than 1 does not mean that the transmitted wave is stronger than the incident wave. It simply indicates a phase shift and amplitude change in the transmitted wave.

## 1. What is the Fresnel reflection coefficient?

The Fresnel reflection coefficient, also known as the amplitude reflection coefficient, is a measure of the amount of incident light that is reflected from a surface. It is calculated by dividing the amplitude of the reflected light by the amplitude of the incident light.

## 2. What is the Fresnel transmission coefficient?

The Fresnel transmission coefficient, also known as the amplitude transmission coefficient, is a measure of the amount of incident light that is transmitted through a surface. It is calculated by dividing the amplitude of the transmitted light by the amplitude of the incident light.

## 3. How are the Fresnel reflection and transmission coefficients related?

The Fresnel reflection and transmission coefficients are related by the law of conservation of energy, which states that the sum of the reflected and transmitted energies must equal the incident energy. This relationship is expressed mathematically as R + T = 1, where R is the reflection coefficient and T is the transmission coefficient.

## 4. What factors affect the Fresnel reflection and transmission coefficients?

The main factors that affect the Fresnel reflection and transmission coefficients are the angle of incidence, the refractive indices of the two mediums, and the polarization of the incident light. The coefficients also vary with the wavelength of the incident light.

## 5. How are the Fresnel reflection and transmission coefficients used in optics?

The Fresnel reflection and transmission coefficients are used in a variety of applications in optics, such as in the design of anti-reflective coatings, optical filters, and optical devices like mirrors and lenses. They are also used in the study of light propagation and reflection at interfaces between different mediums.

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