# Complex Reflection and Transmission Coefficient in oblique incidence

• baby_1
In summary, the phase of the reflection and transmission coefficients is not crucial for Snell's law of refraction, as it only depends on the ratio of the sines of the incident and refractive angles.
baby_1
Homework Statement
Complex Reflection and Transmission Coefficient in oblique incidence
Relevant Equations
Snell equations
Hello,
Something has made me confused after studying the Snell equations these days. Regarding the Balanis Advanced engineering electromagnetic( the pages have been attached), and based on that the reflection and transmission coefficient can be complex I need to rewrite the (5-23a) again:
$$Cos(\theta _{i})e^{-j\beta _{1}xSin(\theta _{i})}+\Gamma Cos(\theta _{r})e^{-j\beta _{1}xSin(\theta _{r})}=TCos(\theta _{t})e^{-j\beta _{2}xSin(\theta _{t})}$$
Due to $\Gamma=a+jb$ and $T=c+jd$
$$Cos(\theta _{i})e^{-j\beta _{1}xSin(\theta _{i})}+\sqrt{a^2+b^2} Cos(\theta _{r})e^{-j\beta _{1}xSin(\theta _{r})+jtan^{-1}(\frac{b}{a})}=\sqrt{c^2+d^2}Cos(\theta _{t})e^{-j\beta _{2}xSin(\theta _{t})+jtan^{-1}(\frac{d}{c})}$$
so it is not easy to say that just (5-24b) equation (Snell's law of refraction) should be correct because of the phase of reflection and transmission coefficients. They can change the equality. How do we count on the Snell equation when these parameters are complex ( as Balanis mentioned that)

?Thank you. A:The phase of the reflection and transmission coefficients is not important for Snell's law of refraction. The only thing of importance is the ratio of the sines of the incident and refractive angles. The phase is essentially a constant, and does not affect the value of the ratio.

## What is the definition of complex reflection and transmission coefficient in oblique incidence?

The complex reflection and transmission coefficient in oblique incidence is a measure of the ratio of the reflected or transmitted electromagnetic wave to the incident wave at a non-normal angle of incidence. It takes into account both the amplitude and phase of the reflected and transmitted waves, making it a complex number.

## How is the complex reflection and transmission coefficient calculated?

The complex reflection and transmission coefficient can be calculated using the Fresnel equations, which take into account the refractive indices of the two media, the angle of incidence, and the polarization of the incident wave. These equations provide separate coefficients for the parallel and perpendicular components of the electric field.

## What is the significance of the complex reflection and transmission coefficient in oblique incidence?

The complex reflection and transmission coefficient is important in understanding how light or other electromagnetic waves behave when they encounter a change in medium at an angle. It helps to predict the amount of reflection and transmission that will occur, and also provides information about the phase difference between the incident and reflected or transmitted waves.

## What factors can affect the complex reflection and transmission coefficient?

The complex reflection and transmission coefficient can be affected by several factors, including the angle of incidence, the polarization of the incident wave, and the refractive indices of the two media. It can also be influenced by the surface roughness of the interface between the two media and the wavelength of the incident wave.

## How is the complex reflection and transmission coefficient used in practical applications?

The complex reflection and transmission coefficient is used in various fields, such as optics, telecommunications, and material science. It is used to design and optimize optical coatings, predict the behavior of light in fiber optic cables, and study the properties of materials at different angles of incidence. It is also used in the development of anti-reflective coatings and in the design of optical devices such as prisms and lenses.

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