# Find Parallel Polarized E Field Reflection Direction

• yungman
In summary, the direction of the incident is described by \hat n_i \;=\; \hat x sin \theta_i + \hat z cos \theta_i, and the direction of the reflected wave is \hat{n}_r=\hat{x}\sin(\theta_i)-\hat{z}\cos(\theta_i). The direction of the reflected E-field can be determined mathematically by considering the relative index of reflection.

#### yungman

For a parallel polarization EM hitting the conductor boundary in an oblique angle. z axis is perpendicular to the boundary and point into the conductor. y-axis it out of the page which give x pointing up. Let the boundary surface by xy plane. With this:

The direction of the incident is:

$$\hat n_i \;=\; \hat x sin \theta_i + \hat z cos \theta_i \;\hbox { and direction of }\; \hat {E_i} \;= \hat x cos \theta_i - \hat z sin \theta_i$$

I know

$$\hat {E_r} \;=\; \hat x cos \theta_i + \hat z sin \theta_i$$

My question is how can I derive the direction of $\vec {E_r}$ by using formulas? I got this by looking at the reflection as I move the incident E towards the boundary...by drawing. I want to find this mathametically. Please help.

Thanks

Alan

You know from reflections that
$$\hat{n}_r=\hat{x}\sin(\theta_i)-\hat{z}\cos(\theta_i)$$
If your E-field is in free space, it must be normal to this outgoing wave vector. Since you had a parallel incident E-field, there are only two possibilities and one is just the negative of the other. Which one is correct depends on the relative index of reflection; see Fresnel equations for parallel plane incidence to show which.

## 1. What is parallel polarized E field reflection direction?

Parallel polarized E field reflection direction refers to the direction in which an electric field is reflected off of a surface. This direction is perpendicular to the surface and is dependent on the polarization of the incident electric field.

## 2. How is the direction of parallel polarized E field reflection determined?

The direction of parallel polarized E field reflection is determined by the angle of incidence, which is the angle between the incident electric field and the perpendicular line to the surface. The direction of reflection is equal to the angle of incidence.

## 3. What is the difference between parallel and perpendicular polarized E field reflection?

The difference between parallel and perpendicular polarized E field reflection is in the direction of the reflected electric field. In parallel polarization, the reflected electric field is parallel to the incident electric field, while in perpendicular polarization, the reflected electric field is perpendicular to the incident electric field.

## 4. How does the angle of incidence affect parallel polarized E field reflection direction?

The angle of incidence plays a crucial role in determining the direction of parallel polarized E field reflection. The direction of reflection is equal to the angle of incidence, meaning that a change in the angle of incidence will result in a change in the direction of reflection.

## 5. Why is it important to understand parallel polarized E field reflection direction?

Understanding parallel polarized E field reflection direction is important because it helps in predicting the behavior of electromagnetic waves when they encounter different surfaces. This knowledge is essential for various applications in optics, telecommunications, and other fields of science and technology.