# Plane of polarization

## Homework Statement

1)I have a basic doubt on polarization. It is given in book that the plane of polarization is perpendicular to the plane of vibration. What was need for defining the plane of polarization to be perpendicular to the plane of vibration? When I searched the internet, I found a site which says that the plane of polarization is the plane in which the magnetic field vector is oscillating and plane of vibration is the plane in which the electric field vector oscillates. In an electromagnetic wave, the electric field vector is perpendicular to the magnetic field vector. So this sounds to be true, but I would like have the opinion of this forum.

## The Attempt at a Solution

Päällikkö
Homework Helper
I'm not quite familiar with the concept of "plane of vibration", however this I found with Google: "A plane including the direction of light propagation and the direction of electric field is called the plane of vibration. For a linearly polarized light wave, the plane remains fixed."

Polarization describes the direction of the electric field. The electric field of an electromagnetic wave is perpendicular to the direction of light propagation (this follows from Maxwell's equations). Therefore polarization is constrained into the plane perpendicular to the direction of light propagation. As the plane of vibration is parallel to the direction of light propagation, the plane of polarization is perpendicular to the plane of vibration.

This plane (polarization) also contains the magnetic field vector (which is perpendicular to both the electric field vector and the direction of light propagation, as you pointed out. This too follows from Maxwell's equations).

I hope I understood your question right .

This plane (polarization) also contains the magnetic field vector (which is perpendicular to both the electric field vector and the direction of light propagation, as you pointed out. This too follows from Maxwell's equations).

When I referred Griffith's book on Electromagnetism I came across the fact that the polarisation vector defines the plane of vibration. Doesn't this mean that the plane of vibration is parallel to the plane of polarization? It also says that an electromagnetic wave propagating across the z-direction with its electric field vector along the x-direction and magnetic field vector along the y direction is said to be polarized in the x-direction.(Because by convention we use the direction of Electric field vector to specify the polarization of an electromagnetic wave).

Päällikkö
Homework Helper
Sorry for the slow response, I've been away for a couple of days. Apparently no one else answered your question.

One vector alone does not define a plane. I suppose what Griffith means is that the plane of vibration is the plane spanned by the polarization vector and the vector that points into the direction of light propagation. The plane of polarization, on the other hand, is the plane spanned by the electric field vector (which you can replace with the polarization vector, for they are parallel) and the magnetic field vector. Thus the planes are perpendicular.

When I referred Griffith's book on Electromagnetism I came across the fact that the polarisation vector defines the plane of vibration. Doesn't this mean that the plane of vibration is parallel to the plane of polarization?

I'll explain with an example (since you're reading about EM waves anyway):

$$\vec{E} = E_{0}\sin(\vec{k}*\vec{r} - \omega t)\hat{n}$$

Now, $\vec{k}$ is the propagation vector whereas $\hat{n}$ defines the direction of vibration (the plane of polarization is the plane containing the propagation vector and n itself).

As EM waves are transverse the direction of vibration is orthogonal to the direction of propagation. So, $\vec{k}\dot\vec{r} = 0$.

To cite a specific example, consider

$$\vec{E} = E_{0}\sin(kz - \omega t)\hat{x}$$

The oscillations are in the xz plane with the positive z axis as the direction of propagation of the wave.

It also says that an electromagnetic wave propagating across the z-direction with its electric field vector along the x-direction and magnetic field vector along the y direction is said to be polarized in the x-direction.(Because by convention we use the direction of Electric field vector to specify the polarization of an electromagnetic wave).

The electric field component is written above. The magnetic field is given by

$$\vec{B} = \frac{\vec{k}X\vec{E}}{\omega} = \frac{E_{0}}{c}\sin(kz - \omega t)\hat{y}$$

Does that convince you? As you said, by convention the direction of polarization of the EM wave is the direction of polarization of the electric field component.

Hope that helps...

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Thanx guys.