7.8.2: Explorations

Exploration 1: Polarization Tutorial

The animation shows the result of adding two perpendicular electric fields together. Each field is part of an electromagnetic wave traveling along the \(z\) axis. Each electric field is shown separately on the two graphs on the left. The graphs show the electric field at one point on the \(z\) axis for various times. On the right the animation shows both electric fields and their sum at the same point on the \(z\) axis and at the same times as the graphs on the left. It is as if you are looking down the \(z\) axis at the electric fields. Restart.

You can change the electric fields and the phase difference between the two fields and see the resulting waves.

Enter the following values: \(E_{x} = 8\text{ N/C},\: E_{y} = 0\text{ N/C}\), and phase difference \(= 0\ast\pi\) radians. You have created a light wave, traveling along the \(z\) axis, with its electric field in the \(x\) direction.

1. What kind of polarized light did you create?
2. What is the vector equation of the wave you just created?
3. The wave you just specified is polarized in the \(x\) direction. What equations for \(E_{x}\) and \(E_{y}\) would result in light that is linearly polarized along a plane \(45^{\circ}\) above the \(+x\) axis?
4. What equations for \(E_{x}\) and \(E_{y}\) would result in light that is linearly polarized along a plane less than \(45^{\circ}\) above the \(+x\) axis?

Light is linearly polarized when its electric field is in a plane. Circular and elliptical polarization occurs when two or more linearly polarized waves add together such that the electric field of the wave rotates in the plane perpendicular to the direction of propagation. For circularly polarized light, the direction of the electric field rotates but its magnitude stays the same. For elliptically polarized light, both the magnitude and the direction of the electric field vary. For example, if you enter the following values, \(E_{x} = 8\text{ N/C},\: E_{y} = 8\text{ N/C}\), and phase difference \(= 0.5\ast\pi\) radians, a wave that is right-circularly polarized will result. Now consider the values needed to answer the following questions.

5. What equations for \(E_{x}\) and \(E_{y}\) would result in light that is left-circularly polarized?
6. What equations for \(E_{x}\) and \(E_{y}\) would result in light that is right-elliptically polarized?

Exploration authored by Melissa Dancy.

Exploration 2: Polarizers

This animation shows a traveling wave incident on a polarizer. The direction of the polarizer is indicated by the black line. Click-drag to the right or left to rotate about the \(z\) axis. Click-drag up or down to rotate in the \(xy\) plane. Restart.

1. Since the light is linearly polarized along the \(x\) axis, explain why, when the light is incident on a polarizing film that allows light polarized along the \(y\) axis, this light does not pass through.
2. Suppose this light is incident on a polarizing film polarized along a plane \(45^{\circ}\) from the \(x\) axis. What do you predict will happen? After making your prediction, try it.
3. Notice that for (b), the amplitude of the wave passing through the polarizing film is reduced since only the waves with components in the direction of the polarizing film pass through. Now, suppose the light is incident first on the polarizing film of (b) and then on the film of (a). What do you predict will happen? After making your prediction, try it.
4. Explain what you see with two polarizing films set up in this way. This explains why, sometimes, two polarizing films let more light through than just one.

Exploration authored by Anne J. Cox.
Script authored by Mario Belloni and Wolfgang Christian, modified by Anne J. Cox.

Physlets were developed at Davidson College and converted from Java to JavaScript using the SwingJS system developed at St. Olaf College.