Executive Summary:

These sources describe and provide a JavaScript simulation of a circular electromagnetic wave polarizer. The core concept revolves around how electromagnetic waves, initially elliptically or circularly polarized (where the electric field components Ex and Ez are equal in the circular case), interact with linear polarizers. Passing through a polarizer forces the wave to become linearly polarized along the polarizer's orientation. Subsequent polarizers further filter the wave based on their relative angles, leading to potential blockage of the wave if the angle difference reaches 90 degrees. The simulation allows users to visualize this process and manipulate key parameters like polarizer angles and positions, as well as properties of the electromagnetic wave itself.

Main Themes and Important Ideas/Facts:

1. Nature of Circular/Elliptical Polarization:

• The simulation starts with a more general elliptical polarization, with circular polarization being a specific case.
• Quote: "An more general elliptical (circular is a special case where Ex=Ez) polarized Electromagnetic Wave travels from left to right." (SLS Source)
• This highlights that circular polarization is a state where the magnitudes of the electric field components in the x and z directions are equal.

2. Interaction with Linear Polarizers:

• The fundamental principle is that a linear polarizer allows only the component of the electromagnetic wave's electric field that is aligned with its transmission axis to pass through.
• Quote: "After passing through the first polarizer, the Electromagnetic Wave now is linearly polarized along the direction of the polarizer, θ₁ .This is usually how linearly polarized light is formed." (SLS Source)
• The angle of the polarizer determines the direction of the resulting linear polarization.

3. Sequential Polarization and Blocking:

• Multiple polarizers placed in sequence interact with the already polarized light.
• The relative angles between consecutive polarizers are crucial.
• Quote: "If θ₂=θ₁, the light passes through without any difference. If θ₂-θ₁=90 degree, the light passes through is completely blocked." (SLS Source, describing the effect of the second polarizer relative to the first)
• This demonstrates the principle of polarization filtering – when polarizers are crossed (90 degrees apart), no light passes through (ideally).
• The introduction of a third polarizer further complicates the interaction, depending on its angle relative to the preceding ones. Even if the first and third are crossed, the introduction of a middle polarizer at an intermediate angle can allow some light to pass.
• Quote: "If θ₃ = θ₂= θ₁,the linearly polarized light passes through without any difference. If θ₃-θ₂=90 degree and θ₂-θ₁=0 degree, light inbetween polarizer 2 and 3 is unchanged, still linearly polarized, but light after polarizer 3 is completely blocked." (SLS Source)

4. Visualization of Electromagnetic Fields and Polarizers:

• The simulation provides a visual representation of the electromagnetic wave.
• Quote: "Electric Field is represented as Red color segments" (SLS Source)
• Quote: "Magnetic Field is represented as Blue color segments" (SLS Source)
• The polarizers are also visually distinct.
• Quote: "Polarizer 1 is Orange color" (SLS Source)
• Quote: "Polarizer 2 is Green color" (SLS Source)
• Quote: "Polarizer 3 is Magenta color" (SLS Source) (Note: The third polarizer is mentioned in the text description but not explicitly in this color list in the provided excerpt, though it is included in the controls).

5. Controllable Parameters in the Simulation:

• The simulation allows users to manipulate various parameters to observe their effects on the polarized wave.
• Polarizer Angles: θ₁, θ₂, and θ₃ can be adjusted.
• Polarizer Positions: yp₁, yp₂, and yp₃ can be changed.
• Electric Field Components: Ex and Ez magnitudes can be modified.
• Phase Difference: The phase relationship between the electric and magnetic fields can be altered.
• Wave Velocity (vy): Influences the relationship between the electric and magnetic field magnitudes (Ez/Bx = vy).
• Wave Period (T) and Wavelength (wavelength): Related by the wave velocity (wavelength = vy * T).

6. Educational Purpose:

• The sources are associated with "Open Educational Resources / Open Source Physics @ Singapore," indicating their use in teaching and learning.
• The JavaScript simulation applet embedded in the HTML 5 format suggests accessibility and interactive learning.
• The inclusion of "For Teachers" sections further reinforces the educational intent.

7. Technical Aspects (Implicit):

• The mention of "Compiled with EJS 6.0 (191124)" indicates the software used to create the simulation (Easy JavaScript Simulations).
• The embed code (<iframe...>) allows for easy integration of the simulation into web pages.

Conclusion:

The provided sources offer a comprehensive introduction to the concept of circular electromagnetic wave polarization and its interaction with linear polarizers. The accompanying JavaScript simulation provides a valuable tool for visualizing these abstract concepts and allowing users to explore the effects of varying parameters. The material is clearly designed for educational purposes, making the principles of polarization more accessible through interactive engagement.

Frequently Asked Questions: Circular Electromagnetic Wave Polarizers

1. What is a circularly polarized electromagnetic wave?

A circularly polarized electromagnetic wave is a type of wave where the electric and magnetic field vectors rotate as the wave propagates. The provided text indicates that a more general case is an elliptically polarized wave, where circular polarization occurs as a special instance when the magnitudes of the electric field components in the x and z directions are equal (Ex = Ez).

2. How does a linear polarizer affect a circularly polarized electromagnetic wave?

When a circularly (or elliptically) polarized electromagnetic wave passes through a linear polarizer, the wave becomes linearly polarized. The direction of this linear polarization is aligned with the transmission axis (the angle θ₁) of the first polarizer. This is a common method for creating linearly polarized light.

3. What happens when linearly polarized light encounters a second linear polarizer?

If the linearly polarized light encounters a second polarizer with its transmission axis (θ₂) aligned with the first (θ₂ = θ₁), the light will pass through without any change in polarization or intensity (ideally). However, if the second polarizer's axis is perpendicular to the first (θ₂ - θ₁ = 90 degrees), the light will be completely blocked, and no light will pass through. For any other angle between the two polarizers, only a component of the electric field aligned with the second polarizer's axis will pass, resulting in a decrease in intensity.

4. What is the effect of a third linear polarizer placed after the first two?

The effect of a third polarizer (with angle θ₃) depends on its orientation relative to the first two. If all three polarizers are aligned (θ₃ = θ₂ = θ₁), the linearly polarized light passes through all of them unchanged. A more interesting scenario occurs if the first and second polarizers are crossed (e.g., θ₂ - θ₁ = 90 degrees, blocking all light), but a third polarizer is placed between them at an intermediate angle. In this case, some light will pass through the third polarizer, and then a component of this light, now polarized along θ₃, will pass through the second polarizer (which would have otherwise blocked all light from the first polarizer).

5. How are the electric and magnetic fields visualized in the provided simulation?

In the interactive simulation described in the sources, the electric field is represented by red color segments, and the magnetic field is represented by blue color segments. The polarizers themselves are also visually represented with different colors: Polarizer 1 is orange, Polarizer 2 is green, and Polarizer 3 (if present in the simulation) is magenta.

6. What parameters can be controlled or modified in the simulation applet?

The simulation applet offers several controls that allow users to explore the behavior of polarized electromagnetic waves. Key adjustable parameters include: * θ₁: The angle of the first polarizer. * θ₂: The angle of the second polarizer. * θ₃: The angle of the third polarizer (in some versions). * yp₁: The position of the first polarizer along the wave's path. * yp₂: The position of the second polarizer. * yp₃: The position of the third polarizer. * Ex: The magnitude of the electric field in the x direction. * Ez: The magnitude of the electric field in the z direction (controlling the polarization state). * phase: The phase difference between the electric and magnetic fields. * vy: The wave velocity. * T: The period of the wave. * wavelength (λ): Which is related to velocity and period (λ = vy * T).

Users can manipulate these variables through sliders and combo boxes within the applet's interface.

7. What is the relationship between the electric and magnetic fields in an electromagnetic wave traveling in a vacuum?

The provided text notes that when an electromagnetic wave travels in a vacuum, the electric (E) and magnetic (B) fields are in phase. Additionally, the wave velocity (vy) is related to the magnitudes of the electric field in the z-direction (Ez) and the magnetic field in the x-direction (Bx) by the equation vy = Ez / Bx.

8. What educational resources and tools are associated with this Circular Electromagnetic Wave Polarizer simulation?

The simulation is part of the Open Educational Resources / Open Source Physics @ Singapore project. It is implemented as a JavaScript HTML5 applet, making it embeddable in webpages via an iframe. The resources include links to the simulation itself, blog posts providing further context and versions, a related YouTube video, and connections to the Easy Java/JavaScript Simulations (EJS) Toolkit used to create it. These resources aim to provide interactive learning experiences for students and educators in the domain of electromagnetic waves and polarization.