- #1
henil
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how can he we derive equations for semi major and minor axes of the polarization ellipse?
Semi major and minor axis of polarization ellipse
- Thread starter henil
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- Axis Ellipse Major Minor Polarization
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SUMMARY
The discussion focuses on deriving the equations for the semi-major and semi-minor axes of the polarization ellipse using trigonometric identities and rotation matrices. The user rearranged the equation Ex/Ax=cos(wt-kz) and applied trigonometric identities to derive a third equation. The final step involves using a rotation matrix to express the axes, but the user encounters a challenge with the absence of the cos(delta) term in their result. This indicates a gap in the derivation process that needs to be addressed for a complete solution.
PREREQUISITES- Understanding of polarization ellipse concepts
- Familiarity with trigonometric identities
- Knowledge of rotation matrices in coordinate transformations
- Basic proficiency in manipulating equations in physics
- Study the derivation of the polarization ellipse equations
- Learn about rotation matrices and their applications in physics
- Explore trigonometric identities relevant to wave equations
- Investigate the role of the cos(delta) term in polarization analysis
Students and professionals in physics, particularly those studying optics and wave polarization, as well as anyone involved in mathematical modeling of polarization phenomena.
- #2
DrDu
Science Advisor
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From what?
- #3
samcarano
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Use these equations
to derive this equations
I just thought of one delta as dy-dx so only one of the first 2 equations actually has a delta in it
Rearranged one of the first equations, the one that no longer has a delta in it, for Ex/Ax=cos(wt-kz)
I then used a few trig identities on the second equation
squared the result then substituted the rearranged equation 1 into the cos(wt-kz) spot and the cos2(wt-kz) spot to get equation 3
Now to derive these equations from the result which are the semi major axis and semi minor axis
just use a rotation martix
where x'=a, y'=b, x=Ax, y=Ay and square each component
This is where I am stuck as I do not have the cos(delta) in the final answer so anyone that knows better can help you (and me) with the correct answer
to derive this equations
I just thought of one delta as dy-dx so only one of the first 2 equations actually has a delta in it
Rearranged one of the first equations, the one that no longer has a delta in it, for Ex/Ax=cos(wt-kz)
I then used a few trig identities on the second equation
squared the result then substituted the rearranged equation 1 into the cos(wt-kz) spot and the cos2(wt-kz) spot to get equation 3
Now to derive these equations from the result which are the semi major axis and semi minor axis
just use a rotation martix
where x'=a, y'=b, x=Ax, y=Ay and square each component
This is where I am stuck as I do not have the cos(delta) in the final answer so anyone that knows better can help you (and me) with the correct answer
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